Fictitious play for multi-player games

[jukofyork]

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@juk:
The problem with your approach is imo, that pusher & caller are treated differently. The caller is basically playing some non-zero-sum version of minimax, while the pusher sticks to maximally exploiting the callers strategy. I guess we would want to use the same assumptions for both players?

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Yep, I suppose it might be just as valid to consider "spite-pushing". Whether it's really possible in real SNGs, I don't know, but I guess another toy game could be made where the pusher could also spite.

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But i ll run the numbers on this later, definitely before xmas [img]/images/graemlins/smile.gif[/img]

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Cool! [img]/images/graemlins/smile.gif[/img]

Juk [img]/images/graemlins/smile.gif[/img]

[trojanrabbit]

Depending on how you set up the game, whomever can "lock in" their action first will push 100%. That lock can come in the form of pushing your chips into the middle of the table or some artificially binding strategy declaration. There's nothing that the other player can do about this and it is the only stable equilibrium you can find. I firmly believe that the only way you'll be able to solve for spite calling is if you consider the EV of future hands beyond this one. That's what I'm going to be looking into.

Tysen

[jukofyork]

[ QUOTE ]
Depending on how you set up the game, whomever can "lock in" their action first will push 100%. That lock can come in the form of pushing your chips into the middle of the table or some artificially binding strategy declaration. There's nothing that the other player can do about this and it is the only stable equilibrium you can find. I firmly believe that the only way you'll be able to solve for spite calling is if you consider the EV of future hands beyond this one. That's what I'm going to be looking into.

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A bit OT, but I managed to get a copy of your new book and from initial impressions it looks awesome! It's basically what I had hoped both Chen's "Mathematics of Poker" and Moshmans's "Sit 'n Go Strategy" would be about: applicable theory, as opposed to toy-game theory and/or endless HOH-style hand examples.

Great work! Juk [img]/images/graemlins/smile.gif[/img]

[trojanrabbit]

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A bit OT, but I managed to get a copy of your new book and from initial impressions it looks awesome! It's basically what I had hoped both Chen's "Mathematics of Poker" and Moshmans's "Sit 'n Go Strategy" would be about: applicable theory, as opposed to toy-game theory and/or endless HOH-style hand examples.

Great work! Juk [img]/images/graemlins/smile.gif[/img]

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Thanks, Juk! I've heard that before that KE is the book people were hoping to get when they bought those two. Perhaps some of this effort here can make its way into another volume... [img]/images/graemlins/tongue.gif[/img]

Tysen