Poker With An Edge Playbook Cash Games And Tournaments

The reason you should be playing poker is because you intend on extracting a mathematical edge to win money. If you aren't doing this, you are gambling. Gambling is losing. The casinos make billions because they have the mathematical edge over thousands of players a day. So what exactly does it mean to be playing with an edge?

Strategical thinking may allow for a mathematical edge even without the best cards, but that's something we will cover later. For now, we want a greater than 50% chance of starting with the best hand before continuing. For reasons I won't get into too much depth, you can widen this since opponents will sometimes fold, and to reduce predictability, but if you do it makes playing after the flop more complicated so for now rather than complicate things, we will stick to only playing known edges.

Some tight players play 12.5% of their hands with the mentality that there are 8 other players so as long as they play the top 1/8 hands they have a good chance of having the best hand. That logic sounds good and I used to believe in it until I saw that the math was wrong. Each individual is given a hand so each individual has a 1/8 chance of being dealt such a hand. The chances that 8 other players are not also dealt that hand is (1-(1/8))^8 or (7/8)^8=34.36%. That means there is a  65.64% that a single opponent DOES have an equal or better hand.

They key advantage over the players that play the top 12.5% of hands and us is that we take into consideration how many opponents are left and adapt by position. More folds and fewer opponent's left increases our chances that our hand is best.

Since you will likely be continuing aggressively with the hand, you may even wish to start a little bit stronger than 50%, particularly if you are playing a tournament and the tournament has a deep stack and slow blind structure. You will still have to occasionally fold the worst 20-25% or even 30% of flops, the worst 20-30% of turn cards and the worst 20-30% of rivers, plus adaptations for players, but if you are starting out strong, you will often be betting and winning lots either by getting to showdown with the best hand, or by taking down uncontested pots.

Unfortunately hand ranges are not quite black and white as in this theory I will introduce, but it's a good starting point. Some hands are higher ranked for multiway pots of 5+ players, while others fair better against a single player. With that being said, there also is a personal ability to play the hand and avoid trouble that must be considered.

If you are the first to act, we can actually solve for the hand range that gives you a 50% chance of having the best hand. If you play a 25percentile ranked hand when you are first to act with 8 people to play, assuming they only play top 25 percentile hands, you have only a 10% chance they will fold. .75^8=.10. That means there is a 90% chance your hand is NOT best. So playing 25% of hands is NOT tight enough if we are first to act under the gun. If several people have folded to us on the button, certainly it's acceptable.

Now defining which specific hand should be played is another story. THAT I will give you the flexibility to choose. If you tend to get a lot of action with top pair type hands when you flop a set and draws and middle pair, you can play any pair and hope to flop a set. If you do NOT get a lot of action, you may lose a big pot to set over set and only win a small one. The results are the same with 45s on a 29K flop as with 22, except that if you only get a bit pot against 99,KK and maybe AK with a flush draw, flopping a set has little REAL value in practice. Of course this is an extreme. There always is SOME added value in flopping sets, but the point is to illustrate that 45s type hands are easier to get away from, and it is much more rare to have 3 flush cards on board and lose flush over flush than set over set. You flop a set 10% of the time and opponents tend not to call off all their chips on a flush draw.

That isn't to say that 45s and the like are always better than 22. It depends on the player and the opponents. While it would be nice to have a definitive ABC style that would have an edge against all opponents, this is the one area in which you have to find what works for you. While I always like suited connectors, I only like to play all pairs when I am playing a nutball supersystem style. The reason for that is I am playing draws fast with this style that I am more likely to get action with inferior hands and draws when I flop a set. With a supersystem style, I am much less worried about a higher set since I am more likely to get paid off when my opponent doesn't have one that it will probably pay for when he has a better set. However, when I am not playing super fast on the flop and overbetting the pot, I prefer to just fold lower pairs.

So here is the hand percentages that give you a 50% chance hand is the best preflop rank:
8 8.3%
7 9.43%
6 10.91%
5 12.95%
4 15.91%
3 20.63%
2 29.29%
1 50%
PLEASE keep in mind that we shouldn't totally ignore the folds. People who fold are less likely to fold an ace meaning that when it folds to you in late position, the math is probably skewed towards not having as good of hand relative to our opponents then we think. However, positional advantage provides an advantage on every street, and I didn't mix in bluffs so you perhaps can ignore it, just be super aware of this when you are playing hands with non ace kickers and the lower part of that range that you may be better subbing them out for drawing hands and bluffs.

Deciding what hands YOU personally have the largest overall edge with is going to be individualized but you should play your best X% of hands to match this that can be determined using tracking software.

8 8.3 88+, AJ+,ATs+,KTs+,QJs
7 9.43 88+, AJ+, KQ, ATs+,KTs+,QJs,JTs
6 10.91 66+, AJ+, KQ, ATs+,KTs+,QTs+,JTs,T9s
5 12.95 66+, AJ+, KQ, ATs+,KTs+,QTs+,J9s+,T8s+,98s,87s,76s,65s,54s
4 15.91 66+, AJ+, KQ,QJ,JT, A8s+,KTs+,QTs+,J9s+,T8s+,97s+,87s,76s,65s,54s
3 20.63 55+, AT+,KT+,QT+,JT,A7s+,KTs+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
2 29.29 22+, A9+,KT+,QT+,JT,T9,98,87,76,65,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
1 50 Just a bunch of hands. Any king any ace, gap connectors, suited 2 and 3 gappers, etc

Tournaments

Now the adjustment for tournaments is that once the antes kick in, you need to adjust. Because you are already committing 1/3rd to 1/6th of a small blind in every single hand and there is more to fight for in the middle, you don't actually need to be a favorite to win money. If you can put in 2.5 big blinds and have a player on the button call and blinds fold, you could check down the hand to the river, win 1/3rd of the time, and still break even. The technical reason we can't raise anytime we have a 33% chance of having the best hand is because that would make us very vulnerable to resteal 3bets and it's very suboptimal preflop strategy. If opponent always 3bet us, our pot odds require us to be a 43% to win with a standard raise to call. Since this is not the case with a wide range of hands, we'd too often be giving up the 2.5 big blinds we risked by raising.

If antes are involved you can fight with more hands because if you do worse than break even, you can pick up the blinds and antes when you either have opponent fold or when you win a showdown. Even if you are reraised you still get good enough pot odds to be able to make plays on 4bets with a wider range. That small extra advantage makes it worth playing more hands. But you can't be too loose initially either.

If you have a real good intuitive feel for how opponents play after playing for awhile, you may also consider occasionally widening range a little. I like aiming for a 40% chance of the best hand with antes. You might prefer keeping 50% and just playing post flop differently and flat calling or 3betting more or playing differently post flop or 30% and exploit a lot after the flop or mix up your strategy to coming in much stronger if opponents begin playing back at you.

I won't put in the wider ranges that are possible. I think if you want to play wider ranges, do so in late position by flat calling raises, betting any two but not every two when in position (don't raise twice in a row, don't raise twice from the same position in a row), and mixing in occasional bluff sin addition to this range. This will keep your overall range on average much stronger, but still provide the possibility of you having any two cards, and allow you to exploit opponents and positional advantages to be really aggressive.

So here is the range that gives you a 40% chance of best hand (for use when antes are involved)
8 10.82% 77+, AJ+, KQ, A8s+, KTs+, QTs+,JTs
7 12.27% 77+,AJ+,KQ,A8s+,K9s+,QTs+,JTs,T8s+,98s,87s,76s,
6 14.16% 77+,AJ+,KQ,A2s+,K9s+,Q9s+,JTs,T8s+,98s,87s,76s
5 16.75% 77+.AJ+.kQ,Qj,JT,A2s+,K9s+,Q9s+,J9s+,T8s+,98s,87s,76s,
4 20.47% 77+,At+,KT+,QT+,JT+,A2s+,K9s+,Q9s+,J9s+,T8s+,98s,87s,76s,
3 26.32% 22+,A9+,KT+,QT+,JT+,A2s+,K6s+,Q8s+,J8s+,T7s+,97s,87s,76s,65s,54s
2 36.75% 22+,A9+,KT+,Q9+,J9+,T8+,98,87,76,A2s+,K2s+,Q7s+,J7s+,T6s+,96s,86s,75s+,64s+,53s+,43s
1 60% Too many to name. Basically everything except like Q2-Q4,J or lower with 6 high or lower kicker, and a few really bad suited cards.

Note: This range does not include lower pairs because flopping a set AND getting action AND having the set not be beat by a higher set, AND hold up to any potential draws as the best hand by the river isn't as good as advertised. In the earlier stages when we are aiming for a 50% chance of having the best hand it is a little better payout proportionally to our stack if we flop a set as well.

If you play a supersystem style as mentioned before you want to play more pairs and balance the suited connectors, but that's a different strategy.

If you only want a REALLY strong edge to see a hand, you might look for the 60% chance your hand starts best. This will allow you to continue more aggressively than most a very high percentage of the flop, turn, and river. If you play the above range PLUS add in a lot of bluffing hands when folded to you for awhile, this is a slower "gear" to switch to, to confuse opponents.

60% chance of having best hand
8 6.19 99+,AQ+,AJs+,KQs,QJs,JTs,
7 7.04 88+,AQ+,AJs+,KQs,QJs,JTs, T9s,98s
6 8.16 88+,AJ+,AJs+,KQs,QJs,JTs,T9s,
5 9.71 88+,AJ+,KQ,A9s+,KJs+,QJs,JTs,T9s
4 11.99 88+,AJ+,KQ,A2s+,KJs+,QJs,JTs,T9s,98s
3 15.66 77+,AJ+,KQ,QJ,JT,T9,A2s+,KTs+,QTs,JTs,T9s,98s
2 22.54 22+,AT+,KJ+,QJ,JT,T9,A2s+,K2s+,QTs,JTs,T9s,98s
1 40 22+, A2+, K9+,Q9+,J9+,T9,98,87,K2s+,Q8s+,J8s+,T8s+,97s+,86s+,75s,64s,54s,43s

For those who want to fire on  virtually every street or multitable a lot without thinking too much, or if you find yourself at a very loose table where you will get action, you can be very patient and make your money from calling stations after the flop. Also at volatile tables when you have enough chips to perservere, or late in tournaments when folding into the money is more important, you may want to open much stronger.

75% chance of having best hand
8 3.53 JJ+,AK,AJs+
7 4.03 JJ+,AQ+,AJs+
6 4.68 JJ+,AQ+,AJs+
5 5.59 TT+,AQ+,AJs+,KQs
4 6.94 99+,AJ+, ATs+,KQs
3 9.14 77+,AT+,A9s+,KQs,
2 13.40 66+,At+,KQ,A2s,KQs,QJs,JTs,T9s
1 25 22+,A8+,KT+,QT+,JT+,A2s+,K7s+,Q9s+,J9s+,T8s+,98s,87s,76s

Rather than confuse the issue, with multiple hand ranges, let's reset and start with the basics.

So your hand range when folded to is:
8 8.3% 88+, AJ+,ATs+,KTs+,QJs
7 9.43% 88+, AJ+, KQ, ATs+,KTs+,QJs,JTs
6 10.91% 66+, AJ+, KQ, ATs+,KTs+,QTs+,JTs,T9s
5 12.95% 66+, AJ+, KQ, ATs+,KTs+,QTs+,J9s+,T8s+,98s,87s,76s,65s,54s
4 15.91% 66+, AJ+, KQ,QJ,JT, A8s+,KTs+,QTs+,J9s+,T8s+,97s+,87s,76s,65s,54s
3 20.63% 55+, AT+,KT+,QT+,JT,A7s+,KTs+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
2 29.29% 22+, A9+,KT+,QT+,JT,T9,98,87,76,65,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
1 50% Just a bunch of hands. Any king any ace, gap connectors, suited 2 and 3 gappers, etc

This gives you a preflop edge with every hand you play. You should therefore raise to either win the pot or get a weaker hand to call if you are first to act.

Now, opponents probably won't play this way, but let's imagine they do to establish a baseline that is approximately correct even against opponents who play incorrectly. The farther they deviate, the stronger your range against them and the more profitable this style should be. In order to have a 50% chance of being on the upper half of THEIR range, you need to play HALF the amount of hands that they do. In other words, assume they only raise you if they are in the upper half of your range. You need to proceed as if you were starting from there position and play the hands that give you a 75% chance of being best.

When opponent raises with this many players remaining 3bet (reraise) with these hands:
8 3.53% JJ+,AK,AJs+
7 4.03% JJ+,AQ+,AJs+
6 4.68% JJ+,AQ+,AJs+
5 5.59% TT+,AQ+,AJs+,KQs
4 6.94% 99+,AJ+, ATs+,KQs
3 9.14% 77+,AT+,A9s+,KQs,
2 13.40% 66+,At+,KQ,A2s,KQs,QJs,JTs,T9s
1 25% 22+,A8+,KT+,QT+,JT+,A2s+,K7s+,Q9s+,J9s+,T8s+,98s,87s,76s
If you have information about opponent, 3bet with roughly half of opponent's range. You can mix in some occasional bluff raises.

Rather than calculate the 87.5% chance hand is best to determine what you will 4bet, I will do things a bit differently. If we risk 3 big blinds on a raise, fold 3 times and win 9 on the 4th then we break even. But we still have to pay the cost of blinds so we should 4bet slightly more often. Although we may only risk 2.5 or 2 big blinds in many cases, we will get reraised for possibly 2 or 2.5 as well. This makes it correct to call often so the equation gets tricky. Also, "balance" for 4bet isn't as necessary because the move is much more rare and will get called often enough that you may wish to be strong. Additionally, you have PLENTY of time to adapt your raise range. So if opponent is exploiting you with 3bets twice, you can just tighten your raise range so the 3rd time you are very likely to have a hand and if opponent does it again, you tighten it further and loosen 4bet range so the next time you are almost sure to have a hand.

If opponent folds a lot or just calls and makes mistakes after the flop, they probably won't 3bet you enough for it to matter since you are gaining enough chips when you are faced with calls or folds to make up for it.

With that being said, just for the sake of being thorough, here is the hand range that gives you a hand to 4bet 1/3.5 times that you raise. I would prefer being tighter unless I think I am being exploited, and looser if I know my opponent is exploiting me, and I can always just flat call.

THEORETICAL 4bet:
9 players: JJ+,AKs
8 players: JJ+,AKs
7 players: TT+,AKs
6 players: JJ+,AK (and add in two red tens)
5 players: TT+,AK,AQs
4 players: 99+,AK,AQs bluff:T9s (you could put AJs or 88 if you like instead)
3 players: 88+,AQ+ bluff:T9s (you could put AJs or 77 if you like instead)
2 players left:55+,AJ+ I would possibly remove some of the lower pairs and AJ and replace them with bluffs but it doesn't matter too much.

I don't really like playing the theoretical 4bet range because you should have plenty of time to adapt and the last thing you want to do is 4bet against an opponent who only 3bets with QQ+. Opponents should 3bet infrequently. If they don't, you will make money from them eventually anyways. Plus you can simply tighten your raise range and prepare to 4bet a higher percentage of your raises. If you ARE 3betting infrequently, then your opponent will usually have you crushed when you have JJ or TT. Opponents typically won't adjust for position as much as they should so 4betting as light in late position also may not be a great idea.

Also, more often than not you may have the odds to see a flop so you may wish to just call. If you choose to call you also theoretically should call with strong hands as well, but against most opponents that just isn't necessary to "balance" your range. Just play to exploit and if opponent adapts, then you can try to adapt and move closer to balanced each time.

Bluff is done mostly for image, to discourage 3bets and encourage much looser calls when you 4bet.

Okay so now let's back up a little and get back to calling or 3betting opponent. Rather than assume they play in this same manner, you can use information to enter in more opportunities for profit. If you are very confident that they play a wider range, you can play half the hands they do which represents more hands. Like the 98s bluff 3bet, it is not necessary. If you wait for a hand in the upper half of their range, you will play half the hands, but since they raised, you will probably at least win twice as much. If you don't, you simply start with a stronger hand, in position against an opponent.

If opponent will raise or fold only, the correct move would be to bluff raise more but also flat call more with hands strong enough to raise, but not strong enough to face an opponent reraising and fold a few hands like AJ that are only going to win a small pot or lose a big one if the ace or jack pairs. So if you have 99 or TT it may be strong enough to 3bet but if opponent 4bets you will fold. Then you look to continue to the turn if there is only 1 overcard to your 9's that isn't an ace and you might bet and fold to reraise or check call, check the turn and if opponent checks behind and you don't have other overcards, check the river hoping to catch a bluff more often than opponent value betting. These types of hands you should then call, and put in a 3bet "bluff" in it's place.

But that is exploitative theory, and it makes things VERY complicated. It also changes depending on stack sizes. It also depends on you KNOWING opponent plays a certain way which is speculation... more on this in a bit.

If you bet and opponent raises you, you need to be able to force opponent to break even if he were bluffing. If he bets 3 times the pot, he can pick up the pot 3 times and you can reraise on the 4th and he will break even on bluffs. If opponent is going to continue to not adjust, you will show don a better hand than he will often enough to win a pretty big pot.

The actual application shouldn't be to fold that often. But if you do, it isn't that bad. Especially if when you get in a hand you continue aggressively a high percentage of the time. Even if your opponent has a better range, your hand should be good enough with the pot odds to be able to call and fold more frequently than normal conditions suggest and still profit from the decision.

The problem is if you call only with the hands that have pot odds and raise with the hands that are stronger, you are giving away information and opponents can use that information. As such, if you choose the more complicated game of say folding 1/2 times you are raised instead of 30% of the time, you must mix calls and raises so that you give away nothing about the hand strength. One randomizer trick is to look at the left card. If it is a black suit (spades,clubs) call, if it is a red suit (hearts,diamonds), raise. Aside from giving away information about the probability of having a flush draw, this is relatively safe and opponents are not that astute to realize it. Even if they were, every 30 minutes you could change what the red card and black card means to be opposites.

Now theoretically raising always gives your opponent the chance to make a mistake by folding. However in real application this changes implications of future street and may prohibit future betting by forcing an all in action before the river. So earlier on, particularly in position I am slightly more apt to call if I am in position. But note that doing so is SPECULATIVE.

The word Speculative comes from speculari which means to look at, view, observe. If you haven't given yourself a long enough time to observe or do not have confidence in your observations, you should not "speculate". It shouldn't mean "gambling" it means making a calculation based upon what you see, observe and believe to appear clear to you. That means one must have a REASON for taking an action and there is no reason it should not be a pure, calculated edge.

I am fine with "speculating" if it is because I have a clear reason to do so. Doing so may have slightly more risk because your eyes can deceive and because opponents can deceive. But if you have grounded assumptions, and if you curb those assumptions to the conservative side you can still play with an edge more often.

If you noticed a player raise 40% of all hands he could be playing a 40% range... or he could be getting a catch of cards in the 20% range and your eyes may deceive you. OR he could have played a lot of 60% hands at first and now he's tightened up to 20%. It would certainly LOOK like 40%, but in reality he may have a stronger hand. Or he may have just gotten a rush of cards and really playing tighter than he appears. You are speculating by playing 20% of hands if the raise comes from say middle position and you are on button because opponent MAY not actually be playing the 40% of hands. So it has more risk than just assuming opponents play this same way and only playing your cards and position.

You are being even MORE speculative if your alleged 40% range opponent raises and you call from the cutoff because you wouldn't normally raise if folded to and you have 3 opponents who could pick up a stronger hand than you. So you are also betting on the players in the button and blinds respecting your raise or call enough since it's less than 50% that you have a better hand then them...

If they assume you aren't speculating they are correct to fold... but if THEY know that YOU know opponent is loose, and that you are a speculative player, they can correctly widen their range and play more hands and you run into trouble, particularly if they speculate with a "squeeze play" by raising both you and your opponent.

I am comfortable in speculating with HALF of my opponents range (after 40-50+ hands) most of the time if I would also have a strong enough hand to open for a raise because:
1)Opponents will likely not play perfect against me.
2)Even if they do, I should have a small edge if I also play perfect.
3)Provided my opponent doesn't just hit me with an isolated event of a single steal then not try it again, I may have time to adapt if they respond by trying to squeeze me.

So I have to be both wrong about my opponent being less than perfect AND about my range AND/OR not play perfect myself for it to be a mistake. Even so, I will almost always be doing it with position. That may be a risk, but it's a calculated one and one where the probability is in my favor.

I also am comfortable betting or raising to isolate the loose player by playing about half his range some of the time. This means that if a player is raising with 70% of all hands, I want to come in with the top 35% and raise or call.... But I don't want to do this every time, so if I went after him once when I had that range, I probably will pass the second time unless I have a hand that is strong enough to 3bet or call a standard raise assuming my opponent plays optimally.

However, I will not be comfortable regularly speculating like that by calling or raising too often IF it isn't at least a hand that I'd normally put in the FIRST raise with or at least isn't very far off. In other words, I still usually want a 50% chance of the hand being best vs the rest of the table, even though I would normally never call or 3bet with such a hand in normal circumstances.

If opponent is early position and I am middle position I won't usually call because I am too vulnerable to my remaining opponent's left to act. If they end up raising and I would HAVE to give opponent credit and fold more than 3 times since they are representing a very tight range of hands.  So this makes you exploitable, however as long as you make more by exploiting it may be worth it. This is why you don't want to create too many obvious patterns, you want to shy away from middle position decisions like this and you want to do it sparingly. Even though the raise size plus dead money from initial raiser would allow where I could fold 4 or 5 or 6 times and reraise, even then I wouldn't probably be comfortable that I am in the top half of my opponent's range unless it was a common pattern. And smart opponents know that after a few times they should tighten up so if I think it's a pattern on the 3rd or 4th time they are more likely to have a hand than I think they do. So this is where intelligent speculation is at risk of being poor speculation.

TO combat this take the occasional shot and the moment you get squeezed, back off and pass up the next 2-3 opportunities... Then maybe mix in one more after passing up several and then try it again... This way you are buying time to set a trap with AA or KK playing this manner and still testing the waters on your regular move. If you aren't squeezed again, maybe pass up the next opportunity or two and try again, and then go back to every other.

With that being said I may try it a time or two and if I am reraised tighten up considerably to say the top 10 or 15% of hands and just call with them to trap. If I am squeezed again, and don't have a really strong hand I want to be even tighter the next time so it is far more likely that my call will contain a hand I am willing to put it all in with.

Speculative speculation... That is getting pretty close to just gambling without an edge. It's very important to know the difference between a calculated risk based upon what you see that still has some theoretical edge exploiting opponents and being vulnerable to setups and traps as well as streaks that deceive you as to the nature of how opponents play.
However, the "solution" for "optimal" play makes the incorrect assumption that opponents have clairvoyance about your particular strategy. In reality they don't. If you raise with 60% of hands and then 20%, will opponent know you aren't playing EITHER really tight OR really loose but not somewhere between? If they don't, they may just think you are getting a rush of good cards at first and play too tight initially and allow you to exploit them, and THEN when they figure out you are too loose, you may have tightened up. So all speculation makes some assumptions that may not be true. As long as you are aware of this as well as aware of how opponents at these levels typically play, I believe your edge is ggreater and it is worth the risk, but you absolutely can play with an edge assuming opponents are fairly close to perfect preflop and postflop if you know how to also be pretty close to perfect and you select tables with people that aren't. True, you could make a bit more playing exploitative poker, but the more exploitative poker you play, the more vulnerable you are to counter-exploitation.

That same realization that opponents may incorrectly assess your range of hands can allow you switch between a really tight strategy (75% chance of having the best preflop hand) and a really loose one (35% chance) to trap opponents who try to exploit you. Of course, if opponents have good notes on you and they correctly anticipate that, you may assume they are falling for the trap when really they know your strategy.

But speculation to the degree of making guesses or hoping opponents guess incorrectly rather than calculations becomes very close to "gambling" if your guesses aren't not only right more often than not, but right to a great enough degree that the gains when right make up for the losses when wrong. Taking a poor risk with a poor choice will lead to decline of money over time. Speculation itself isn't necessary, but speculative speculation where you not only are going based off of what you observe, but are doing so in a way that makes you vulnerable and exploitable and doesn't respect the mathematics in hopes opponents don't notice is usually far too risky. In other words, observing a post flop mistake by your opponent and intentionally making a preflop mistake yourself of playing virtually every hand vs that opponent is going too far. Even bad players can recognize patterns and respond. There are some rare spots where it may be acceptable to do on very rare occasion, but that requires you to really know more than your opponent about a lot of different things. This can be exploited. Even if your assumptions about the initial opponent are correct, well that is a slippery slop that leads to gambling rather than speculating and is about as close as you can get to not playing with an edge since your edge is no longer clearly defined, nor is it invulnerable and is a bet on yourself. The tendency to bet on oneself beating the odds is why casinos make so much money. They are exploiting this tendency. It is human nature. You must be aware of this and avoid it.

However, I will suggest speculating on opponent's ranges provided it doesn't make you too vulnerable. In other words, while normally you should ASSUME opponents' play optimally and only play HALF of opponent's OPTIMAL preflop range if he raises, IF your hand is ALSO strong enough to raise if it were folded to you AND opponent has been seen raising in that spot with approximately twice your raising range or more from your position (if it folded to you)) THEN you can play half his "range" (provided you make a relatively conservative assumption about what that is) as long as it isnt done every single time. In other words play HALF opponents raising range IF that range also is strong enough to open with a raise if it had folded to you. Let other people try to flat call or reraise him light and then when you notice THAT pattern, you can exploit it by squeezing with a raise more often. Do that pattern yourself just often enough so it doesn't look like one, and by the time it does, you have a hand. For instance, raising the same player two times in a row looks like you are playing too many hands to your opponent, but if you never raise twice in a row vs the same player UNLESS you have a strong hand, pattern recognition of opponent works in your favor. Just don't assume they are recognizing a pattern just because they raised or YOU have fallen into the pattern recognition trap.

This type of strategy will both allow you to fold the rare situations where very tight opponents raise and you normally would call or raise and save some money and it allows you to find more profitable opportunities against bad players that play too many hands, while also perhaps making your image look much different to some players . If you 3bet 25% of all hands every other time against someone who raises 50% of all hands, your opponents may asssume you always 3bet light, when it is just against this opponent, and they may give you action on 3bets or 4bet light and you will have a monster hand often enough to really make them pay.

The poker strategy as defined in this article (Technically optimal play allows more hands since you can bluff and force opponents to have to reraise loosely to cause you to break even on bluff attempts) is tight enough where you will build up an image that will probably allow you to speculate a bit by flat calling or reraising a loose opponent more often than you would normally and make a "squeeze play" yourself at some time if you spot the right situation.

But what is the math of a squeeze play?

The math of THAT situation is tricky since you need a 50% chance that your hand is best BUT we have at least a little information provided. So a 10% range would be the top 25% of the 40% raiser and the top 50% of the reraiser. Our hand would have only a .75*.50 of opponents folding if they only played a hand in our range. That means we only have 37.50% chance hand is best. We actually find we can only squeeze with 7.6% of hands IF our assumptions are correct about the hand ranges. We don't KNOW that opponents aren't stronger, but it's a good speculative guess/educated guess based on what we've seen. It's also probably likely that opponent would respect our reraise a bit more often which may make it profitable to steal with a wider hand range on the squeeze, but doing so is "speculative speculation", and if we only raise with 7.6% of hands the possibility our assumption of opponents range actually are too wide cancels out the possibility that they fold to this action too often.

I went over exact hands and how to calculate it in optimal squeeze poker assuming the caller only plays a hand that is better than opponent's range. That assumption is a bit too conservative probably, but if we want to stick to winning poker with confidence it is fine since our estimation about our opponent's opening range may be wrong. I used the optimal pushing chart in the book "Kill Everyone" to determine which specific hands to use as displayed below. I used the method mentioned above assuming the caller played half range as the raiser.


100%:22+,A9+,KJ+,A3s+,K9s+,Q9s+,J9s+,T8s+,98s,
50%: 66+,AJ,A9s+,KTs+,QTs+,JTs,
40%: 88+, AQ+, ATs, KTs+, QJs+, JTs
30%: 99+,AQ+,AJs+,KQs
25%: 99+,AQ+ (sometimes fold AQ)
20%: 99+,AK
10%: JJ+

If players are calling the raiser more loosely you might open up the squeeze steal range slightly. This is really hard to tell though so I would not speculate too far away from the norm here.

I am okay with putting in the squeeze play if your observations lead you to believe there is a more than 50% chance you have the best hand. Speculative speculation would be something like how often you think opponents will fold to a bet and possibly being profitable with any two but just in case only widening from this list slightly.

Solving for every unique situation like this is probably not something you can do at the poker table, but having a few general ideas such as the above is a good few starting points to figure out.

In the same regard I may deviate from this "playing with an edge" mathematically if I have confidence in a particular read. If my opponent appears to have a weaker range of hand I can say that maybe I'm 80% confident he is weak. Then the math can be worked based upon that observation. THAT is how speculation should be done. I also may add in some bluff raises if opponents tend to fold and to increase chances of getting action with the hands that have an edge but you have to really know your stuff postflop, so that is another strategy entirely.

You probably don't NEED to speculate to make money, but you can make more money if your speculations are more accurate than not. You also will endure greater variance which is more responsible for destroying bankrolls than anything else. Greater variance usually occurs because people play too high of stakes, but it can also occur because of a more volatile style of playing for very small edges for a large percentage of your stack frequently as well.

Most playing the player should be done after the flop once you start with a strong base of always having the best preflop hand.

So aside from always playing HALF our opponents range, and assuming HE plays optimal from his position (unless we opt to speculate and know better), how shall we continue?

Well before we continue to the flop, another speculation I have made about players in general is they are NOT good out of position with bets on every street in no limit games. So another speculation I tend to make is raising with a larger percentage of hands in late position, and fewer out of position. If my opponents will each defend the blinds less than 20% of the time, I can profitably raise with any two. However, doing this SHOULD skew everything that is done after the flop as I will be an underdog when opponent calls and thus should not try to bet nearly as often as in normal circumstance. THAT type of speculation gets expensive in terms of strategizing and determining the proper theory, and table image, but if you don't optimally adjust after the flop and instead just play way too tight, it STILL is probably a good idea to raise with any two... at the expense of some other profitable situations in mid and early position. Just don't play too loosely after the flop if you raise with any two...

Exploiting opponents in Antes Stages with raises:

If your raise range of any two vs calling range of opponents has zero equity when opponents don't fold, you can raise with any two if remaining players defend this often assuming you bet the amount in the pot:


8: All opponents each must play 8.2996% of hands or less to a raise for steal to be profitable.
7: 9.43% of hands or less.
6: 10.91% of hands or less.
5: 12.95% of hands or less.
4: 15.91% of hands or less.
3: 20.63% of hands or less.
Button: Steal profitable if blinds play 29.29% of all hands or less.
Small blind: Steal profitable if opponent plays 50% of all hands or more.
Big blind: Opponent must fold 50% of the hands he completes with or more.


If you have 20% equity when called (and all bets on and after flop break even), steal must succeed 35.56% of the time.

Raise with any hand that has 20% equity if remaining opponents call this often or less:

8    12.13%
7    13.73%
6    15.83%
5    18.70%
4    22.78%
3    29.16%
2    40.37%
1    64.44%


If you have 30% equity when called (and all bets on and after flop break even), steal must succeed only 3.333% of the time. I think when you account for opponents playing back at you this is pretty close to a reasonable standard assumption.

Raise with hand that has 30% equity if remaining opponents call this often or less:
Hand % of opponents needed given X players remaining:

8    34.64%
7    38.49%
6    43.27%
5    49.35%
4    57.27%
3    67.82%
2    81.74%
1    96.67%
 Big blind: Profitable if opponent gives up 50% of all of HIS hands that he has in that spot. So if he only completes small blind and never raises with 50% of all hands that means you need him to fold 50% or only limp and call or raise with 25% of all hands to make a steal profitable.

This seems pretty crazy, with 2 remaining opponents, they have to average 82% defend rate if all they do is call and they give you enough equity on the flop, turn and river by not betting and raising enough. So raising with any two and even "every two all of the time" may actually have some merit if it folds to you in the ante stage. But opponents adjust so disguising this strategy is the most important, and remember we want to avoid too much "speculative speculation"

Steal attempts when you are playing cash games will probably be twice what's in the middle generally so you need for them to succeed more often. I have not calculated this just yet.

There are plenty of weaker games that players play tighter than that in those circumstances. But raising nearly any two from the cutoff and button (say 70%) should still be profitable in weaker games even in cash games, particularly since positional edge is more powerful in weaker games.

After you have played tight for a few rotations, assume games to be weak until proven otherwise from cutoff and button but fold a few times just so they don't think you are playing any two or every two and also fold some of the weakest hands. That's the speculative approach I take after playing enough situations in which it is profitable to steal with any two. Try to make yourself not look like the top target for resteals.

Since I am relatively tight from everywhere else and will on rare occasion, (especially on first impression) fold an opportunity, I will maintain the image up that I am not raising any two. I also will occasionally pass multiple opportunities and resteal so it looks like I am willing to take chances with my chips and I may even 4bet on a bluff against a loose 3better and show it and never do that again but open raise a lot. That is usually enough to prevent opponents from adapting. I also might limp and fold to a bet or check/fold once to set a trap later potentially. I can limp and bet the flop and have the delayed steal attempt so it may be less obvious I am always looking to steal preflop as well.

Limp and Limp raise shove:
A lot of mathematical people will tell you to NEVER limp. I'm okay with that in most cases. But in tournaments where blinds always escalate and setting up traps is increasingly valuable to capitalize in the later rounds, I would say that shouldn't be the case.

The reason to limp is for pot control and all in math. You want the person to be forced to commit themselves on the last move or overbet shove. I would begin to mix in occasional limps with both playable hands and even some that are outside of the range provided when everyone is around 50 big blinds or less. You are training people to think you limp in two wide and fold too frequently to a raise.

When you get under 30 big blinds you can limp closer to your normal range and 3bet resteal pretty wide since it's an all in move that opponent can't simply wait 1/3 times to 4bet and make everything back. He has to either call or fold. Rather than limp shoving for half the opponent's range, you can aim for around 60% of his range. Since you are also limping tighter this means you can limp shove with close to your entire range.

If you limp with say 88+, AJ+,ATs+,KTs+,QJs and some suited connectors, plus mix in some more limps occasionally, then you might even shove with 99+,AQ+,AJs,KQs over the limps. That may be a little too wide, but because opponents have seen you limp a lot from early and middle position and even late position previously they will probably raise wider and fold tighter to shoves than they should which is even more profitable.

If you limp from middle position, you might shove with 66+,AJ,A9s+,KTs+,QTs+,JTs. However, if opponents aren't raising over the top of your limps a lot in the earlier phases, you probably should give them more credit. Since some of these hands are effectively bluffs vs the calling range, you may prefer to polarize the range and call with your midstrength hands that have showdown value instead and on occasion call premium hands.

This may be mathematically incorrect to limp and fold as often as you do, and it may be mathematically incorrect for your opponents to raise you as often as they likely will when stack sizes mean a shove will be a perfect size to force them to fold too often. But overall it tends to work. Opponents correctly assess you as someone that limps in too much, punishes the limpers with raises with a wider range of hands, and likely continue because it seems to be working.

You give up maybe 3 big blinds from limp-folding when blinds are 500/1000 and 600/1200, You limp less frequently when blinds are 800/1600 and when blinds are 1000/2000, you get one single limp shove from here and it's about 10,000-15,000 in chips you gain after losing say 5,000 in the earlier stages. Get two and NOW opponents adjust, but you've taken about 5 times what you lost in the previous stages. That will go a LONG ways to buying you time to find very good cards and a highly profitable situation later.

When stack sizes are such that 3betting all in is not an overbet, you don't want to raise as often and you prefer to be the one shoving on a 3bet. Opponents won't have a hand often enough unless they raise with a tighter range of hands than normal. This is the reason to limp rather than open. Some people taper their bets lower based upon stack sizes so they eventually minraise but that only works for so long before a minraise is also an easy 3bet shove without overbetting, or to where a 3bet requires a 4bet overbet shove. Squeeze play and flat call or limp and 3bet to avoid being the one with the big overbet.

A similar tactic works by being the "weak target" on the big blind and letting people steal your blinds a LOT early on. First if you're lucky you may get someone else to realize the initial raiser raises wide and 3betting even wider and end up picking up a good hand for a 4bet squeeze. Secondly, if you call a couple times as well and check fold or check call and then fold on turn opponents are still going to target your blind. But if you begin 3betting a few times you'll get away with it. Then if you call and then check raise the flop, you'll get away with it. Then if you call and make a small bet on flop and check raise the turn you'll probably get away with it. It may be a large risk, but I'd rather take say 3 big risks like this when the blinds and antes are very large to where if I get away with it I can go the entire tournament without calling all my chips off and only moving all in myself a few times.

Also, if I can limp in more as a result, I can see more flops with the stack sizes large relative to the size of the pot. This can still allow me to act as if I'm deeper stacked far later in the tournament than most and continue to accumulate chips when most people are just hovering and dwindling raising and being 3 bet, or 3betting and risking their entire stack. That means I can see hands to river and accumulate chips without high varience later and prolong the inevitable all in game for much longer than most.

OKAY!

That is out of the way. Now we covered preflop strategy pretty well let's move to postflop play.

Flop play and turn play and river play should be very loose aggressive because you start out tight. You should call with air on the flop to take away the turn. You should call with air on the turn to take away the river even. You should bet the flop turn and river. You should consider raising instead of just calling as well. Once you have a preflop edge you are going to HAVE to continue a high percentage of the time because you have a lot of equity most of the time. Make your opponent play against your entire range of hands rather than just your specific hand you have in a given deal.

Ask yourself if opponent were to bluff on every street, how often would I have to call to force his bluffs to break even? On the river that's easy. If he bets the pot he is risking say a pot bet to win the pot then he has to win 50% of the time for a bluff with any two to be profitable. With a half pot bet he needs it to work once after failing twice or one out of 3 total times for ANY TWO bluff to be profitable. So you have to call at LEAST that often on the river, but that assumes the opponent hasn't been able to bluff you on previous streets otherwise he doesn't even need to break even on the river.

With the flop defining a large percentage of your hand you COULD choose to fold more on flop but you don't want to be too predictable.  You have to have the right frequency.

That usually will be like 70% of the time with the typical bets of 1/2 to 2/3rds the pot or so on EVERY street. If opponent bets larger on some street, you can afford to be a hair more patient on that street. If you have observed patterns, you MAY consider speculating a bit by playing a different frequency but it is NOT necessary.

Now BECAUSE opponents aren't perfect and will often give you free cards and BECAUSE opponents tend not to double barrel as much and BECAUSE opponents tendnot to float nearly often enough on the flop, and because many opponents always continuation bets, certain strategies like floating the flop MORE often, always betting the turn if opponent bet the flop and checked, ALWAYS folding the turn to a double barrel bet if you don't have a really strong hand and always check raising instead of betting out of position... this may be part of a profitable standard strategy even though it shouldn't be. Once you observe more check raises and active turn play you can adjust. This is a bit speculative but it is very reliable. Occasionally checking the dry high and paired flops and either floating the turn or betting with a delayed continuation bet on dry boards may look stronger and give your continuation bets more credibility while even occasionally checking the wet boards with strong hands and strong draws to control the pot and make semibluff look stronger and slow play less predictable... and even seeing more hands preflop because the free cards and predictable actions of opponents allow for you to fold "too often" and be profitable... Plus, with a stronger range than your opponents you kind of want to get to the river on dry flops and punish opponents for drawing on low card and wet flops. And DO NOT pay opponents off on the turn and river when they show strength until you know they are capable of bluffing very frequently on these streets.

All these are possible ideas on how you might be able to speculate and deviate from "optimal play".

Now optimizing which hands that frequency (based upon bet size) of calls represents given the cards on board requires lots of work. Trying to further optimize the play by looking at how you'd play against various hand ranges opponents have also requires additional work.

Mostly though if you come in with a stronger hand and have really sound flop play and a decent idea for what turn cards are in the worst 30% for each hand such that you'd fold about 30% of your range on the turn given each situation as it develops should allow you to have a real good balance and do well regardless of what opponent does. And if opponents are not playing enough hands you should be the one betting. Certainly having the ability to shove all in and break even on semibluff and also do that with a monster hand is a tactic that can be employed occasionally as well, but if that's your goal you'd have to be careful your range doesn't give away too much if you keep a small pot which means you have to occasionally not play a monster fast and a draw fast and instead just continue with it.

If you are calling to the river on a draw, you need to occasionally bluff as if you hit a more obvious draw. Perhaps you act as if you hit a straight when you really just paired your cards because you had 97 on a 456 board and a 7 hit instead of an 8 or a 9 hit. That's 3 outs to bluff at it or a 6% chance with 1 card to come to bluff and a 8% chance to hit. That's a little bit too frequently if you only make your hand 8% but it's okay if opponents are likely to fold often enough and the bet isn't a huge overbet.

Exploitative Play: While most of this is focused on "correct" play or "optimal" play if opponents were optimal, the solution against opponents who are bad is often to exploit. I am okay with doing that after the flop more than before the flop as opponents get themselves into a hole with worse cards than you and can't help but make mistakes in some manner, plus inexperience is easier to spot after the flop, and the type of boards you face provides an advantage over the novice. This provides a different type of "speculation" that is possible.

While playing 50% of your opponent's range makes it very easy to profit even if you bet half the pot blind on every street and fold blind to any raises on the turn and river... If you make some mistakes later on, there are situations in which playing two jokers would be profitable. ANY TWO cards even those which have zero chance of winning can be played profitably if opponents are "exploitable".
For example on the river if opponents fold over 50% of the time to a pot sized bet you can raise and bet with any two on every street (provided you save enough to bet the river) and build up a pot and bet the river and over a very long period of time make money.

Maximum exploitation would often mean playing every single hand and identifying the spot in which opponents are too weak. Many opponents aren't quite so poor that you could play any two all the time.  But you could certainly play a much wider range of hands and probably wouldn't need to start with superior cards. I still prefer it, but maximum exploitation would be maximally speculatively. The time to try this is during tournaments when you only risk a buy in and winning the maximum chips per hand will prolong the requirement for all ins at expense of risk.

The flaw in the concept of maximum exploitation is that it assumes players won't counter adjust. Even basic players eventually do. In the long run not exploiting maximally every time will probably yield more chips because it causes fewer adjustments. By trying to exploit a flaw, you leave yourself vulnerable to counter exploitation as well. For example, say opponent never checks the turn and always bets when you check to him and always folds to a check raise. To exploit that, always check raise. But if you always check raise and opponent learns this, you now give opponent free cards when he wants him and a big pot when he wants it and he can now call your checkraises with much more hands if he wants as well. He can totally flip the table and your plan backfires and now YOU are being exploited.

So I'm not a fan of maximum exploitation, but I would work up to it.

START with mild exploitation as described as starting with a stronger hand than opponent and betting it very aggressively, and picking apart flaws on flop, turn, and/or river where opponent's fold too often. If they instead call too often to very large bets on every street you can still play it fairly aggressively but maybe fold on the flop a bit more often and bet larger when you're in.

After awhile, see how opponent has reacted. If he hasn't reacted, loosen up a little preflop. Play 75% of opponent's range then 100%. Then scale back to where you were and then try 100% again and then more hands than opponent. Scale back to 75% then test 125% and 150%. Pay attention to other players too. Now some hands are an underdog to opponent's range. If opponent still hasn't adjusted, now play 70% of all hands. IF opponent has the wrong call/raise frequency on certain streets and folds too much you literally profit from betting 100% of the time as long as you don't pay them off.

You aren't just testing the specific opponent, but also seeing if the other opponents notice you are targeting this opponent to see if any of them retarget you.

Work your way up to playing any two if you must.

Personally I'd rather keep scalping the flaws off of players at a reasonable rate while hoping that the other players allow the most exploitable opponent to beat them. I want people checking like crazy against the players who fold too much on the flop and turn. I want them calling or folding to opponents that always fold to raises on the flop. This keeps them filled with chips. If I bust their roll, they may stop playing and I ONLY double up. That isn't necessarily best. Worst case scenario I end a player's poker career or tournament life at that casino/website as opposed to just milking him at a reasonable rate, letting him win from other bad players and lose to me for as long as possible.
"You can sheer a sheep many times, but you can skin him only once"

In a tournament if you can get a huge chunk of chips at the RIGHT moment great, but don't fight for 15 big blinds when you have 100 if the alternative is say letting opponent think you only 3bet with a monster hand until the blinds get much higher and you can call and call and then raise and get tons of big blinds at much higher levels which equates to much more chips. Especially if that decision creates volatility that risks tournament life without a large enough reward to compensate for the opportunity cost you give up by potentially busing out.

I think if you are going for maximum exploitation you need to vary bet size. Tight players look for excuses to fold when they are tight and may become married to their hand on other streets once they continue. Loose players look for excuses to call or raise although they may tighten up on other streets. Know who you are playing with, and know they are looking for an excuse. The loose players look at a suddenly larger bet as a bluff or a midpair and they call and look for a high card flop to bluff at. The tight players looks at the suddenly larger bet as scary. THe tight player thinks "well he had been betting a lot now he bet large instead of big, it means something different but I dont know what it means so I have to fold.  sometimes betting or raising the minimum is enough to get people to fold despite massive odds they just gave you.

Cash games and tournaments are fairly similar in terms of game theory and exploitation but the thing that changes is the deep stack vs short stack play and the bubble and inflection points and how players play differently when ratios of the pot to the stack changes.
These differences are enough that few players are good at both tournament and cash games. the fear of elimination is different, the penalty of elimination is different and the bubble factors change the nature of how people make decisions. The changes in blind are more rewarding to set up images and then exploit them when the blinds are higher and there is a much steeper penalty for "calling to gain information to use later" You also don't stick around at the same table long enough to play the player.

But, the nuances of preflop and partly after the flop in terms of how you should  get an edge and accumulate chips should remain roughly the same in my view.

Final Table Bubble Nittery

Let's say you're on the final table bubble with KJ on the cutoff. It folds to you and you have 10 big blinds. In most situations, it should obviously be a shove. But you have a feeling you'll get called with nearly 20% of hands. A range of 77+,A2s+,KTs+,QTs+,JTs,A7o+,K9o+,QJo vs KJo is going to be behind with 42.665% to win. Foretunately, you have fold equity still. If 3 opponents fold 80% of the time each, that's about a .80^3=~51% chance they all fold.

However, on the bubble there are bubble factors you're supposed to adjust for. The chips you lose are supposed to be worth about 1.6 times more than the chips you win because losing chips threatens you being unable to fold up the money and make considerably more.

So when you lose, you aren't losing 10, you're losing 16.
If you get folds 51% of the time and pick up 2.25 (EV of 2.25*.51=1.1475), and you get called and win 12.25 .49*.42665 or expected value of 12.25*.49*.42665=~2.56 and called and lose 16 for EV of -16*.49*.57335=~-4.5, the total sum is 1.15+2.56-4.5=-.79. So the individual result of shoving with KJo is actually losing money. While technically acceptable to shove with some losing hands to force opponent to widen call off range and collectively make more shoving WITH KJo than without it, I think it's a fair assumption that opponents are highly unlikely to adjust very much to you.
Also, opponents probably SHOULD be calling you much tighter than this due to bubble factors themselves, but if you think they probably won't, then shoving becomes incorrect, because their decision to call with hands like A7 and QJ ends up hurting BOTH of you.

A standard "push/fold" chart that doesn't account bubble factors will say to push with
22+ A2s+ A2o+ K6s+ KTo+ Q8s+ QTo+ J8s+ JTo T7s+ 97s+ 87s 76s

But I believe pushing this wide on the bubble is almost certainly a mistake.

Nevertheless, there is a very strange concept with regard to tournaments. If everyone is pushing with wider and calling with wieder, the probability of you being able to continue without having to withstand multiple all ins is low. If you preserve a raise/fold range you can either play very tightly and call off appropriately according to the bubble factors and rarely have an opportunity to steal. This is because the assumption is that "all skill is equal" and thus, all players will play the same way. This isn't the case, so what are the implications? The implications are now that either you have to wait for the best spot you can afford to wait for, or you have to try to play much looser before you have 10BBs.

If tight play forces you to go into this ultra tight blind yourself to death strategy or close to it, it would seem that it's of a huge advantage to eliminate the skill factor of short stacks and put them at the mercy of their cards by raising more widely, particularly in early position than any "chart" might suggest.

There's a reason Phil Helmuth has so many bracelets, so you have to at least entertain some of the ways he plays. When he has 8 big blinds, he will still minraise/fold. That is on much slower structures, mind you, but nevertheless, I think the idea of raise/folding down to 9 big blinds isn't all that bad if
1)You are much more likely to have a monster
2)Opponents are unlikely to really adjust their call range all that much between a minraise and a shove
3)You are close to the final table and thus survival is important, but the difference in chips is not nearly as important as the difference between living to see another hand... A double up will make you so much more likely to final table, and a steal will buy you a lot more hands that will make a difference in how other short stacks are now forced to make a move (and they probably are more likely to move in and bust than you). Consider buying 9 more hands when you win, and pretty much having roughly the sam amount of fold equity if you fold and have 6 big blinds or under 4 if you pay big and small blind and
4)You can raise without having the pot odds adjusted for the bubble factor to call. This is tricky. I tend to have a very polarized range. Either I am getting desperate and will raise with any two from UTG or UTG+1 but will do so infrequently enough that there's a real good chance I have a very strong hand, or I have the very strong hand that I've been waiting for. For example, in 3 rotationsI might try this once with air. If there's 7 opponents that's 21 hands. In 20 hands you have about a 50% chance to get a hand in the TT+, AQs+ range (not including AKo). In 30 hands, JJ+, Aks. Since you're also going to be raising with some hands like 88,99 and widening that range in later position when it folds to you, there's a more likely chance you have a premium hand or strong enough hand to call than a poor hand.

Let's look at the math.There are many different ways to dissect this problem depending on how you view bubble factors and whether or not you want to include your equity from raising preflop. I want to just isolate making the raise from the decision once you are raised.

So your risk is worth 1.6 times more than you gain. You are not risking 6 to win 8+2.25+ your 2 back or risking 6 to win 12.25. Instead you are risking 9.6 to win 12.25. With 1.276 to 1 odds adjusted for bubble factors, you are going to have to be 44% to win. With a hand as bad as 23o, you most certainly are not, so there is an argument to folding. You have to then argue why raise at all? Well, if you only raise about twice every 21 hands with a polarized range of either "any two" or TT+,AKo,AQs+  your opponent is pretty much going to have to all in or fold. So he either risks 8 and is against a very tight range where he is behind, or he picks up 4.25. He is risking 8 (and then some because others could wake up with a hand) to win 4.25. If you adjust his decision for bubble factors, he is risking 12.8 to pick up 4.25. But of course when he shoves and gets called he can still win. So if your opponent gets called 60% of the time that he shoves, being 35% to win when he gets called isn't enough. He needs to be 35.7% vs your range of TT+,AQs+,AKo. If we want to get really accurate, we can say there's a 58.2347% chance that you get dealt TT+,AQs+,AKo+ in 21 hands. If you don't raise in 21 hands you will have to raise with whatever you can come up with. So if you factor that in, he only needs to be 34.25%. I actually think his chances are much worse since you probably will widen range when folded to in later position, so the probability of you not raising within 21 hands is probably much lower.

In theory, he should require the exact same range as you to be able to move in on your raising range, and probably tighter because he has to concern himself with other opponents.

So if there are 6 opponents left to act and they need TT+,AQs+,AKo, what's the chances that you get reraised? In reality it SHOULD be only 22% . Slightly more because opponents that have you covered can call off lighter than you as bubble factors are smaller to them than they are to you if they have you covered in chips.

Raising "any two" vs these opponents should be profitable since 77.9% of the time you pick up 2.25 and 22% you lose 2*1.6 or 3.2. That means you can pick up 1.046 big blinds every 21 hands. Hopefully you get a walk, or find another spot, or also at some point find a spot to get your money in good by opponent that makes a mistake, but losing chips at less than 2 big blinds per rotation on average when you are on the final table bubble is not all that bad. You are losing about .26444 per rotation which means if blinds stay the same, you can survive in this manor an average of 45.37 hands if you have 12 big blinds. Obviously blinds go up and as you become shorter, decisions become more desperate. But even so, everyone else will grow more desperate, and you are still giving yourself a good chance of making the final table and make a lot of money from moving up the money.

You can look at this "hands left" and adjust for the blinds going up by calculating your "burn rate" based upon your strategy at the given level and adjust as you become more desperate. I would say when you move to all in or fold mode to just calculate being on autofold from there.
With 45 hands left or even 35 hands left you can afford to wait for JJ,QQ, KK or AA...

If you can find an equivalent spot where your overall expected value is as good as getting your money in with jacks you should go for it. If it's less, you may have to reconsider even if you have JJ+ if the supernit shoves.

But since there's added value in raising, or having fold equity PLUS being ahead when called, you can widen the range, and adjust for spots. However, what you cannot do is try to justify waiting for any better than this.

3Betting Vs a Static Opponent Given Certain Bubble Factors

In poker, aggression is important, but it's also important not to take things too far since you can never get 100% of the prize pool and you are simply helping your opponents make money if you are always too aggressive. Tournaments have bubble factors that should adjust your decisions as we've shown. We've even shown a strategy for unexploitable opening ranges with 20 and 30 big blinds at different bubble factors and vs different 3bet ranges.

But what about your aggression? What about when someone raises 2.2 BBs and you are trying to decide whether or not to jam? How should bubble factors affect your jam range given certain assumptions about your opponents?

Let's say opponent has a "static" or unchanging strategy. He does not adjust at all to bubble factors, and he is predictable in always open raising when it folds to him with 10% of hands regardless of position. He will call 3bet shoves with 99+,AK,AQs (calls with 42.2% of his range). If these assumptions are correct, how often can we Jam vs this player from the button if both the blinds are on autofold?

First we determine how often opponent calls a shove. This is 4.2232/10 since he calls with  4.22% of hands out of 10% or 42.23%. We then run the math assuming we gain 4.5BBs when he folds, and when called we win 22.25BBs when we're called AND win, and lose 20 when we lose. We then multiply that total expected loss by the bubble factor since chips we stand to lose are not equal to the chips we gain. We can adjust until we find the break even point. Based upon these percentages we can find which hands a shove is break even with or better. The real optimal solution may have some flat calls in there, and thus might shove with more premium hands and a small percentage of bluffs and just call with the remainder, but it's not a huge mistake to ignore these and jam or fold.

Jam with:
Bubble Factor of 0.8 jam such that you are 25.74% to win when called:
22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
Bubble Factor of 1.0 jam such that you are 32.77% to win when called
TT+,AQo+,AJs+,KJs+,QJs
Bubble Factor 1.2 Jam such that you are 38.58% to win when called
TT+,AKo,AKs
Bubble Factor 1.4 Jam such that you are 43.47% to win when called
JJ+,AKs
Bubble Factor 1.6 Jam such that you are 47.64%  to win when called
JJ+

Charted neatly below to eliminate the wording
bubble factor|% to win| hand range:
0.8 25.74% 22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
1.0 32.77% TT+,AQo+,AJs+,KJs+,QJs
1.2 38.58% TT+,AKo,AKs
1.4 43.47% JJ+,AKs
1.6 47.64% JJ+

As our opponent folds more than 57.8% of his hands we can push with a lower percentage to win vs whatever calling range he calls off with.

With a larger number of big blinds like 30, you need to Jam with a tighter range of hands since you are giving your opponent a better payout when he calls, and gaining less proportionally to what you lose when you are called and behind.

Obviously a tight player isn't the ideal target to 3bet, but if you have a decent hand you can certainly go for it.

What about other player types? Although I haven't gone through to do the work to define the exact hands, I have came up with the percentages of a few scenarios.

20BB 3 betting over
% to win needed when called if opponent opens with

35% of hands and only calls with 99+,AQ+,AJs,KQs (calls 13% of the time he opens)
bubble factors
0.8  0% any two
1.0  0% any two
1.2  6.55% any two
1.4  13.99% any two
1.6  20.34% any two

30% of hands and only calls with 88+,AJ+,KQ (calls 20.61% of the time he opens)
bubble factors
0.8  0% any two
1.0  6.32% any two
1.2  14.42% any two
1.4  21.23% any two
1.6  27.04%

opens 25% hands and calls with 88+,AJ+,KQ (calls 24.7% of the time he opens)
bubble factors
0.8  any two
1.0  any two
1.2  22.29% any two
1.4  28.47%
1.6  33.75%

Opens 15% of hands and calls with 55+,AT+,KQ (calls 70% of the time he opens)
0.8 36.88%
1.0 42.86%
1.2 47.80%
1.4 51.95%
1.6 55.50%

Opens 20% and calls with 55+,AJ,KQs (calls with 42.2% of the time he opens)
0.8 25.74%
1.0 32.77%
1.2 38.58%
1.4 43.47%
1.6 47.64%

Opens 10% and calls with 99+,AK,AQs (calls with 42.2% of the time he opens)
Jam with
0.8 25.74% 22+,A2o+,KTo+,QTo+,JTo,A2s+,K2s+,Q2s+,J3s+,T6s+,97s+,86s+,75s+,64s+,53s+
1.0 32.77% TT+,AQo+,AJs+,KJs+,QJs
1.2 38.58% TT+,AKo,AKs
1.4 43.47% JJ+,AKs
1.6 47.64% JJ+

It's important to notice that opponents SHOULD call off much tighter as bubble factors increase, but if they don't, you'll have to shove much tighter yourself.

Against an opponent who calls off with the SAME range of hands and raises with the SAME range of hands, you are going to have to tighten up dramatically as bubble factor increases both in your opening range, your call off range and your 3bet range.

However, what tends to happen is opponents might try to exploit by opening just as wide near the bubble, but fold more tightly because they are aware of bubble factors or give too much respect to the 3bet believing that an opponent wouldn't 3bet shove without a huge hand. Or they raise without anticipating the possible reraise and then once it comes they start worrying about the money so they tighten up.  So I believe there are certain types of opponents where your range won't change that much, and other types in which it will actually WIDEN because of how they play, but for now until I run the math to prove it, that remains speculation.

What I'm very interested in seeing is if an opponent opens up with say 20% of hands and always assumes a certain 3bet range and actually adjusts his calling off range for the bubble, but not his opening range. Since his calling off range will tigthen up as the bubble factor increases, it becomes correct to raise more, if not for the fact that our bubble factor also increases. There is definitely a point in which WIDENING your 3bet range as you get closer to the bubble is correct to certain opponents, but I will be interested to see how great of an adjustments to call off range opponents have to make for that to be the case.

In the future I hope to work some of those numbers.

How To Avoid All Ins To Crush the Early and Middle Stages Of a Tournament

Summary:
Given our assumptions on blind structure and hands per hour, with 40% chips coming from preflop raises plus postflop action, 40% of chips coming from 3bets plus postflop action, and remaining 20% of chips coming from: blind defends, dead money grabs, squeeze plays, blind defends, walks, flat calls, etc. we can theoretically sustain our chipstack for an entire tournament without ever being all in with a preflop raise on 16.16% of hands dealt and a 3bet on 6.5% of hands. Variance and the assumptions not always being consistent with reality will force us to call off most tournaments in reality, but it's a good starting point to understand the value of applying consistent pressure.
---------------------------------------------------------------------------------------------------------
The interesting aspect of tournaments, is that if you have a high enough win rate at low enough variance, you can in theory avoid ever being all in. At a minimum, if you maintain a pretty high winrate at relatively low variance, you can at least prolong the all in for a considerable amount of time... This can result in an enormous boost to your chances of doing well in a tournament. It's not uncommon for me to triple up my starting stack before I'm all in, and at slower structures I could probably go much longer, but I have a tendency to make a very infrequent mistakes that are very, very large in magnitude, as it can be difficult for me to focus for more than 5 hours.

In a few tournaments I have analyzed, you can avoid an all in if you can steal 3 blinds AND antes successfully per rotation. You can get very close with 2 steals and in slower structures, 2 steals may be enough if the speed of play is fast enough (around 80-120 hands per hour rather than 60-80).

The WSOP And Other Big Events are the Exception, not the rule

You should adapt to structure, but the WSOP main event is obviously the exception to the rule. This level has 2 hours before blinds go up and you start with 300 big blinds and the blinds rise at a rate of about 0.40% per hand on average after the first couple levels of the antes. This tournament is such a slow structure that you can for a very long time till have an enormous chipstack relative to the blinds if you just maintain your chips or even if you lose your chips gradually over time. You may not even need to maintain the number of big blinds to get deep, you can just play a few big hands and get a few decent pots every rare once every so often. If you autofold I estimate that you will see 440 hands before you exit the tournament. If you steal one per rotation to maintain your chips until the antes gets involve, then steal 1.3 times per rotation successfully after you get down to 25 big blinds, you will hover above 20 big blinds for the entire tournament until you win if variance doesn't get you. In a tournament like this, coolers and high variance gets in the way and it's sometimes a liability to have good cards in some ways since it keeps you in the hand in an inflated pot that you would prefer to just take down or fold.

If good hands are such a liability, why not just fold if the pot gets too big? Because as much as you'd love to get through an entire tournament without ever being all in, eventually you will. Plus if you don't occasionally show them a big hand your raises may not get as much respect after awhile.

Certainly an average gain equal to 2 steals per rotation plus a few good hands and the very occasional spot where you have a premium hand AND an opportunity to double up is usually enough to have a great ROI. You can still dramatically reduce your chances of elimination, which will translate into a huge win percentage.

Requiring 2 steals per rotation does not mean you should raise 2 times per rotation because your attempts aren't 100% successful. So how many blind steals should you attempt? That really depends on the probability of success.

If you successfully get everyone to fold 80% of the time, expected value of 4.5 big blinds requires that you steal 2.8846 times per rotation or raising about 32% of the time total.

If you get through 70% of the time you need to come up with a steal attempt 46% of the time, and if it works 60% of the time, you need to come up with a steal attempt a whopping 80.65% of the time.

But hold on, This is assuming that your failed steal atempts always lose. If you are called, you will be forced to muck and never flop a good enough hand to stay, and if you are raised, you will never have a good enough hand to stay.

However, I would say that if you KNEW for a fact that you could steal the blinds his frequently, you probably SHOULD never play a big pot, because you can win without conflict. Why take a 30% chance of elimination if you literally never need to. But you never will have that knowledge with certainty, so even if you are 80% confident, you still must have some threshold since there is a chance you are overconfident, and there is still the 20% of the time that you factored in that things won't go your way.

Obviously if opponents recognized this strategy, they'd reraise more actively, your success would decline and it wouldn't be worth folding, and most importantly, you never KNOW that the conditions will remain. In fact, they probably won't... As such, the idea that you can play that perfect tournament 100% of the time and never be all in is probably nothing more than a deluded fantasy. Nevertheless, it's one in which we still should determine correct play IF it were true, so we can adjust from there.

Often times you may get knocked out after getting short and forced to take a less premium hand and regret not calling off with the premium hand earlier. That doesn't mean you shouldn't be aware of the strategy and try to adjust strategically based upon how close or far away from reality you think this is.

It certainly is a worthy calculation to determine how frequently you need to come up with chips to avoid all ins. Since you are all ins, accepting a lower win rate is perfectly acceptable, but not too much lower.

So you certainly should plan on having some threshold where you will fight back if you flop good enough, you certainly will see some rivers, and you certainly will pick up aces and it will be worth playing to a reraise...

One side of the argument is that you will be 3bet, you will be called and faced with calls more often, and opponents will raise ahead of you enough that you couldn't possibly steal that many blinds if you raised when folded to 100% of the time. The other side is that when called or raised, you have more equity than is calculated. You can still maintain relatively low varience chip accumulation with high percentage Cbets, occasional 4bets when facing 3bets, occasionally calling 3bets, occasionally 3betting yourself (plus a Cbet), and occasionally you will see showdowns and have a chance to win, plus implications of the turn and river.

So let's imagine instead you are called 80% of the time instead of 20%, but your Cbet succeeds 50% of the time. Let's imagine there is no raising by your opponent, and that when your Cbet fails you still have 25% equity in the hand. Let's also assume that if your Cbet is called that the turn and river are always checked.

In this scenario, you need to come up with a steal ATTEMPT plus a Cbet attempt about 40.4% of all hands dealt to be able to sustain your umber of big blinds in the ante stages.

But what if only 40% of your chips came from steal+Cbets and another 40% came from 3bets and 20% came from a mixture of walks, flat calling in position and big and small blind defenses and maybe a few turn and river takedowns and showdown wins? That certainly would require us to steal less often.

So let's first try to factor in your 3bets. In a 3bet you are going to be risking 2.5 times the standard raise of we'll say 2.25xBBs for a total of 5.625BBs to win 4.5xBBs when opponent folds. The intention is not to always get a fold, but set up a profitable Cbet in an inflated pot and taking a pot where you have position throughout the hand.

So we will assume your 3bet works more effectively and that you do this with fewer hands, and as such your Cbet is more effective. We will say that you win the hand 25% of the time when your Cbet fials still. If you were to only 3bet/Cbet because table never folds to you, you only need to succeed 16.22% of the time. But there's a HUGE caveat in that you are personally putting over 12 big blinds into the play when you Cbet and in reality probably more. The strategy can no longer REALLY be said to be all that low varience, so there is a definate tradeoff that occurs. Nevertheless, a preflop raise plus a Cbet risks as much as 5.6  big blinds. So if you have 30 big blinds that's still 18.67% of your stack.

The equivalent of risking potentially 18.67% of your stack means that if you 3bet/Cbet at 66 big blinds, it is about the same as a raise+Cbet is at 30 big blinds. At 20 big blinds a PFR+Cbet is about the same as a 3bet/Cbet is at 44 big blinds. Since the 3bet can be done less frequently with a stronger hand and is thus more successful and has with it a slightly bigger edge, in terms of risk/reward you can actually say that it's more preferable to make. As such, it may be about the same risk/reward profile at 30-50 big blinds as a PFR/Cbet is at 20-30BBs.

Since the result of not accumulating chips early on in the ante stages will inevitably result in fewer chips which will force you to raise more liberally anyways, it may make sense to 3bet in the 30-50BBs range before you are forced into a position to take on that amount of risk, and potentially more. You never know if your opponents will fold to you often enough to keep up with big blinds.

So if we get 40% of the 4.5 per rotation we need from PFR+Cbets, 40% from 3bets and 20% from "other", how frequently should we make each play?

Well, we need 1.8 per rotation from each since 40% of 4.5 is 1.8. Based upon some assumptions we made, the EV per PFR is 1.2375, the EV per 3bet/Cbet is  3.0825 per attempt.
1.8/1.2375 means that we need 1.4545 times more than the preflop raise gets per rotation. Or 1.4545 raises per 9 hands or 1.4545/9=~16.16% of hands dealt should be raises. 1.8/3.0825=.583942 means we need only ~58.4% of the EV we get from a steal or we can 3bet 58.4% of all rotations or about .583942/9=~.06488% of all hands dealt should be 3bets.

Since not every hand we get will both be strong enough to 3bet AND not be 4bet before it gets to us we should be willing to raise more than 6.9% of all hands on average, and we should adjust this based upon the position and hand range of the initial raiser. An early position raise indicates more strength, late position raise indicates less such that given optimal opponents we should still 3bet a tighter range vs an early position raiser and a looser range vs a late position raiser.

Also, since it will not fold to us every time we have a raising hand that isn't strong enough to 3bet, we need to widen our preflop range and adjust for position as well.

Overall though, coming up with a preflop raise on 16.16% of hands dealt and a 3bet on 6.5% of hands dealt is definitely attainable. Picking up chips from isolation raise+Cbets or dead money grabs after multiple limbpers and blind defends and flat calls in position of course has to also be done enough and profitably to meet the approximate quota as well.

Additionally the success rate and expected value of each move will change, and the varience caused by a 3bet or large isolation raise may make it less desirable to make as frequently as implied.

So in reality you might 3bet far more frequently when you have over 40 big blinds and raise less often, particularly at a more active table and particular as specific spots come up than implied, but you may make up for it later by not 3betting frequently at all around 20-30 big blinds and then once again you may shift when a 3bet is all in and a PFR gives your opponent the perfect shoving stack such that you have to tighten up your range once again.

Additionally, who knows if your raise will succeed 20% of the time or 80% of the time at a given table, and possibly your Cbet will succeed much more often, or much less often than 50%. Certainly it's possible to set up a spreadsheet or more of these calculations to try to get a better picture of individual situations that favor either one or the other, or where the steal attempt is less profitable. It may also be more accurate to adjust the EV as you increase the frequency of hands since our showdown value and table image will be different and the response should be different.

But ultimately this post is just to get you to understand and respect the fact that if you are profitable enough with just the right amount of activity in the right way at a table, you can in theory dramatically reduce your chances of having to be all in. Certainly if you are more active you can accumulate more chips and as such when you finally get it all in your stealing attempts are so profitable that you have everyone outchipped and you can still recover and accumulate until the next all in you have everyone out chipped and so the next all in you can survive until eventually you win one of those. Or you could get it all in a few times and be much more patient and steal much less often.

The more capable you are of maintaining your big blinds or even staying ahead of them, the more willing you can be to make big laydowns in big pots when you know you have the best of it, when you should fold when you have great pot odds because the pot is inflated to the point where you don't need that varience to advance deeply and when you can continue to apply pressure and at times not care about your two cards as much as the situation.

In reality though, there is ALWAYS varience, and even low varience can force you to take on higher varience or play less active in your 3bets+Cbets or less active in the hands you make a preflop raise with.

Are we optimistic?
Accumulating chips at a high rate has to be done to win a tournament. Two steals per rotation is 2/9 hands which is 22/100 and these aren't big blinds but "M". That translates into 33.33bbs/100 before the antes and 50bbs/100 afterwards. Even though people underplaying the ante stages and overvaluing their survival which allows for consistent accumulation, it PROBABLY isn't enough to maintain that win rate over any very long term period of time with low varience...

That doesn't mean that attempting to do so won't frequently produce enough accumulation plus adding in some all ins with an edge that can give you a pretty darn good shot overall at making a deep run and giving yourself a chance to win.

Unexploitable Bubble Factor Call off for 20 and 30 big blinds

Based upon the pot odds you are getting when facing a shove for your tournament life, the hands you call off with will depend upon your "bubble factor" in a tournament. Bubble factor is basically the multiple of the pot odds you need to call off your tournament life assuming equal skill and a bunch of other assumption the ICM makes. The ICM usually will calculate an ICM close to 1 near tournament starts and it drops somewhat close to one following the money bubble burst when you are far from the final table. It rises to around 1.6 near money bubble and again just above 1.6 at final table bubble, or closer to 2.0 if the money bubble and final table bubble are the same in a top heavy payout.

Utility theory and opportunity cost theory may attempt to adjust these factors based upon the assumptions of there being skill involved. Both try in their own way to determine how to adjust those bubble factors given the skill.

The Utility Theorists believe the skill you have is proportional to the number of chips you have. A larger number of chips creates higher bubble factors for opponents who face you, and thus more fold equity and a greater probability of accumulating more chips without as great of risk on your tournament life, and greater probability of forcing other people to risk their tournament life.

The opportunity cost theorists believe that players do not respect ICM and thus will knock each other out sooner as well as provide much more "future value" which means survival is more important than expected value. An all in not only risks your tournament life which is more valuable if you do have skill, but that it also costs you the opportunity to see more profitable spots in the future plus all the hands you would have been dealt if you were not eliminated. If you still have plenty of room to accumulate chips, all in becomes unnecessary, particularly since it's possible you may not have to be all in to win a tournament.

Also, as blinds and antes rise proportional to everyone's chips, not only do you stand a better chance of getting called, possibly getting called twice and tripling up.... You also have the additional fold equity from someone raising another player out of the pot and the ability to wait for a dominant hand. Youalso build up a tight image that becomes relevant if/when you win a double up that increases your chances of additional blind steals when blinds are much, much higher than whatever they were when you passed up an edge. It also increases your probability of survival deep, and requires fewer steals or more hands before you have to double up before you can get back to where you were before you started blinding off.

I believe both have some merit. Between 15-30 big blinds there's an argument for taking slightly more risks than the ICM suggest to gain utility and make up for the edge you may give up by stolen pots in the future. There's also the argument for taking some risks vs some good players and loose aggressive players to your immediate left that otherwise might hinder your ability to accumulate chips.

Between 5-25 there's the argument that because of the antes rising, and blinds rising, you can win around 20% more on a blind steal a level later which allows for a tighter strategy to still be profitable, but also that ensuring your survival  and increasing the probability of a double up and triple up when you do get that hand.

Because of theses bubble factors dictating a different "call off" range, it should change the opening range if you want to avoid being exploitable to a raise.

So the first step is determining a few guidelines for the "call off" percentages. These can be determined by a formula that relates the pot odds and bubble factors to the win percentages. Once we have these, we can assume that opponents 3bet such that you have a 50% chance of being 3bet by one opponent. We then need to calculate which hands have the equity to call off. When we have the "call off" range we can extrapolate the raise percentage.

The raise percentage must not only be unexploitable, but also compensate for bubble factors in which the chips we lose or may lose are worth more than the chips we gain.

The assumption is that when opponents are faced with a raise where the iniaial raiser had this many players left to act, they 3bet with the following:

8 8.3% 88+, AJ+,ATs+,KTs+,QJs
7 9.43% 88+, AJ+, KQ, A9s+,KTs+,QJs,JTs
6 10.91% 66+, AJ+, KQ, A9s+,KTs+,QTs+,JTs,T9s
5 12.95% 66+, AJ+, KQ, A9s+,K9s+,Q9s+,J9s+,T8s+,98s,87s,76s,65s,54s
4 15.91% 66+, AJ+, KQ,QJ,JT, A8s+,KTs+,QTs+,J9s+,T8s+,97s+,87s,76s,65s,54s
3 20.63% 55+, AT+,KT+,QT+,JT,A7s+,KTs+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
2 29.29% 22+, A9+,KT+,QT+,JT,T9,98,87,76,65,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
1 50% 22+,A2+,K4+, Q8+, J9+,T8+,98,A2s+,K2s+,Q2s+,J5s+,T6s+,96s+,85s+,75s,64s+,54s

I only ran the calculations for 8 players, 5 players, and 2 players since I think having optimal call off vs 8.3% 3bet range, 12.95% range and 29.3% range is enough to get an idea. I may also add in a tighter range like top 4% later just because tighter 3bets are certainly common, especially with regards to shoves.

Keep in mind this is just as a means to calculate our opening strategy though so we aren't easily exploitable relative to our call off. I believe our call off range should actually be tighter because they 3bet less often than they should and because they are exploitable enough with raises that exploiting with calling 3bets is less necessary.

So with 30 BBs and a 0.8 bubble factor we need to be 36.69% to win (raise 2.25x BBs with antes)
So with 30 BBs and a 0.8 bubble factor we need to be 39.15% to win
So with 20 BBs and a 1.0 bubble factor we need to be 42.01% to win
So with 30 BBs and a 1.0 bubble factor we need to be 44.58% to win
So with 20 BBs and a 1.2 bubble factor we need to be 46.51% to win
So with 30 BBs and a 1.2 bubble factor we need to be 49.11% to win
So with 20 BBs and a 1.4 bubble factor we need to be 50.35% to win
So with 30 BBs and a 1.4 bubble factor we need to be 52.97% to win
So with 20 BBs and a 1.6 bubble factor we need to be 53.69% to win
So with 30 BBs and a 1.6 bubble factor we need to be 56.27% to win

So for example, if we raise UTG with 30 BBs and are shoved on and call with QQ+ and assume our opponents have a range of 88+,AJ+,ATs+,KTs+,QJs, then we are collectively are 72.568% to win vs that range. So 72.568% of the time we win say 32.5 and the remaining 27.432% we lose 48 (adjusting for bubble factors of 1.6 the chips we lose are worth 1.6 times more). Overall we can multiply .72568*32.5 plus .27432*-48. This is about 10.4.

What that means is that we can raise and fold X times and break even without being exploited. The X is what we have to solve for. Keep in mind that when we are raising, although we are losing 2.25 BBs when reraised, we actually are losing 1.6x more accounting for bubble factors. So we are risking in effect 3.6BBs on our raises and when we call, we gain an average of 10.40. So this means we can raise fold with 10.4/3.6=~2.89 times and call on the next one. Or we need to have QQ+ 1/3.89 times that we raise in this spot. Or we can raise 3.89 times more than we are willing to call off with, or with about 5.28% of hands

That translates into an opening hand range UTG 9 handed on the stone cold bubble with 30 big blinds of about 5.3% (roughly 88+,AQ). The actual call off range should try to account for the opponent because we need to be 56.27% to win a 30BB shove, but only 53.69% vs a 20BB shove. If a shorter stack shoves the bubble factors might even change and also, the opponent's hand range are most likely tighter than "cash game optimal" and a raise is probably profitable all of which means we should play tighter when calling off (and perhaps slightly looser when raising).

Nevertheless this is all work to establish a reasonable BASELINE to give us a better feel of approximately correct play.

What you have to understand about the bubble is IF opponents adjust and tighten up their 3bet range, you can profitably open much wider and call off very tight to the point if you want to exploit opponents. Even to the point where  you are very exploitable such as raising 70% of hands and only calling off with KK+. Obviously if opponents even 3bet you once you should dramatically reduce your raise percentage and reevaluate after a couple more raises on whether or not you should tighten or loosen it up. If on the other hand you are seeing opponents 3bet shove every single hand, you should call off much looser (remember a 30BB shove you should be 56.27% to win on the bubble, so 57% over a random hand vs any two shover ), but basically only open with a hand that you are willing to call off with.

30BBs opening range and call off
(before separator are hands you are willing to call off a shove with)
0.80 bubble factor
8 players left to act (vs 8.3% reraise shove range)
99+,AJ+,KQ+|28.13%
4 players left to act (vs 15.91% reraise shove range)
77+,A3+,A2s+,K9o+,K6s+,QTo+,Q8s+,JTo+,J9s+,T9s|71.25%
2 players left to act (vs 29.29% reraise shove range)
22+,A2+,K2+,Q3+,Q2s+,J6o+,J3s+,T8o+,T6s+,98o+,96s+,86s+,76s|100%
1.0 bubble factor
8 players left to act (vs 8.3% reraise shove range) 
TT+,AQ+,AJs+|17.65%
4 players left to act (vs 15.91% reraise shove range)
88+,ATo+,A8s+,KJo+,KTs+,QJs|33.33%
2 players left to act (vs 29.29% reraise shove range)
44+,A3o+,A2s+,K7o+,K3s+,Q9o+,Q7s+,JTo,J9s+,T9s|67.36%

1.2 bubble factor
8 players left to act (vs 8.3% reraise shove range)
JJ+,AQ+ | 11.18%
4 players left to act (vs 15.91% reraise shove range)
99+,AQ+,ATs+,KQs|19.23%
2 players left to act (vs 29.29% reraise shove range)
66+,A9o+,A5s+,KTo+,K9s+,QTo+,QTs+,JTs|31.45%
1.4 bubble factor
8 players left to act (vs 8.3% reraise shove range) 
JJ+ | 6.89%
4 players left to act (vs 15.91% reraise shove range)
TT+,AKs | 10.56%
2 players left to act (vs 29.29% reraise shove range)
77+, ATo+,A9s+,KQo+,KTs+,QJs |20.49%

1.6 bubble factor
8 players left to act (vs 8.3% reraise shove range)
QQ+ | 88-JJ,AQ+
4 players left to act (vs 15.91% reraise shove range)
TT+|77-99,AQ+A9s+,KQs,87s,54s
2 players left to act (vs 29.29% reraise shove range)
88+,AQ+,ATs+ | open with 13.7% of hands

20 BB opening range and call off
0.80 bubble factor
8 players left to act (vs 8.3% reraise shove range)
99+,AJo+,ATs+,KQo+,KTs+|23.11%
4 players left to act (vs 15.91% reraise shove range)
66+,A2o+,K7o+,K2s+,Q9o+,Q2s+,J9o+,J9s+,T8s |100%
2 players left to act (vs 29.29% reraise shove range)
22+,A2+,K2+,Q2+,J3o+,J2s+,T6o+,T2s+,96o+,94s+,87o+,85s+,75s+,65s,54s|100%

1.0 bubble factor
8 players left to act (vs 8.3% reraise shove range) 
TT+,AJ+,KQs|14.05%
4 players left to act (vs 15.91% reraise shove range)
88+,A8o+,A2s+,KTo+,K9s+,QJo+,Q3s+,J8o+,J7s+,T8s+,98s|46.21%
2 players left to act (vs 29.29% reraise shove range)
33+,A2+,K4+,K2s+,Q6o+,Q3s+,J8o+,J7s+,T8s+,98s|41.64% (note: I used propoker tools to determine the call off range, and pokerstove to do the remaining math.... In propoker tools J9s means J9s,Jts,Q9s,QTs,QJs,K9s,KTs,KJs,KQs where as I've always interpreted it as only J9s,JTs. As a result, whenever low suited one gap connectors or low offsuit cards like 97o+ were in the calculation it include more than I intended like Q7o so it messed with some of the results like this one. In most cases, it didn't change the results very much if at all unless facing a wide 3bet range.)

1.2 bubble factor
8 players left to act (vs 8.3% reraise shove range)
TT+,AQ+|9.88%
4 players left to act (vs 15.91% reraise shove range)
88+,AT+,A9s+,KQo,KTs|17.94%
2 players left to act (vs 29.29% reraise shove range)
44+,A7o+,A2s+,KTo+,K9s+,QJo,QTs+,JTs|32.77%

1.4 bubble factor
8 players left to act (vs 8.3% reraise shove range) 
JJ+,AK,AQs+|6.93%
4 players left to act (vs 15.91% reraise shove range)
99+,AQo+,AJs+,KQs| 11.51%
2 players left to act (vs 29.29% reraise shove range)
66+,A9o+,A7s+,KTo+,KTs+QJo,QTs+|18.94%

1.6 bubble factor
8 players left to act (vs 8.3% reraise shove range)
JJ+|4.42%
4 players left to act (vs 15.91% reraise shove range)
TT+,AKs|6.77%
2 players left to act (vs 29.29% reraise shove range)
77+,ATo+,ATs,KQo,KTs+|11.62%
===========================================================================
I believe I have provided enough of a context for you to get a good idea of how to adjust based upon everywhere between these numbers or even outside of these ranges as a good approximation. But a 3bet range of TT+,AK,AQs may be more common from early or middle position. So

Early and middle position strategy for different bubble factors.
20 BBs

0.8 bubble factor
TT+,AK,AQs|12.41%
1.0 bubble factor
JJ+,AK|7.94%
1.2 bubble factor
JJ+|5.33%
1.4 bubble factor
QQ+|4.18%
1.6 bubble factor
QQ+|3.35%

30BBs
0.8 bubble factor
TT+,AK|15.55%
1.0 bubble factor
JJ+,AKs|9.54%
1.2 bubble factor
QQ+|6.82%
1.4 bubble factor
QQ+|5.22%
1.6 bubble factor
QQ+|4.02%

Note:Raising more often will probably still be profitable since opponents 3bet range is tighter, but because of complications about them potentially just calling in position, it's probably not that great.

The "optimal 3 bet range" we used was one in which opponents deny you the odds to profitably steal with any two, and thus it's a very wide range, particularly in bubble situations, and probably looser than is realistic. Thus in real life you probably can raise wider to exploit and fold tighter and assume opponents aren't trying to exploit. IF you get 3bet, you might reduce the raise percentage and increase the call off percentage and reevaluate later. On the other hand, It probably is correct on the bubble to 3bet much wider IF opponent's open with the same range and fold very tightly.

I think 88+,AJ+ is a common 3bet range vs a late position raiser plus maybe some rare bluffs we won't include because they aren't common enough and enough people will shove tighter than this. I will add this calculation in later.