Pure Theory Question

[reubenf]

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The question states that your opponent raised you in the dark. You are only assuming its two random cards.

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What does "in the dark" mean to you?

[Jacob_Gilliam]

Unknown

[reubenf]

I'm pretty sure J6 is better than Q7 because it's closer to 50% equity. I think there are more hands that J6 calls with than Q7 folds with.

[Benman]

Need further clarification. If he refuses my offer, do I have to call with all hands that "are favored", meaning over two random cards, or can I fold?

[Top_Set]

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You are playing heads up no limit holdem. No ante. No blinds. Your opponent moves in $1000 in the dark. This is the one and only hand. You will call him with all hands that are favored. Except that he now makes an offer to you. He will expose his cards if you pay him something. You get to look at your cards before you make him an offer.

Hopefully you see that it is worth giving him something with any hand exept AA or 32. My question is what two cards would be in your hand that would pay the most for his exposure.

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I don't need to look at my cards. I will simply reply, "My, what a sporting and generous offer." Then, after PAYING him this compliment, I will demand that he turn his cards over.

[Jacob_Gilliam]

This strategy works even better when just by coincedence you also happen to have a gun on you.

[David Sklansky]

The amount you should pay is the probability that seeing his cards will make you switch strategies, times the average EV gain (or savings) that you get from such a switch. I don't know the answer but common sense says that K2 offsuit will be way up there.

[iversonian]

My answer is: the hand whose sum of EV-gains when his decision (fold/call) changes is the greatest.

Say, J7o. Suppose that is the median hand (?) and a folding hand against an unknown random hand. The difference in EV from folding (EV=0) and calling when the opponent turns out to have a weaker hand than J7o, is gained by the information. When it turns out he has a better hand than J7o, that information did us no good, we would have folded anyway.

I think the answer is found by finding the hand for which, summing the abs(EV) versus opponent's hand for which decision changes x the % of time opponent will have said hand, is the maximum. If it a hand that would call with, it would be the EV against opp hands that beat you x % he has that hand. If it's one you'd fold, SUM EV against hands you beat x % he has hand.

So which one is it? Dunno. But I think it's probably a hand like K2. Pretty close to even against a random hand It's a slight favorite, as most hands have 2 cards in between K-2. It dominates only a few hands, and when it's dominated, it's drawing slimmer than most (unlike say 98, which can make straights and has overcards to many pairs). Because the hand characterized by its small edge against the many hands that are slightly worse and the large, um, un-edge against the better hands, my vote is for K2o. Sorry, no numbers.

Geez, I just checked the thread and David posted his K2o comment. Gonna post this anyway.

[M.B.E.]

When you have K2, you can profitably pay up to $114.34 to see your opponent's cards. The information would be worth about $24 more if your cards are J7, by Pzhon's calculations.

[Slade]

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Hopefully you see that it is worth giving him something with any hand exept AA or 32.

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32o would be worth about 1.133 cents.