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.
