Re: typed solution
 

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I've already done the overall EV calculation and it's:

EV(A) = 0.5062
EV(B) = 0.4938

and I'm pretty sure it's right.

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I just did this myself, and got the exact same answer.

I can't believe how small A's edge is.

Re: Classic Type Game Theory Problem
 

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Would you rather that the players were dealt integers uniformly distributed over the range [0, N], where N is a large positive integer?

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This doesn't come close to approximating the intent of the original problem. But if that's what we want to make the problem, that's fine. At least it makes sense.

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Sure, David's initial formulation was not completely precise, but why should that stop a mathematician from tackling this problem? This problem deserves more effort and attention than David's initial (which you claim incorrect) assumption.

Re: typed solution
 

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I've already done the overall EV calculation and it's:

EV(A) = 0.5062
EV(B) = 0.4938

and I'm pretty sure it's right.

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I just did this myself, and got the exact same answer.
I can't believe how small A's edge is.

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I'm glad you verified it. If you both got that number, I must have made a mistake in my EV spreadsheet. I agree it's unbelievably low.

alThor

Re: typed solution
 

I thought about it more, and I think it makes sense that A's edge is very small.

If A's strategy were to never pat-bluff, and B was aware of this, then B would always draw if A stood pat. This would be equivalent to a game in which both A's and B's first card were dealt face up. In this case, neither player has any advantage (either player would automatically draw if his card is worse than 0.5, and if both cards are > 0.5, the better card would stand and the worse card would draw).

So A is able to achieve a small edge only because of his ability to pat-bluff.

Re: typed solution
 

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I'm not about to get into a pissing match over it.


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I'm not into pissing matches either and I don't want to take away from your fine contributions but in all fairness I felt it necessary to point out BBB's explicit mention of the correct strategy for A when B's upcard is in the interval [0.5,0.586].

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Ok, sorry if I sounded harsh there. In fact I was (trying) to say that part of the strategy in my very first post. Now I see I wrote "when A does", which looks like "A does draw", but I meant "A does stand", which is what is in alex/M's quoted post. I certainly didn't say anything as clear as BBB did.

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It was far from obvious since at least 2 fine mathematicians had trouble with it at first.

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We also have "mathematicians" claiming that the uniform distribution doesn't make sense. Since I don't know all the handles around here, I am wary of who is legit. I hope that doesn't offend anyone legit. There's no reason for anyone to think I should have any credibility, either, unless I posted my real life info, which I'm not planning to do right now.

It's all cool.

alThor

EDIT: I just verified your EV via simulation, and agree.

Re: typed solution
 

No problem, everything's cool by me too [img]/images/graemlins/cool.gif[/img]

Too bad we can't have a big eraser fight among all the mathematicians here. [img]/images/graemlins/shocked.gif[/img]

Re: Classic Type Game Theory Problem
 

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No! It's not being a nit. The problem doesn't make sense!

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Ive posted the same remark in other forum before reading this. Its not nitpicking, the problem doesnt make sense to me too as all analysis done so far, cause they all refere to some other problem.

Re: Classic Type Game Theory Problem
 

BluffTHIS, in poker previous hands dont matter at all as there exist optimal mixed strategy which is the same for all hands dealt no matter what "history is". In real live game you (and other good players) often think about "history" because you try to find "holes" in overall strategy of your opponent in hope that he play bad and will repeat his mistakes in other words: when analyzing "history" you hope that your opponent is weak enough to give you some clues about his play in following hands but theoretically previous hands doesnt matter at all. (implication which many ppl find hard to accept is that you can be godlike poker player without ANY memory about previous hands [img]/images/graemlins/wink.gif[/img] )

Best wishes