Optimal EV/risk tradeoffs in tournament poker

[eastbay]

I think there are some interesting questions at the heart of tournament poker strategy that relate to weighing risk vs. reward, and finding the optimal balance according to context.

Consider the following highly simplified model of tournament poker that is clearly wrong and insufficient in many respects, but may be of some value anyway:

You start with N chips. A "tournament" consists of a series of pots and bets of exactly known EV. The pots can be any percentage of your stack, from a few percent to your entire stack. If you bust out, you lose B dollars. If you double your chips, you win 2B dollars. (This part of the problem should be parameterized and varied, but let's start there.)

Some strategies for playing the game:

1) make every bet that is +EV, independent of the number of chips at risk (you might call this the Raymer strategy /images/graemlins/wink.gif )
2) have some criteria based on %of your chips at risk which sets a threshhold for +EV bets to take.
3) by some criteria, even make bets that are -EV if you have a chance of winning there or soon at sufficiently small risk to your stack

Is there an optimal strategy? What does it look like?

I have no experience in game theory and I'm sure that shows to anyone who does. Critique of the model appreciated.

If there's enough interest, I could do some programming to implement various strategies to see how they fare against one another.

Regards,
eastbay

[Louie Landale]

I don't see what this has to do with tournament poker. [1] in a tournment when you double your stack size you DEFINATELY do NOT double your EV for the tournament [2] you can increase your EV in a tournament by simply maintaining your stack size [3] its possible but rare that you can deliberately reduce your stack size while increasing your EV [4] in a real tournament you don't know the EV of bets [5] in a real tournament you must get the opponent to agree with you on how much to bet.

Anyway, I don't think I read your game rules correctly, but it seems that you are playing against the house and there are an infinate number of pots of known EV, any of which you can bet any amount on. Since there seems to be no time limit you can simply adopt a strategy of betting a fairly small %age of your bankroll, maybe 20%, but only on the best pots. Keep passing all the negative and small EV pots.

- Louie

[Greg (FossilMan)]

Does your game presume some knowledge as to what type of bets are likley to become available on future hands? If we know that we can pass on all the -EV bets, and just wait for +EV bets with no downside except time, then you could simply make small bets on all the +EV situations, and guarantee a win eventually.

But, of course, to the extent this is like real poker, you lose money while just sitting there. This, or something like it, has to be part of the game for it to be a useful model.

Later, Greg Raymer (FossilMan)

[eastbay]

[ QUOTE ]
Does your game presume some knowledge as to what type of bets are likley to become available on future hands? If we know that we can pass on all the -EV bets, and just wait for +EV bets with no downside except time, then you could simply make small bets on all the +EV situations, and guarantee a win eventually.

But, of course, to the extent this is like real poker, you lose money while just sitting there. This, or something like it, has to be part of the game for it to be a useful model.

Later, Greg Raymer (FossilMan)

[/ QUOTE ]

I neglected to point out there is an ante or blind involved.

However, there's a bigger flaw that I will address with a new idea for a model in my next post.

Regards,
eastbay

[eastbay]

[ QUOTE ]
I don't see what this has to do with tournament poker. [1] in a tournment when you double your stack size you DEFINATELY do NOT double your EV for the tournament [2] you can increase your EV in a tournament by simply maintaining your stack size [3] its possible but rare that you can deliberately reduce your stack size while increasing your EV [4] in a real tournament you don't know the EV of bets [5] in a real tournament you must get the opponent to agree with you on how much to bet.

Anyway, I don't think I read your game rules correctly, but it seems that you are playing against the house and there are an infinate number of pots of known EV, any of which you can bet any amount on. Since there seems to be no time limit you can simply adopt a strategy of betting a fairly small %age of your bankroll, maybe 20%, but only on the best pots. Keep passing all the negative and small EV pots.

- Louie

[/ QUOTE ]

Louie,

I neglected to mention there is an ante or blind, without which the model is completely worthless; you simply wait for a big edge and then place your bet.

The major remaining flaw in my original proposal is that it is a non zero sum game. When you pass up +EV to reduce risk in the original game, it does nothing to affect the risk of subsequent "hands." In a tournament, every time you give up +EV you have given those chips to someone else and subsequently, they can put you to "riskier" bets on following hands. So that rather than ducking risk, you have at best deferred it and probably compounded it to return on later hands. I think this effect is far too important to the questions I am trying to investigate to neglect it.

So I reworked the basic idea into a zero-sum game between two opponents who play for winner take all.

Your comments on my newer model are appreciated.

Regards,
eastbay