There are certain frequencies that opponents need to call with in order to prevent you from bluffing with any two. With multiple opponents they should at a minimum act in aggregate to call enough to force you to break even on bluff attempts. So if you are betting preflop for 2 times the pot or 3 big blinds into a 1.5 big blind pot when opponents fold they should each call at least this often given you raised with this many opponents. That will cause them to effectively fold about 2/3rds of the time. They should call slightly more than this, but this is a good baseline that you can apply on any street where you bet 2 times the pot.
1)33.33%
2)18.15%
3)12.50%
4)9.53%
5)7.7%
6)6.46%
7)5.56%
8)4.89%
When the antes kick in you are betting pot preflop (and sometimes minraise is less than pot) and your opponents must call you at least this often.
Defend range for a 1x pot bet:
1) 50%
2) 29.29%
3) 20.63%
4) 15.91%
5) 12.95%
6) 10.91%
7) 9.43%
8) 7.41%
For post flop considerations given the number of opponents you face let's also look at half pot and 1/3rd pot bets
Defend range for half pot bet:
1) 66.66%
2) 42.27%
3) 30.66%
4) 24.02%
5) 19.73%
6) 16.73%
7) 14.53%
8) 12.83%
For 1/3rd pot bet they need to collectively defend 75% of the time.
Some caveats to this.
The more streets left over, the more opponents can/should call, and the higher frequency you can/should bluff.
A toy game example by Matthew Janda showed 2/3rds pot betting where you bet 33% value and bluff 66% on the flop, then 49% bluff, 51% value on the turn, and then 30% bluff and 70% value on the river. I assume that also applies preflop. Also with an increased price such as in the big blind you can call more often to defend and you don't have to continue as often on the flop because of the pot odds you got on the prior round of betting. Also to be considered, in real poker hands that can draw to very strong hands or be used in bluffs when they miss are more valuable while hands with weak kickers, low cards that can be outkicked and out drawn and marginal hands that can only be used to bluff catch lose value.... particularly those that are not always strong enough to beat bluffs when we bluff catch.
If you actually work out hands, you need to use equity calculators to determine which specific hands these are on specific flops, and how opponents can shed these hands on each street with a round of betting.
Given this defend range, you want to only raise with hands that have value. If opponents call too often you don't really want to add in bluffs but if opponents call more than this the value hands go up and the hands that were considered bluffs now have value.
You only need about 33% equity to call a preflop raise of 2.2 big blinds when the blinds and antes are involved which means you can flat call very widely. While technically we have your opponent defending much less often, that is the minimum threshold to where bluffing with zero equity assuming the betting ends after the hand is profitable.
Nevertheless, we can consider anything that has equity when you call a bet to also be of value to bet. technically we may prefer a smaller pot with hands with 33% to 50% equity but raising gives us a chance at the blinds so in my mind this is close enough. Technically we'd probably have a mixed strategy and sometimes want to just call with the mediums strength hands plus occasionally stronger hands to protect it.
So what hands have equity?
Given we raise with number of opponents left and opponents defend often enough to force our bluffs to break even.
Pre-Ante stage:
1: 22+, A2+, K3+, Q8+, J9+, Q4s+, J7s+, T7s+, 98s, 87s
2: 22+, A4+, KT+,QJ,A2s+, K8s+,Q9s+,J9s+,T8s+,98s
3: 44+,A9o+,KQo,A7s+,KTs+,QTs+,JTs
4: 55+, AT+,KQ, A8s+, KTs+,QTs+,JTs
5: 77+, AQ+, ATs+, KQs
6: 88+, AK, AQs+
7: 99+, AK, AQs+
8: TT+, AK, AQs+
I would personally want to shed hands with kicker troubles and insert hands with more drawing potential. I would be very comfortable flat calling with this range as well if an opponent bet from a given spot with a number of opponents left before he raised.
Nevertheless, we can also bluff. We may wish to bluff with those hands not quite strong enough to flat call, or use those hands just on the bottom end of the range, particularly those without great drawing potential but that might make a lot of stronger kicker hands to fold like A2 or K3 or KJ or A9 or suited connectors or suited jacks, queens and kings (as opposed to suited aces which can draw to the best possible flush).
I would totally be comfortable playing an equal amount of value bet to bluff ranges. If we double our hand range total we roughly end up with the following hands:
value plus bluffs:
1: Any 2 (minus some bad hands)(85%)
2:22+,A2s+,K2s+,Q2s+,J2s+,T6s+,96s+,85s+,74s+,63s+,52s+,42s+,32s,A7o+,K9o+,Q9o+,J9o+,T7o+,97o+,86o+,75o+,64o+,54o,43o,32o (52%)
3:22+,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,86s+,75s+,64s+,53s+,42s+,32s,A9o+,KTo+,QTo+,J9o+,T9o,98o
(29.4%)
4:22+,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,86s+,75s+,64s+,53s+,42s+,32s,AJo+,KJo+,QJo,JTo (23.2%)
5: 44+,A9s+,K9s+,Q9s+,J8s+,T8s+,97s+,86s+,75s+,64s+,53s+,43s,32s,AQo+,KQo (16.4%)
6: 55+,A2s+,KJs+,QTs+,J9s+,T8s+,97s+,86s+,76s,65s,54s,43s,AKo (13.9%) - sometimes fold the weaker hands
7: 66+,ATs+,KQs,QJs,JTs,T8s+,98s,87s,76s,65s,54s,43s,32s,AKo (9.8%) - sometimes fold weaker hands
8: 77+,AQs+,A5s,KQs,QJs,JTs,T9s,98s,87s,76s,65s,54s,AKo (8.1%) (sometimes fold weaker hands)
But remember, we can probably bluff a little more than this, but if our opponents call too often we don't need to bluff (we could if our opponents also make post flop errors) and if they fold too often we can always bluff with as many as possible. Given the possible postflop errors if our opponents fold too often we can actually play any two. If our opponents call too often we have to have sufficient pot odds and implied odds to make up for the hands that are behind to call which means we can't really play any two without being really deep and to do so profitably will require more variance than is helpful in the early stages of tournaments. But we can play a wider range against worse opponents in general but it's also profitable to play a tighter range against loose opponents as we will get more value.
Ante stages: In the ante stages the eqution changes.
This is our value range vs what should be looser opponents:
equity to have value: 33%
1:22+,A2o+,k2o+,q2+,j2o+,T3o+,95o+,85o+,75o+,64o+,53o+ (85.5%)
2:22+,A2o+,K2o+,
3:22+,A2o+,K2o+,Q8o+,J8o+,T9o+,98o,87o,76o,A2s+,K2s+,Q2s+,J4s+,T6s+,95s+,84s+,74s+,63s+,52s+,43s (55.4%)
4:22+,A2o+,K8o+,QTo+,A2s+,K2s+,Q4s+,J8s+,T7s+96s+,85s+,74s+,63s+,53s+,43s (38.8%)
5:22+,A2o+,KTo+,QTo+,A2s+,K2s+,Q8s+,J8s+,T7s+,96s+,85s+,75s+,64s+,53s+,43s (35.1%)
6:22+,A2o+,KTo+,QJo,A2s+,K2s+,Q8s+,J8s+,T8s+,97s+,86s,76s,65s,54s (32.1%)
7:22+,A2o+,Kto+,A2s+,K4s+,Qts+,J9s+,T8s+,97s+,87s,76s,65s,54s (29.4%)
8:22+,ATo+,KTo+,A2s+,K5s+,QTs+,JTs,T9s,98s
We could probably play any two cards most of the time if we wanted to and we wouldn't have to have that wide of a preflop bluff range to do so.
value+bluffs when bluffs equal value
1:100%
2:100%
3:100%
4:77.6%
5:70.2%
6:64.2%
7:58.8%
8:39.6%
However, this doesn't quite consider how we might counter light 3betting and as a result it becomes more intricate to analyze and so we're better off probably playing a little bit tighter.
When our opponents bet we can 3bet as well. In general, if our opponents fold often enough we can 3bet any two, if they fold or call we want to have the bottom end of our calling range (or just slightly worse) in adddition to our strongest hands. If they tend to call widely we could 3bet for thin value with suited broadway strong aces and mid pair or better.
With one opponent, when we get to the river after 3 streets of large betting we need to have trips, two pair, straights and flushes if we fold such that we force our opponent to break even on bluffs on each street. But we should be calling with most pairs and most draws and even backdoor draws on certain flops, then we need to improve to a strong pair or a pair with a draw or top pair or better and then we need to have the big hands by the river. We can probably be a little bit looser than this because our opponent should bluff more on the flop and turn than on the river. With smaller betting overpair and top pair is probably good enough to call.
The above is all solid poker fundamentals. There are two more things to consider, bluff catching vs bluff frequency.
If we arrive on the river and we have the nuts or a total bluff, we want to bluff with a frequency that will cause our opponent to break even on bluff catches. If we were to bluff any more than this, our opponent should always call and profit off doing so. If we were to bluff less than this, our opponent would never call.
Conversely, our opponent should call such that he forces our bluff to break even. If he were to call more than this we should never bluff and if he folds more than this we should always bluff.
So if we bet the pot our opponent is getting 2 to 1 on his calls. If he bluff catches he can call twice and lose and be right on the 3rd and break even. So we should make him right exactly 1/3 and we should bet with a bluff 33% of the time and with value 66% of the time.
If we bet half the pot our opponent is getting 3 to 1, we should make him right exactly 1/4 times or bluff 25% of the time, value 75% of the time.
If we bet 10 times the pot our opponent, we should bluff 10/2.
We should never bluff more than half the time unless we know our opponent folds more than he should.
Our opponent should call a pot sized bet 50% of the time, a 1/2 pot sized bet 2/3rds of the time, a 2x pot bet 1/3rd of the time a 10x pot bet 1/11th of the time, a 1/10th pot sized bet 10/11 of the time. If our opponents call less often we can profitably bluff with any two and should find ways to enter this situation more often if possible. If our opponents call more often, we should try to eliminate hands that will end up only being bluffs and we should avoid bluffing.
This is how great poker is played, by working out the perfect strategy, determining how strategy changes as frequencies are higher or lower, and knowing what it looks like so when we see an opponent call down with only a pair we know he calls one or more streets too often and we can bluff less against him and value bet more. Our profit comes from mistakes by opponents.
TOURNAMENT POKER
Tournament poker is a little bit different. Accumulating 100% of the chips does not yield 100% of the prize pool but more like 20% of the prize pool. According to some poker theorists this means that the chips we stand to win are not worth the chips we risk losing. I think the opposite is true to the degree by which you sufficiently manage to reduce your chip varience to where you aren't at risk of ruin or elimination.
https://forexboat.com/wp-content/uploads/2015/03/Slide2-1024x576.png
We should take on as much risk as we can without reducing our edge or unnecessarily increasing our volatility. Eventually, we run out of options without taking risk and accumulating chips with no risk of ruin becomes impossible. Knowing this, there is some logic in seeking excess risk even with a negative return with the idea being that when we survive we will gain the ability to accumulate more chips for longer that will hopefully pay for the cost of the unnecessary risk when we don't survive. The chips we are able to accumulate following a double up are worth more than the chips we risk, meaning that with 60 big blinds we can accumulate chips safely at a faster rate with less risk than the alternative of not taking that risk so that it probably is worth more. A skilled player in the right structure can parlay a well timed double up into never having to be all in for the rest of the tournament! Conversely, early on in the tournament, a skilled player can parlay an increased chance of survival into significantly more chips without ever being all in and continue to grow until the blinds become say 20% of the starting stack or more. Survival is clearly super valuable early on, but when we get too short stacked the remainder of the tournament we will resort to more of a luckfest if we don't double up and if we do we can then make small constant, continuous pressure to accumulate chips. Therefore, making a just slightly a little bit too reckless bluffs and shoves and all in calls to stay above certain levels knowing that if we get caught we still have a decent chance of doubling up and once we do we will be hard to deny a final table may actually be the best strategy. It's hard to know for sure as under a certain amount of big blinds I actually think being tighter than 99% of tournament pros not named Phil Hellmuth suggest is actually correct. The chances of tripling up go up and although a top skilled player's EV increases from 40 big blinds to 80 big blinds and higher there's a certain spot as a short stack where you have no leverage and so going from 8 big blinds to 16 doesn't do you much good, but going from 6 big blinds to 4 actually does because you now have a larger side pot and leverage of opponents stack to push other players out with a chance to more than triple up with a big favorite to win if you are patient enough.Sit a pro in with 20 big blinds and he might be able to have a decent win rate. Stick one in with 10 big blinds and antes and way more hands become way more profitable. To some players this means they can't pass up any opportunity to profit but I say they should pass up more because they will get even more profitable opportunity if they don't risk elimination on only a slightly profitable shove like 98s or K6 or something.
Let's look at the kelly criterion (risk management) based strategy for accumulating chips as our stack declines and we have to creatively come up with new ways to maintain an edge without variance.
No Ante:
Above 150 Bbs you can
raise 3BBs and 2/3rds pot bet 3 streets of value
100-150Bbs raise 3BBs
and pot bet 2 streets of value or 3.5BBs 50% pot 3 streets of value
60-100BBs raise 3BBs
and 2/3rds pot bet 2 streets of value OR 2BB 50% pot 3 streets of
value
40-60BBs raise 2BBs and
2/3rds pot bet 2 streets of value Or 40% pot 3 streets
30-40BBs raise 2BBs and
½ pot bet 2 streets of value. OR 30% pot 3 streets of value
20-30BBs raise 2BBs and
40% pot bet 2 streets of value. Or 20% pot 3 streets
Antes:
80-150BBs 3bet 6BBs+2 streets of value half pot.
50-80BBs minraise+3 streets of value 55% pot down to 40%
~50BBs 3bet 2.75, Cbet steal attempt
25-50BBs minraise+2 streets of value 70% pot down to 40%
25BBs-50BBs minraise+ overbet one street 2.5x pot down to 1x pot. or check back and minraise 1 street 1.25pot down to .50 pot.
15-25BBs minraise+2 streets 40% pot down to 20% pot
12.5BBs-15BBs minraise min bet 3 streets
10BBs-12.5BBs minraise min bet 2 streets
7-10BBs minraise min bet 1 street
7-15BBs minraise steal muck if wrong
MOVES given # of blinds:
75-50 3 bet bluff and continuation bet
35-50 bluff raise flop (no ante) after a 3BB call
35-50 3bet bluff with greater discretion and more selective 3betting
30-50 bluff raise flop (ante) after a 2BB call.
25-45 minraise flop & Cbet bluffs (ante)
25-40 check behind your backdoor draws and gutshot on the flops and bluff raise turn with low pair and some kind of draw by the turn as a semibluff. You will also be checking for pot control most of the time with good hands anyways.
20-30 Float flop wide to bluff after a minraise preflop
15-25 check back flop and float turn wider rather than bluff raise and bluff some rivers when checked to
12-25 minraise+really selective cbet bluffs. You won't be Cbetting often and when you do Cbet you will often check back the turn instead, but you can occasionally Cbet bluff if you are really selective about it.
7-30BB minraise steal attempt with no plans to continue
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[Ideally you never have to enter the wildly volatile strategy that risks your entire chips or even close to it but realistically you will. As such, at some stage that is way before it becomes a shovefest I believe it's acceptable to accept a wildly voltile strategy willing to risk it all once and go back to more profitable, lower risk chip accumulation. It's better to risk it all once while you have a lot of chips and can gain a lot of chips for a lot more levels of increasing blinds than have to get it all in 3 times with the best hand. A 60% favorite only has a 21.6% chance of advancing after 3 all ins]. If during volatile play you get knee capped or you decide you're better off waiting it out until conditions change you have a little bit of wiggle room left and looking to triple up rather than double up and you are more looking to protect survival with only the best cards you can wait for. Knowing the best situation you can wait for given your edge and the blind structure, I would be willing to risk it all with a hand that was As strong as I could expect 50% of the time to see at least once given the hands left. I would ideally want to adjust this for flops turns and rivers as well as preflop but you can only do what you can do.
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Let's discuss the moves.
In order to bluff you have to identify someone that can fold. When that's the case you want hands just at the bottom or just below the hands that have value to call so that you either aren't giving up that much, or you aren't giving up anything at all in exchange for using them to bluff... Preflop that's probably going to be any ace, King6-King 9, Queen4-Queen 8, JT,JT suited 2 and 3 gap connectors, low suited connectors, suited K2-K5 and Q2-Q5 and J5-J8 and unsuited connectors and unsuited mid and high gappers (J9,T8,97,86) plus maybe weak broadway hands. That does NOT mean by any means to ALWAYS use these hands to bluff. But when you have these hands it's better to use them to bluff than others and you probably don't have to worry about missed opportunity as there will be plenty of opportunity to come.
So you want to look for a loose preflop raiser capable of folding to aggression and either passive or straight forward after the flop in case you get caught so you at least have some ways to win if/when you decide to.
After the flop if you are going to bluff raise you want to remove all the hands that are capable of calling except maybe the bottom end of them. That is, bottom pair, lowe pocket pair, gutshot draws. And then you are going to look for the high end of hands that you have decided to fold. Backdoor straight & flush draws, ace high with a backdoor gutshot, backdoor 3 to straight draws backdoor straight flush draws with 1 gap (45 with a 7 and the suit to a flush) and other nuances.
This is your "trickery" range. Your "trickery range" is what you are willing to use to float or bluff with IF the conditions are right but you may prefer to fold some or most of the time. Your trickery range is where you either bluff raise or call to represent something and bluff raise some percentage of turns given some specific action and specific cards. You are going to take a free card on most good draws while bluffing most longshot draws and improved to one pair and you are going to give up some cards and you are going to bluff on some scare cards as well.
You might sometimes float more widely if the opponent always Cbets and folds too often on the turn or if he never check raises the turn and has some combination of checking a lot, check/folding a high % of the time he checks, betting the flop too widely or having too many weak hands preflop that he has to get rid of somewhere after the flop.
Everything else is knowing your situation, knowing the flop, knowing your opponent, knowing what to look for and then just taking advantage of it. You should know what percentages opponents should call you and then whether they call more or less and as a result what that might look like on the flop or turn, and what your action might be on each street as a result. You should know your percentages as well
You should know the structure and identify soft spots where the ante is larger relative to the small blind such as 1/3rd the small blind and also where large increases in the amount to steal is and you should be aware of where the final table is. If the final table occurs with an average stack of 15 big blinds, you simply take the number of chips in play divided by 9 for the average chips at the final table and then divide it by 15 to get the big blind you expect. You can figure out how many you have left by paying the blinds and antes plus or minus a low varience skill edge and see where that gets you and at what point you may have to take on more risk if you fall below a certain amount of chips. You may have to work a little harder and take a little more risk at risk of volatility/survival in order to maintain enough chips if the structure is fast enough. but figure this stuff out.
You also want to know aside from calling and bluffing frequencies that you should raise with the top and bottom parts of your range and check your medium strength hand but you should occasionally vary your play. Maybe 75% of the time you bet with the value range plus some percentage of bluffs and 25% you check/call those hands (or check/fold the bluffs), you may need to check raise bluff and check raise value bet some too which complicates things a little but as long as you have a general idea of when and why to do this, that's okay. If your opponent calls too widely you don't want to bluff but you instead increase your value range.
There's probably a lot of other details to know such as adjusting to tournament structure, adjusting to the bubble, 4betting vs 3betting range, 4bet bluffing, etc and in the money considerations but I'm a little unconventional about that stuff. I like to flat call more and manage the risk even with big hands so I end up trapping but I'm really not trying to as much as I'm trying to control pot size. If you constantly do this and opponents don't see you show down a big hand and you 3bet or 4bet for the first time in forever, they're going to assume you have a good hand if they're a thinking player capable of folding and so you probably can get away with a bluff, but at what cost? I could see an argument for playing this way just before the antes or just after or in a really big tournament where you know there's a lot of poker to be played and a fairly fast structure. Maybe some percentage of the time you get knocked out but when you don't you get a lot of chips and if you show a willingness to risk it all your opponents might not 3bet you anymore unless they want action or are willing to take risk themselves. Either way, that is an informational advantage and you gain fear equity that allows you to increase your rate of stealing. So I have seen players fold 30 hands in a row that then start raising every hand and then when they get 3bet they 4bet shove with 26off and they may even do it again. Sure, it's probably an unprofitable play but if you induce enough weak/tight play and a little bit wider range willing to risk it all (you'll get paid off when you have the absolute nuts) it's worth the cost of one hand, particularly if you can get such a big stack that risk no longer is a concern and you can play a pretty much max EV strategy until your stack reduces in size or others catch up.
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