What if I told you one of the most famous theories in poker could be partly wrong? The Fundamental Theory of Poker by David Slansky roughly states that when your opponents make mistakes you win and when they play correctly you lose. With that logic, if opponents in low stakes games continue to call with weak hands and chase unlikely draws when you have a strong hand like top pair with best kicker and they don't have the correct power dots to do so. this seems advantageous for you. However, it appears that these opponents frequently manage to complete their draws which suggests an issue.
You'll often hear players expressing frustration about the unbeatable nature of low limit games. They argue that the massive number of callers is hard to counter, making it difficult to safeguard your strong hand once the pot becomes substantial which is kind of true in one sense. The large number of calling stations combined with a few early raises leads to pots in these games growing much larger compared to the initial bets.
This has the effect of reducing the magnitude of the error made by each individual caller at each individual decision. This fact led to the birth of Morton's Poker Theorem, which is quite interesting and controversial. Morton's theorem states that in multi-way pots, a player's profit may be maximized by an opponent making a correct decision.
In other words, when you have the strongest hand and are facing two or more opponents with additional cards to be dealt, it's often more profitable if some of them fold even if their decision to fold is correct and not a mistake. In essence, you would prefer your opponents to make the right fold as their misguided attempts to chase you will actually lead to long term losses for you. Now you might find this pretty surprising, but Morton tries his best to convince us with this example. Suppose in Limit Hold'em you hold Ace of Diamonds and King of Clubs, and the flop is King 9-3, two-tone, giving you top pair, best kicker. When the betting on the flop is complete, you have two opponents remaining, one of whom has the nut flush draw, say, Ace-10 of Hearts, giving him nine outs, and one of whom, you believe, holds second pair, random kicker, say, Queen 9, leaving you with all the remaining cards in the deck as your outs.
The turn card is an apparent blank, say the 6 of diamonds, and we'll say the pot size at this point is P expressed in big bets. After the player bets on the turn, opponent A who holds the flush draw is certain to call. Their decision is likely justified by the pot odds they're receiving, though this wouldn't hold true in a no-limit game due to reverse implied odds.
Once opponent A makes the call, opponent B is left with a choice between calling or folding. To determine the best option for opponent B, you will need to calculate the expected value for each scenario. This calculation takes into account the number of remaining cards that can improve opponent B's hand and the current pot size at the moment of their decision. It's important to note that in these considerations, all players are assumed to possess complete information about each other's cards. Opponent B doesn't win or lose anything by folding.
When calling, he wins the pot 4 out of 42 times and loses one big bet the remainder of the time. Setting these two expectations equal to each other and solving for P lets us determine the pot size at which he is indifferent to calling or folding which comes out to be 7.5 big bets. When the pot is larger than this, opponent B should continue otherwise it's in B's best interest to fold.
To figure out Which action on opponent B's part the player would prefer, calculate the player's expectation the same way. The player's expectation depends, in each case, on the size of the pot, in other words, the pot odds B is getting when considering his call. Setting these two equal, we calculate the pot size P where the player is indifferent whether B calls or folds, which comes out to be 5.25 big bets. When the pot is smaller than this, the player profits when opponent B is chasing, but when the pot is larger than this, the player's expectation is higher when B folds instead of chasing.
In this case, there is a range of pot sizes where it's correct for B to fold and you make more money when he does so. This range of pot sizes marked with an X is where the player wants his opponent to fold correctly, known as the paradoxical region. Our partners VIPgrinders.com is hosting an exclusive $15,000 free roll for the WPT World Championship which will likely be the biggest live tournament ever held and there is no buy-in required. Check the video description.
or the pin comment to know how to participate. This situation appears to contradict the fundamental theory of poker which arises because the game is not limited to a head-to-head scenario but involves multiple players. While David Slansky mentioned that his theory does not hold true in specific multi-way scenarios, it might be more accurate to assert that it generally does not apply in multi-way situations. In the given example, when opponent B makes a call within this paradoxical region, they are overpaying for their weaker draw.
However, you are no longer the sole beneficiary of this costly mistake. Opponent A now shares in the profit, specifically when A hits their flush draw. Compared to the case where you are heads up with player B, you still stand the risk of losing the whole pot, but you are no longer getting 100% of the compensation from B's loose calls due to opponent A's involvement.
These type of situations are common in Hold'em occurring both on the flop and turn. The presence of these immediate range of pot sizes where you prefer some opponents to fold correctly explains the widely adopted poker strategy of reducing the number of players in the hand when you believe you have the best hand. Even players with incorrect draws end up costing you money because part of their wagers contribute to the stacks of other players who are drawing against you.
In most cases, when you flop a strong but vulnerable hand, the pot size tends to fall within this middle range where having some opponents fold is beneficial. Typically, the pot size is such that you'd prefer your opponents to fold even if they would be making the right decision. In loose games, the pot size often leans towards the larger size where you might hope they fold but due to the odds they have to call, their seemingly questionable calls becomes mathematically justified.
Here's another interesting observation. In the three-player scenario mentioned earlier, both you and opponent B experience losses when B makes incorrect calls. This implies that opponent A benefits from his call. Since poker is a zero-sum game, opponent A benefits even more from B's call than the actual size of B's mistake in calling.
Due to the decrease in your expected outcome caused by B's call, It logically follows that the collective results of all players involved must be positively impacted by B's call. In essence, if opponent A and B were to split their profits, it would seem like they were colluding against you. This is sometimes referred to as implicit collusion. One conclusion of Morton's theorem is that, in a loose hold'em game, the value of suited hands goes up because they are precisely the type of hands which will benefit from implicit collusion.
This sounds all good in theory, but the interpretation of this concept in practice is difficult. Perhaps what is needed is an additional theorem, the fundamental theorem of poker for multi-way pots. Let us know in the comments what you think.