Head Up Theory Question

[diddle]

How is it conceivable to fold 999,999?

How?

I repeat, HOW?

You realize it is akin to folding quads to a straight flush for one bet in a 100 BB pot in a limit game?

You never fold 999,999 in this question. I wish DS would write this down in the original post.

[M.B.E.]

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You realize it is akin to folding quads to a straight flush for one bet in a 100 BB pot in a limit game?

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If, given the action so far, the probability your opponent has the straight flush is greater than 100/101, then of course you'd fold quads.

[donkey69]

Ok. Assume that there are only 5 numbers, 1-5. Please illustrate how my strategy can be beaten. What decision rules would you use?

The fact that you dont make money is not of significance. In any game breaking even against expert players is in no way a bad result.

[diddle]

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You realize it is akin to folding quads to a straight flush for one bet in a 100 BB pot in a limit game?

[/ QUOTE ] If, given the action so far, the probability your opponent has the straight flush is greater than 100/101, then of course you'd fold quads.

[/ QUOTE ]

PLEASE show me any course of action in which you would know, greater than 100/101, that your expert opponent has a straight flush.

I will pay you $100,000 for this info.

[FishAndChips]

I have to agree with diddle here. You won't know that 999,999 is beat until you are raised a certain number of times; however, the pot odds by then will make it hard to fold. If you anticipate having to fold at any point during the hand to one of your opponent's reraises, just don't raise yourself-- simply call. Then you at least get a showdown, and can not be bluffed out of a large pot.

It seems to me that you need to think multiple bets ahead. With the fold equity so low in a multibet pot in this game, folding after one of your raises can't be correct. If you foresee having to fold after the next raise, just call.

[M.B.E.]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
You realize it is akin to folding quads to a straight flush for one bet in a 100 BB pot in a limit game?

[/ QUOTE ] If, given the action so far, the probability your opponent has the straight flush is greater than 100/101, then of course you'd fold quads.

[/ QUOTE ]

PLEASE show me any course of action in which you would know, greater than 100/101, that your expert opponent has a straight flush.

I will pay you $100,000 for this info.

[/ QUOTE ]
Against a real-life opponent you would almost never be in a situation where you could put your opponent on a specific hand with over 99% probability. I've played a lot of limit holdem; I've never folded quads on the river for one more bet and I'm pretty sure I never will.

But when we're talking about the game-theoretically optimal strategy in a heads-up game, it is conceivable that you would see some folds that appeared very odd.

[diddle]

just because a strategy is game theoretic optimal doesn't mean the strategy has to have stupid crazy [censored] in it like folding the 2nd nuts for one more bet in a big pot in limit poker

in this thread, people seem to be posting nonsense and then using big words like "game theory" "unexploitable" "optimal" "Nash rebluffing equilibrium douching" without understanding the concepts.

[reubenf]

[ QUOTE ]
just because a strategy is game theoretic optimal doesn't mean the strategy has to have stupid crazy [censored] in it like folding the 2nd nuts for one more bet in a big pot in limit poker

in this thread, people seem to be posting nonsense and then using big words like "game theory" "unexploitable" "optimal" "Nash rebluffing equilibrium douching" without understanding the concepts.

[/ QUOTE ]

Are you claiming to understand Nash rebluffing equilibrium douching better than I do?

[M.B.E.]

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If you anticipate having to fold at any point during the hand to one of your opponent's reraises, just don't raise yourself-- simply call. Then you at least get a showdown, and can not be bluffed out of a large pot.

[/ QUOTE ]
This argument isn't particularly persuasive because you could conceivably be costing yourself by not raising (even though you'd sometimes fold to a reraise).

Suppose that at a certain point in a certain game your opponent raises so that the pot is $95 and you could either fold, call $1, or raise $1 more. If you know that your opponent is playing an optimal strategy, you can put your opponent on a range of hands, and he should be bluffing with probability 1/96. It might be the case that you are holding the unique second-nuts, and if you raise, your opponent will call with the third-nuts, fourth-nuts, and fifth-nuts (each of which is an equally likely holding for him, at this point, as the nuts). But your opponent won't reraise for value again without the nuts (if you raise and he does reraise, there would then be a 1/100 probability he is bluffing).

If you just call, you'd be giving up EV. You need to raise for value because your opponent will call your raise with a worse hand three times as often as he will reraise with a better hand. So the question is, do you

(a) raise and always call a reraise;

(b) raise and always fold to a reraise; or

(c) raise and sometimes call, sometimes fold to a reraise.

The answer here is (c). Read the section "Using Game Theory to Call Possible Bluffs" in chapter 19 of TOP. In the scenario I've just described, your hand, the second-nuts, can only beat a bluff. If your strategy is to always call the reraise, your opponent could exploit it by never bluffing -- then you would be calling all the time with a certain loser. Of course since the pot is so big, you still have to call the vast majority of the time or else your opponent could exploit your strategy by bluffing more. When your opponent bluffs, he is risking $2 to win $97. Therefore your optimal mixed strategy at the end is to call 97/99 of the time and fold 2/99 of the time.

[M.B.E.]

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just because a strategy is game theoretic optimal doesn't mean the strategy has to have stupid crazy [censored] in it like folding the 2nd nuts for one more bet in a big pot in limit poker

[/ QUOTE ]
I never said the strategy has to have stupid crazy [censored] in it. In fact I said that it probably does not.