ROI is (mostly) irrelevant in poker

[Greg (FossilMan)]

[ QUOTE ]
Let me explain what I meant. My use of "ROI" was a little flip and imprecise.

I think a better way to think about it is to say that in a tournament, you cannot calculate EV independently of the chances of busting out. That is, you can't look at two hands, the board, and the pot, and say "this is x EV". Because either the decision is likely to cost you a buy-in, or it isn't. And if it is, that's an expense that hasn't been factored into the usual EV calculation.

So on a hand that is a potential bust, it is easy to get fooled into doing the usual EV calculation and thinking you're +, when in fact you're - because of the probability of having to "rebuy" (probably into a different tourney).

[/ QUOTE ]

Yes, you were not using ROI in the way I normally do, as described in my post.

I use two terms. Chip EV and cash EV. Chip EV is the expected value of a given decision in terms of tournament chips. That is, the same thing we all do in cash games (where chip EV and cash EV are identical).

Cash EV is the expected cash value of a given sized stack of tournament chips at a given point in time. It is very hard to estimate this number more than roughly, and probably impossible to calculate it exactly. However, if we assume that all players have equal skill, you can estimate it with the right software, or in your head, though the resulting numbers are always subject to debate. You can also alter that estimate by taking into account a players relative skill (as compared to the field and their current table).

Since you can make these estimates, you can estimate the cash EV of a given tourney decision.

Let's say you bet enough to put me all-in. I estimate my chances of winning to be 40% if I call, against the entire range of hands I put you on. If I fold, I'll retain T1000 in chips. If I call and lose, I'm broke. If I call and win, I'll have T3000 in chips.

Now all we have to do is estimate the cash value of each of these 3 possible chip positions at this point in the tourney. Zero chips is easy enough. Let's say that the average stack right now is T2000, 100 players remain, 10 places paid, total prize pool is $40,000.

We're so far from the money that all chips have essentially the same value, no matter how big or small of a stack they are in. If somebody has a truly big stack, T20,000 or more, then we would start to worry about this effect.

Chips are worth T5/$1. Let's assume for a minute that we're average. Our T1000 stack would be worth $200, and a T3000 stack $600. This means if we fold, our cash EV is $200. If we call, we have $600 40% of the time, and zero the other 60%. That's a cash EV of $240 for calling.

So we can do the math for this.

Even if we consider you to be a well above average player, the same kind of math holds. If you're twice as good as average, your T1000 stack is worth $400, but calling here is worth about $480 in cash EV (nothing when you lose, $1200 when you win).

Later, Greg Raymer (FossilMan)