a question re poker theory/ ramblings

[cliff]

Some random questions/thoughts after a long tiring day, sorry if they are not coherent...

Has anyone given serious consideration to a second order theory of poker (maybe gambling in general)? Every source (poker books and forums) I have seen deals only with the first order statistics of the game (expected value). I believe that this is based on an assumption of an infinite bankroll? It would seem that under this assumption, the "fundamental theorem of poker" might actually correspond to a statement of optimality ( as opposed to an axiom, which it appears to be; at least in TOP?)

I have seen some discussion of (I think) logarithmic risk functions for evaluating strategy. Is there a good reference for this approach?

I guess that I have a fuzzy notion that if variance were accounted for in poker strategy (in the context of a finite bankroll, for instance), that the optimal approaches may change significantly. I know that this is generally avoided by assuming that a player has "sufficient" bankroll, but is this notion well defined (maybe in limit poker)?

Poker strategy with a finite bankroll reminds me of queueing theory, wherein first and second order analysis yields much different results. In this case we are trying to keep our bankroll large (rather then a queue close to empty), so there may not be a connection, but they seem similiar.

Any thoughts?

[pzhon]

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Has anyone given serious consideration to a second order theory of poker (maybe gambling in general)?

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Yes, many people have considered variance. See this 2+2 magazine article from July.

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I have seen some discussion of (I think) logarithmic risk functions for evaluating strategy. Is there a good reference for this approach?

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Search for the Kelly Criterion. There are many articles on the web, and many discussions on these forums.

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I guess that I have a fuzzy notion that if variance were accounted for in poker strategy (in the context of a finite bankroll, for instance), that the optimal approaches may change significantly.

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A big danger for poker players is to try to lower their variance without understanding how much of an edge they are throwing away. Suppose you are thinking about making a marginal call on the river. The pot odds are 10:1. Do you know how often you will actually be good? Most poker players have very little idea. Their estimates are often wrong by a lot in the hands posted in the limit forums. But, suppose you know for sure that your hand will be good 1/10 of the time instead of 1/11. Is this a good candidate for sacrificing EV to lower your variance? No! Getting 10:1 on a 9:1 gamble is safer and more profitable than playing poker normally. If you want to lower your variance here, you should also quit poker.

There are changes you can make. See the article referenced. However, I think few limit players are in a position to make any significant adjustments postflop. The simplest adjustments might be to give up a few marginal hands preflop, but even with the mountain of preflop data, it is tought to figure out which hands in which situations are really marginal.

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I know that this is generally avoided by assuming that a player has "sufficient" bankroll, but is this notion well defined (maybe in limit poker)?

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I think theorists have a fairly good understanding of the bankroll issues of limit poker.

There is more work to be done on understanding the EV and variance of particular plays in poker, but I think you have a lot of reading to do first.

Welcome to the forums.

[cliff]

thanks for the link, it is a start. i m not trying to lower my variance per say, i am more interested in the mathematical foundation of poker theory (which the referenced article seems promising for).

thanks again.

[jtr]

Some of the published theory on how to play in tournaments as the blinds get large (see e.g., Harrington on Hold'em vol. II) seems relevant to your question. Harrington discusses, for example, changes in your style as your stack becomes shorter relative to the blinds -- things like not playing small pocket pairs any more as you lack the implied odds for hitting a set.

If we imagine a person playing in, say, an NL cash game on a very short bankroll, similar considerations will apply, I think.

Any connection here or were you referring to something completely different?

[ianlippert]

Is there an useful application of the kelly criterion to poker? It seems to deal more with bankroll management, but is there a way to use during actual play. I read the article and it seems just like some abstract mathematical model for blackjack.