ROI is (mostly) irrelevant in poker

[SossMan]

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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).


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This is a classic case of a sunk cost. The buyin is gone. Calling or not calling, raising or folding or calling the waitress for some fried rice is not going to get the buyin back. Therefore all decisions must be made marginally.
I agree that you can't look at two hands, the board, and the pot and say this is +EV or -EV per se. You can say whether or not it is +EV or -EV in terms of tournament chips, but not in terms of dollars. You can, however, look at two hands, the board, the pot, the payout schedule, the opponents (and your) relative skill, the opponents stack sizes, and your stack size and determine +EV or -EV. While this analysis is difficult to do perfectly with a calculator and some time, it is near impossible to do perfectly during the heat of the moment.
Hence, we have twoplustwo to discuss, in general, different situations and how we act and what we do and why we do it.

But to say that the buy-in matters after the fact is like saying the Dodgers should have kept pitching Andy Ashby because they gave him a fat contract. Pitching him wont get the money back.

[eastbay]

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[ QUOTE ]
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).


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This is a classic case of a sunk cost. The buyin is gone. Calling or not calling, raising or folding or calling the waitress for some fried rice is not going to get the buyin back.

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Huh? Of course not.

But you don't want the buy-in "back". You want to win some prize money. This is not possible when busted out. You have to pay again for the chance at it.

That influences any EV estimation (in terms of money, not tournament chips), and that's what I was saying before.

In a tournament, there are discrete cut-off "events" that influence EV, one of which is losing all of your chips. A decision for all of your chips has a different EV than one that is not for all of your chips, with everything else remaining constant (cards, board, etc.)

Does this mean you should try to fold your way into the money? Of course not. But I think just doing a chip EV calculation and saying "it's +EV, I have to go here" is a big mistake.

[SossMan]

I think were saying kind of the same thing...

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In a tournament, there are discrete cut-off "events" that influence EV, one of which is losing all of your chips. A decision for all of your chips has a different EV than one that is not for all of your chips, with everything else remaining constant (cards, board, etc.)

Does this mean you should try to fold your way into the money? Of course not. But I think just doing a chip EV calculation and saying "it's +EV, I have to go here" is a big mistake.


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This is fairly obvious when, if on the first hand of a tournament, you're on the big blind, it's folded around to the small blind who raises all in (no rebuys)...he shows you AKo, and you have pocket 5's. You have positive chip EV, but (assuming your an above average player) negative dollar EV. This we agree on, right?

But to say that the buyin amount of this tourney (other than how it changes the way people are playing, i.e. $3 vs. $100) or the buyin of the next tourney should affect your decisions in the middle of this tourney is simply wrong (assuming you are not playing w/ rent money).

[ QUOTE ]
In a tournament, there are discrete cut-off "events" that influence EV, one of which is losing all of your chips. A decision for all of your chips has a different EV than one that is not for all of your chips, with everything else remaining constant (cards, board, etc.)


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Agreed. However, like I said before, given various assumptions about % chance of coming in X place and winning Y prize money based on remaining chip count, this is not an unatainable calculation. And it has nothing to do with how much this or the next buy-in is, and therefore nothing to do with ROI, necessarily.

[AlanBostick]

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This is fairly obvious when, if on the first hand of a tournament, you're on the big blind, it's folded around to the small blind who raises all in (no rebuys)...he shows you AKo, and you have pocket 5's. You have positive chip EV, but (assuming your an above average player) negative dollar EV. This we agree on, right?

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In the early stages of a tournament, when you are far out of the money, the bottom chip in your stack is worth only very slightly more than the topmost chip. Since your equity in the overall prize pool is proportional to your stack size, chip EV is dollar EV. The difference between the two is much, much smaller than the 5% edge Presto has over the other guy's Big Slick.

The real argument against calling with Presto in this spot is that, if you're a good enough player, an 11:10 edge is not big enough to justify a call, when if you're patient you'll be able to find situations when your edge is substantially bigger. That's risk management. It's the handwaving equivalent of the Kelly Criterion.

If it's the differential in skill that counts, let me ask this: Can there be a player so skillful that, in the very first hand of a large tournament, to call an all-in bet from the small blind when she is holding pocket aces in the big blind is "money-negative"?

[Greg (FossilMan)]

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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).

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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)

[drewjustdrew]

To play devil's advocate a little here greg - can we assume that as more people get eliminated, a person who was once twice as good as average dips closer to average, and changes the equation. So, using your example, the person was twice as good as the average person in the 100 person field. In theory, we expect that person to be less than twice as good as the field at 50 players. Or can this argument not be valid often enough to be true?

[Greg (FossilMan)]

No, you're probably right, in the sense that you're the same person, but more often than not the average skill level of the remaining players is higher at 50 than it was at 100.

Later, Greg Raymer (FossilMan)

[Bozeman]

Don't back down Greg: for the purposes of this example, it is perfectly fine to say that your skill advantage against 98 players is the same as your skill advantage against 99. What the last 50 players are like does not change the value of your stack at 100 players.

However, if your skill advantage is large, it is possible that 100 left 10 paid is close enough to the money that you could have ~5% corrections. (20% would be needed to change this answer).

Craig