The post-flop strategy when playing heads-up is well researched and is constantly being refined, but the transition to multiway pots for many becomes a leap into the unknown. Factors that influence game dynamics work very differently in multi-player pots than they do in heads-up play. Matt Hunt points out in his course that “post-flop in multiway pots is more similar to pre-flop in multiway pots than post-flop in heads-up play.” Indeed, many of the strategies that apply to pre-flop decision making can be transferred to post-flop, since they are more specific not to pre-flop, but to playing against several opponents.
The purpose of this article is to lay the theoretical foundations for further development of your multiway pot skills.
1) Nash equilibrium problem
Before moving on to the nuances, it is necessary to address a fundamental issue: the use of equilibrium strategies in multiway pots. The head-to-head Nash equilibrium provides us with a break-even strategy that begins to make a profit when our opponent deviates from it. However, in multiway pots the situation changes – there is no unexploitable break-even strategy for them. We are no longer guaranteed EV.
When one of the players in a multiway pot makes a mistake, the EV he lost is not distributed among the other participants in the hand, as an inexperienced mathematician might assume. In many cases, one player's mistake lowers the expectation of another, raising the expectation of a third! And there is no strategy that is immune to this problem.
In this case, can we say that solver solutions for multiway pots have at least some value? According to Noam Brown, a game theory researcher and creator of the Libratus and Pluribus bots, the methods of finding equilibrium for heads-up games can be effectively used in 6-max, provided that the individual participants do not cooperate with each other. Indirect evidence of the presence of a solution for playing in multiway pots can be considered the fact that solvers using very different algorithms come to almost the same conclusions.
2) Division of responsibility for defense
To calculate how widely one must defend against aggression in order to prevent an opponent from profiting from any bluff, poker uses the Minimum Defense Frequency (MDF) indicator. It is calculated using the formula “one minus alpha”, where α is the percentage of folds, with an increase in which any bluff becomes profitable.
Let's see what happens in a multiway pot when we bet a full pot-size bluff. To make a profit, he must work more than half the time. When playing one-on-one, your opponent should be defending at least half of their range. In a multiway pot, the responsibility for protection is divided between all participants in the hand. Each of them, one might say, is responsible only for his own area – the main thing is that they do not throw everything out more often than half the time. The probability of winning the pot immediately for the aggressor is calculated by the formula:
Total fold% = Player 1's fold% × Player 2's fold% × Player 3's fold% and so on. The average fold rate of each player in this case is calculated as the n root (where n = number of defenders) of α:
What does this mean in practice? The player closing the action bears more responsibility for protecting the pot than the players before him, since after calling there is no risk of being knocked out of the pot by a raise from someone else. We have summarized the average percentage of distributing responsibility for protecting the pot depending on the size of the bet:
When your opponent bets 10% of the pot in a heads-up game, he forces you to defend 91% of your range. However, when such a bet is made among eight people, the minimum defense frequency for each of them drops to 26% on average! This is a huge difference. Let's take the example to the point of absurdity: when the aggressor bets 1% of the pot, in a heads-up game you need to defend 99% of the range, and when there are eight defenders, only 44%.
The risk/reward ratio of pure bluffs in multiway pots is simply terrible. Your opponents have every right to defend themselves tightly even against very small bets, while preventing you from profitably bluffing. The pot odds do not change, and a hand with sufficient EV is free to call.
3) Tight is right
We showed above that in multiway pots you can defend less often without being exploited much. This leads to a simple but important conclusion:
Tight is rightt!
In multiway pots, we do not see anywhere near the tenacity of protection characteristic of one-on-one pots. The thresholds for minimum hand strength to continue against all sizes are becoming much tighter. Therefore, the betting range becomes much stronger. The aggressor is required to have a narrow drawing range and stronger bluffs. Without a strong draw, you don't have to bluff at all.
4) Range bet ban
The practice of small bets with the entire range on a favorable texture, common in heads-up games, does not work as well in multiway pots. Range bets force your opponent to overfold on a bad texture, giving you EV, but in multiway pots, people share the responsibility of defense among themselves, and their personal overfolds do not give you much benefit.
The simplest adjustment to multiway pots for the preflop aggressor: refuse range bets, give up with garbage, and draw very tight. Check often with medium-strength hands to get them to showdown.
5) The importance of potentially having the nuts
Say you are playing on GGPoker, and the flop is . The hand has poor nut potential as it makes a weak flush, while has strong nut potential. In multiway situations where stackoff ranges become very tight, the nut potential is vital.
When considering a semi-bluff in a multiway pot, take a close look at your outs: do they give you the nuts or not? Maybe the cards that make your draw also make stronger combinations?
The frequency of bets in multiway pots has a strong correlation with the nut advantage. A player who has a range advantage but no polarity advantage on the nuts should generally play passively (unless the SPR is very low).
Think about what the button's range bet against two blinds on a board like . Okay, you have overpairs, but your opponents (combined) have more sets, two pairs, and straights. Your overpairs will generate much less value against marginal hands and will fare much worse against check-raises.
6) The value of dominance and the danger of being dominated increases
The situation is somewhat reminiscent of heads-up in deep stacks. Tighter stackoff ranges require stronger hands and draws for all-ins. Static bluff catchers, average hands without chances for improvement, and even borderline top pairs suddenly lose their attractiveness. The value of a hand becomes more dependent on whether it can make the nuts.
Hands that retain equity well in multiway pots are suited connectors and gappers, high flush draws that can make a nut flush, and so on.
7) Use of small sizings
We have already said that you can defend tightly in multiway pots. Because of this, an aggressor using large sizings can quietly outplay his hand. Pay close attention to whether you'll still be an equity favorite if you get called.
NL500: BTN raises, BB calls. Flop . The button in this spot typically overbet 125%. The BB is forced to overfold slightly, and when he calls, the equity of the button's hands becomes:
The same situation, but both players in the blinds call pre-flop. Against an overbet, each of them should protect about 25% of the range (not 44% as in heads-up play). Let's say one of them calls. Button equity vs. top 25% of blind range:
Please note: we managed to make the opponent a favorite against ours and with just one bet on the flop!
For this reason, a smart strategy for multiway pots is to reduce the sizing. Large bets will isolate you against the top of your defensive range.
In some cases, an overbet turns out to be correct even in multiway pots, but this requires special scenarios in which you have a huge advantage in the nuts. They happen much less frequently than in one-on-one games.
8) The value of position increases
Position advantage is the advantage in awareness that the actions of opponents before us give us, as well as the right to close the action and move on to the next street. In multiway pots, the value of a position increases noticeably – the more participants in the hand, the more information the player in position has.
This principle can be demonstrated by comparing the button's cold-calling range with the small blind's cold-calling range. As a rule, the button can open wider, despite the fact that there are two players behind him rather than one, and the pot odds are slightly worse.
Let's take deep stacks, 200bb, to further highlight this difference. The cutoff raises 2.5bb.
BTN vs CO RFI
SB vs CO RFI
The button defends 8% wider than the small blind! It's not just about the position on the raiser, but also the potential to be in position in a multiway pot. The small blind has better pot odds and is less likely to get squeezed, but due to his poor position, he is forced to play much more carefully.
Yes, being out of position is obviously bad. What about being in the middle? This is also quite unpleasant. A common mistake is to defend the big blind more widely after the small blind raises, under the pretext that our pot odds have improved. The bank's chances have, of course, improved, but the ability to realize equity has dropped sharply.
9) The effect of blockers increases
The importance of blockers in multiway pots increases as blockers overlap with more ranges and their effect is amplified.
NL500 6-max cash, 200 bb. UTG raises: how often will he take the pot pre-flop?
– in the GTO world on average – 50.9%
– with – 48.3%
– with AKo – 55.6%
Quite a significant difference between and ! block a lot of hands that call or raise against UTG, Only folds block. The same concept works in post-flop multiway pots. Blocking the nuts becomes more important, and having anti-blockers hurts us more than heads-up.
10) Capped ranges are harder to punish
The capped range does not contain the strongest hands. When we check too many weak hands in a heads-up game and don't slowplay enough monsters, our range becomes capped and our opponent can punish us by ramping up his aggression. In a multiway pot, capped range is no longer a problem due to the collective responsibility for protecting the pot.
NL500, 100 bb, 6-max cash. UTG raises 2bb. BB protection range:
Similarly, but before the BB, the small blind entered the pot:
One on one against UTG we have to call with AKo, and AQs. This is not fear of an opponent, but traps, without which it is difficult for our range to tolerate post-flop aggression.
When the small blind appears in the pot, we can squeeze harder with the top of the range. This is partly due to the fact that in a multiway pot we no longer need traps.
In general, the play in multiway pots becomes more fair. Betting and raising ranges are more linear both pre-flop and post-flop. Checking ranges in multiway pots are usually weaker and more nut-free than in heads-up games, but when there are multiple defenders, your capped range is collectively protected and cannot be bullied with impunity. All this leads to the fact that after massive checks, the ranges of players on the river become completely capped and weak, so many base researchers suggest aggressively bluffing in multiway pots on the river as an exploit.
– Collective responsibility when defending allows for tighter defense
– Pure bluffs and range bets are not used
– Reduced sizings are widely used to maintain an advantage in equity after calling
– Stronger value hands and bluffs are needed to bet
– Dominance and nut potential become more important
– The value of blockers increases as they affect multiple ranges at the same time
– Attacking capped ranges becomes almost impossible
– Betting ranges become more linear, multiple checks are usually weak
– GTO solution does not guarantee break-even.