SeattleJake
01-26-2005, 07:08 PM
I'm relatively new to poker, and even newer to this forum, but I've been finding so much useful information, and learning a lot from it, that I thought it was time to contribute. I suppose I should hang out here a bit longer before posting something like this, but WTH here goes...
Reconciling the apparent contradiction between Morton's Theorem and The Fundamental Theorem of Poker:
The contradiction comes from the existence of a range of pot sizes in multi-way action, where Morton's Theorem implies that you may want an opponent to fold correctly instead of calling incorrectly, even though Sklansky's Fundamental Theorem states that you lose when an opponent acts correctly and gain when an opponent acts incorrectly. This is usually justified by the caveat that the Fundamental Theorem does not apply to many multi-way pots.
Ideally, we would like to take both Sklansky's Fundamental Theorem and Morton's Theorem as being universally correct, without relying on this "exception to the rule" justification. I submit that to reconcile the apparent contradiction, the correct action for the opponent in question must be neither to fold nor to call.
In Morton's example, you hold AdKc and the flop is Ks9h3h. You believe opponent A to have AhTh (nut flush draw with 9 outs) and opponent B to have Qc9c (second pair with 4 outs). The turn card comes 6d. When you bet the turn, player A is getting the correct pot odds to call. When player A calls, player B must decide whether to call or not.
Player B's expectation when calling, is 4/46 * (P+2) - 42/46 * (1). Setting this equal to 0, gives 8.5 big bets as the threshold at which it would be correct for Player B to call.
Your expectation though, is 33/46 * (P+3) when they call, and 37/46 * (P+2) when they fold. Setting these equal to each other, gives 6.25 big bets as the threshold at which you would want Player B to fold.
This range of 6.25 to 8.5 big bets is what seems to contradict the Fundamental Theorem, since you would want Player B to fold, even though it would seem correct for them to do so as well, which would indicate that you would be losing something.
I think Player B should bluff-raise here.
Player B's expectation, would then be 4/46 * (P+6) when you call, but 37/46 * (P+5) when you fold. The ratio of these two equations, gives about 1 in 10 as the chance that you would have to fold to make this a proper play for Player B.
Your expectation, if you have misread your opponent's hand, is 3/46 * (P+5) - 41/46 * (1). Setting this equal to 0, gives 8.7 big bets as the threshold at which it would be correct for you to call, which is beyond the range in question.
You may argue that you don't have to be right too often to make it a profitable call, but I think the likelihood of a 1 in 10 fold is probably on the mark, facing a re-raise on the turn with only top pair + top kicker.
With this corollary to Morton's Theorem indicating that Player B should raise, and you wanting Player B to fold, The Fundamental Theorem is not violated, and Morton's Theorem stands as is.
I'm sure part of this is correct, and I'm sure part of it is not, but I'm interested in your thoughts so I can either make this raise or not make this mistake in my own games.
Reconciling the apparent contradiction between Morton's Theorem and The Fundamental Theorem of Poker:
The contradiction comes from the existence of a range of pot sizes in multi-way action, where Morton's Theorem implies that you may want an opponent to fold correctly instead of calling incorrectly, even though Sklansky's Fundamental Theorem states that you lose when an opponent acts correctly and gain when an opponent acts incorrectly. This is usually justified by the caveat that the Fundamental Theorem does not apply to many multi-way pots.
Ideally, we would like to take both Sklansky's Fundamental Theorem and Morton's Theorem as being universally correct, without relying on this "exception to the rule" justification. I submit that to reconcile the apparent contradiction, the correct action for the opponent in question must be neither to fold nor to call.
In Morton's example, you hold AdKc and the flop is Ks9h3h. You believe opponent A to have AhTh (nut flush draw with 9 outs) and opponent B to have Qc9c (second pair with 4 outs). The turn card comes 6d. When you bet the turn, player A is getting the correct pot odds to call. When player A calls, player B must decide whether to call or not.
Player B's expectation when calling, is 4/46 * (P+2) - 42/46 * (1). Setting this equal to 0, gives 8.5 big bets as the threshold at which it would be correct for Player B to call.
Your expectation though, is 33/46 * (P+3) when they call, and 37/46 * (P+2) when they fold. Setting these equal to each other, gives 6.25 big bets as the threshold at which you would want Player B to fold.
This range of 6.25 to 8.5 big bets is what seems to contradict the Fundamental Theorem, since you would want Player B to fold, even though it would seem correct for them to do so as well, which would indicate that you would be losing something.
I think Player B should bluff-raise here.
Player B's expectation, would then be 4/46 * (P+6) when you call, but 37/46 * (P+5) when you fold. The ratio of these two equations, gives about 1 in 10 as the chance that you would have to fold to make this a proper play for Player B.
Your expectation, if you have misread your opponent's hand, is 3/46 * (P+5) - 41/46 * (1). Setting this equal to 0, gives 8.7 big bets as the threshold at which it would be correct for you to call, which is beyond the range in question.
You may argue that you don't have to be right too often to make it a profitable call, but I think the likelihood of a 1 in 10 fold is probably on the mark, facing a re-raise on the turn with only top pair + top kicker.
With this corollary to Morton's Theorem indicating that Player B should raise, and you wanting Player B to fold, The Fundamental Theorem is not violated, and Morton's Theorem stands as is.
I'm sure part of this is correct, and I'm sure part of it is not, but I'm interested in your thoughts so I can either make this raise or not make this mistake in my own games.