Tough Game Theory Problem

[pzhon]

[ QUOTE ]

It is just a value bet. You know the second player will call no matter what, so the first player must raise half of the time. For large w, when you get your second card, your previous bet is almost irrelevant. now you have to reevaluate where you are, and thus, bluff raise, call, or value raise accordingly.

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The action on the previous street is quite relevant. Betting changes the size of the pot, even if it provides no useful information.

Even if the initial bet were miniscule, this would not mean it is right to value-bet with a 51% chance to win hot and cold. The first player may have to fold a winning hand more frequently than the second player does.

[MicroBob]

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It's occasionally amusing, as someone who considers himself fairly smart and fairly 'into' mathematics, to look at a message like this one and have absolutely zero clue whether or not it's coherent or gibberish. Heck, even if those words go together to make statements someone up on things would understand, I'm still not sure if they'd go 'uh, no' or 'hmm, that's an interesting point.'

Obviously I'm not insulting your post or your language, it's just funny to realize how out of my depth I am.


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These are my thoughts almost exactly.
In addition to that, I enjoy reading these types of threads to help maintain a relative amount of balance.
When you play against mostly idiots for a living it can be kind of dangerous I think. One can easily get an inflated view of how incredibly intelligent they are even if they know better.

This can sometimes be exaserbated by friends and family who view you as some sort of math-poker photographic-memory type genius just because you can consistently beat the game.

The fact is, I just follow the basic instruction manual of SSHE and the SS-forum, I'm really not THAT smart and I know it.
I read threads like this and think how amazing it is that there are actually people out there who can figure this stuff out...or at least come up with some reasonable theories that I have virtually no hope of understanding.


I picked up a fairly interesting read at a used-bookstore for $4 called Game Theory - A Nontechnical Introduction by Morton Davis of City University of NY...copyright 1970.
I'm not smart enough to know if it should be considered good or not.....but what i have read of it I have enjoyed.

[CK1]

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Hi Waffle:

The solution for the one street problem is known. I believe the answer is:

The first player should raise when his/her cards are between 0 and 1/8, call when his/her cards are between 1/8 and 5/8, and raise when his/her cards are between 5/8 and 1.

If raised the second player should only call if his/her cards are between 1/4 and 1.

If the first player calls, the second player should raise when his/her cards are between 0 and 11/48, should call when his/her cards are between 11/48 and 5/16, and raise when his/her cards are between 5/16 and 1.

If the second plyer raises, the first player should call 75% of the time
(1/4 to 5/8).

Note that you can get these fractions without writing long equations. Someone should double check my numbers.



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I am sorry but the numbers I gave for the one street problem was not correct. The second player should call a raise only with the top 2/3 of the hands (not 3/4).

So all the other numbers should be adjusted. For example the first player should value raise with the top 1/3 of the hands and bluff raise with the worst 1/9 of the hands. Anyway, I am again sorry for posting wrong fractions. I should check things before I post them.

However, I want to make the point that the two street problem is very interesting. This mistake does not affect my other e-mail about the two street problem.

CK