Pure Theory Question

[pzhon]

JTo wins too much against a random hand to be worth paying as much as J7o.

JTo expects to win $105 against a random hand.

JTo win 67.54% against the 664 hands in the range of pairs up to 55 and lower nonpairs, ignoring the possibility of being a favorite over another JTo. Seeing the other hand lets JTo win $190.

JTo should be willing to pay only $190-$105 = $85.

[GFunk911]

David:
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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.

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Myself:
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Value of information = (EV vs all hands where hand is favorite * prob of opposing hand occurance) - max(EV vs random hand,0)

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Is there a way in which these two definitions differ, or was this hint simply you restating what numeroous posters have said, so that people will listen? They appear the same, and I get the same numbers.

Also did you see me at the WPT Championship ... I was the guy people kept referring to as "Tuan." ....time to slink back to 25NL

[felson]

How does Q2o fare? That was my guess.

[Rasputin]

Might I ask two questions of clarification?

When you say "this is the one and only hand" are you saying that if you end up folding he'll walk away from the game with just what you paid him? I assume that's what it means.

More importantly, did he look at his cards before he offered to show them to you for a price? The question doesn't specify either way so I assume not.

[pzhon]

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How does Q2o fare?

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I could compute it, but it doesn't do as well as Q3o, which doesn't do as well as Q4o. If hand A dominates hand B, both offsuit, and both are worse than 50% against a random hand, then hand A wins more after seeing the opponent's hand. That is because the hands that are underdogs to hand B correspond to hands that are underdogs to hand A by about the same amount, but there are extra hands that are underdogs to hand A. (If hand B is more connected than hand A, it may be a slightly greater favorite over undercards, but hand A is a favorite over many more hands.)

Q5o is a tiny favorite over a random hand, worth $2.40 when all-in preflop for a $2000 pot. Q4o values seeing the opponent's hand by at most $2.40 more than Q5o, $131, so that gives you an upper bound of $134 on the value for Q4o-Q2o.

[felson]

Duh. Thanks.

[bigmac366]

i havent read the other replies in this thread.

i read once that Q7s was break even against a random hand. i think it would be +EV to call with any hand better than Q7s.

[Rococo]

I haven't read any of the other responses but it seems obvious to me that the information would be most valuable if I had a mid pocket pair (77-99). I might be a 4 to 1 favorite against a lower pair, a big favorite against random undercards, a 4 to 1 dog to an overpair, a coin flip against two overcards, or a modest favorite against something like A5.

That's a big range.

[FishAndChips]

I have a quick question. Does the $1000 bet by your opponent put him all-in? If it doesn't, and both of your stacks are large in relation to the pot, you should pay to see his hand with almost ANY holding.

There is an example in Matt Matros's new book where he describes going to a BARGE2K event where Chris Ferguson gave a lecture. "Jesus" [img]/images/graemlins/smile.gif[/img] asked everyone what you would do in the following situation playing HU No Limit Hold 'em. Both you and your opponent have $50000 in front you, and the blinds of $1 and $2. Your opponent makes it $5 to go, but accidentally exposes his hand, revealing a wired pair of Aces. He then asked the audience what type of hands you should call with. It turns out that you should call with ANY holding in this situation because you can bluff throughout the course of the hand in such a way using game theory, that your opponent has negative EV. (see pg 129-141) Thus, knowing your opponents cards at the same time he doesn't know yours, puts him at such a huge disadvantage that you can play hands far inferior to his and still have positive EV. (However this only applies if there is subsequent betting in the hand and hence my opening question [img]/images/graemlins/smile.gif[/img])

If his bet puts you, or him, all-in, then J-5s would be my guess for the most valuable hand for which to obtain the info on.

[XChamp]

David said that your opponent "moves in". I'm assuming that means all-in.


I'm also assuming that you have $1000+ in front of you. He doesn't state that.

Also, is the money you give your opponent from your stack or from your pocket?