ROI is (mostly) irrelevant in poker

[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

[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"?

[Che]

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So in the long run is profit all that matters, or is improving your game more important?

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It depends.

If you play poker as a business, e.g. if it is your primary source of income, profits are (basically) all that matter.

If poker is just a hobby, improving your game might be more important although you would need to keep your maximum loss rate above whatever level you could afford to invest in a hobby. Poker is just one of many potentially high cost hobbies.

I guess you could also have a hobby/second income approach to poker which would have some sort of balance of priorities between monetary return (profits) and emotional return (improving your game).

So only you can decide what's important to you. (I'm being serious here and not trying to be condescending or trite. I hope I haven't come across that way.) [img]/images/graemlins/grin.gif[/img]

[eastbay]

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So in the long run is profit all that matters, or is improving your game more important?

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It depends.

If you play poker as a business, e.g. if it is your primary source of income, profits are (basically) all that matter.


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That seems like a strange business sense. It seems equivalent to saying: I have a widget factory that makes 10 widgets. Should I run it 24-7 or should I take it offline for a week so that I can increase the capacity to 15 widgets?

You seem to be saying that you have to run it all the time. I would say it depends how long you plan to be in the widget business, primarily.

[Che]

[ QUOTE ]
That seems like a strange business sense. It seems equivalent to saying: I have a widget factory that makes 10 widgets. Should I run it 24-7 or should I take it offline for a week so that I can increase the capacity to 15 widgets?


[/ QUOTE ]
In my quest for brevity, I was rather vague so I see how this could be confusing and/or strange. I'll be less brief this time...

The question I was answering was:

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So in the long run is profit all that matters, or is improving your game more important?

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What I was trying to say is:
1. If your goal is to make money (i.e. poker is a business for you), then it doesn't matter if you improve your game or not. What matters is how much profit you make relative to your investment (more on this below).
2. If your goal is something other than making money, that's OK. Just because "the object of the game is to make money" (The Theory of Poker, p.5) doesn't mean you have to make a profit for poker to have value in your life. Even if I consistently lost money for the rest of my life, I might still play $3 tourneys on Stars every once in a while since I enjoy the tourneys and I'm not going to miss $3. If I get rich someday, I might choose to donate money to the larger buyin events. How much you pay for your hobbies is relative to the size of your income/net worth (and based on the way they play, a lot of the players even at higher buyins have a hobby-level commitment to the game).

In summary, what's "important" is whatever is important to you - whatever you value.

Now back to point one, we now have to define "profit relative to investment." You invest two things when you play poker: money and time.

IMHO, if your goal is to maximize profits, you should choose the game(s) that give you the greatest expected profit per unit of time invested. How much money you actually invest (i.e. risk) depends on how much it is necessary to invest in order to achieve your maximum expected profit per unit of time invested. As long as the required investment is reasonable given your bankroll/variance profile, you should forget about what your investment in this game was or what the investment in the next game will be and focus on playing your best in the current game.

BTW, when I say "maximizing profits" I don't mean maximizing today's profits. I mean longterm profits. Continuing to earn the same amount per hour you currently make indefinitely is not profit-maximizing unless you have already reached the maximum possible per hour profit or the cost of improving your skills outweighs the NPV of the future increased profits that could be attained with improved play.