ROI is (mostly) irrelevant in poker

[Greg (FossilMan)]

There was a remark in a very recent thread that got me onto this rant again. From eastbay in his thread titled "Grr. PP Multi-table Tourney Hand":

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This idea that "you can always just play again" is a little specious, I think. The idea is maximum ROI, so when going after your R, you have to worry about your I.

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EV matters. Variance matters. Bankroll matters. Return on investment is irrelevant. When you're playing poker, the large majority of your bankroll is NOT working. Most of it is sitting in your pocket, your lockbox, or your bank account, waiting there in case you lose tonight and need to go get it. Thus, who cares how much return you're getting on your current poker investment (that is, the game you're in right now)? Would you rather buy into a 1-3 stud game for $100, earn an expected $5 per hour for 5% ROI; or, would you rather buy into the 10-20 game for $500, earn an expected $20 over the same hour, and only have a 4% ROI?

If your bankroll can afford the variance, you generally want to play in the game that offers you the highest EV per hour. At least in my opinion.

Same thing for tourneys and tourney chips. If the play is one that offers +EV, then who cares about ROI? If a play is going to bust you out when you lose, that's poker. It doesn't become correct to fold just because you will survive longer in this event (without cashing), and thereby put off investing into another tourney right away.

Even if ROI is what matters, you need R to make this number positive, and folding when you've got the best of it does not lead to long-term R.

Later, Greg Raymer (FossilMan)

[CrisBrown]

Hiya Greg,

I agree. I've no idea what my ROI is, but I keep pretty good tabs on my expected hourly rate. I choose games and (try to) play to maximize my expected hourly rate, not my ROI.

To follow your example, I could probably make a higher ROI at $11 or $22 SNGs -- I'd probably win a bit more often vs. softer players -- but I have a higher expected hourly rate at $55 and $109 SNGs.

By contrast, I know some people who have trouble winning at higher stakes, but maximize their expected hourly rate (and reduce their variance) by playing two or three lower stakes touraments at a time. They estimate that their return will be more normalized by playing three $11 tourneys at once rather than one $33 tourney. And I suppose if they can follow three tables as well as they can follow one, they are probably right.

I know I wouldn't play as well trying to keep up with three tables at once, so I take the (somewhat) higher variance of playing in larger-stakes tournaments.

Still, I can see eastbay's point. I'm a lot more dangerous with a relatively short stack than I am from the rail. So I generally try to avoid dicey all-ins early, on the theory that patience will reward me with a more clearly +EV situation later.

Cris

[Guy McSucker]

This is a really good point that comes up quite often.

I think the key is that, in poker, money to invest is not scarce: you (should) have enough for several buyins, tournaments, whatever; but your time is very scarce: before the birth of online poker, you could only play one game at a time.

You therefore want to maximise return with respect to time, rather than cost.

I am sure economists must have a word to describe this concept. Time is the scarce resource, so it is the appropriate denominator for your fractions.

My wife is an economist. I asked her about this, and she agreed: she's sure they must have a word for it too!

Guy.

[CrisBrown]

Hi Guy,

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My wife is an economist. I asked her about this, and she agreed: she's sure they must have a word for it too!

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LOL....

(Making a note to forget all of her economist jokes....)

Cris

[Redhotman]

This is completly true except, some people may believe that one should stay at a certain level until they are cappable of beating it, which is represented through ROI.

This can be shown through small stakes. I play six 3/6 games at a time and make about the same as a player playing 15/30 for a BB/HR.

Now if I sat at that table I'd get killed. So in the long run is profit all that matters, or is improving your game more important?

[eastbay]

[ QUOTE ]
There was a remark in a very recent thread that got me onto this rant again. From eastbay in his thread titled "Grr. PP Multi-table Tourney Hand":

[ QUOTE ]
This idea that "you can always just play again" is a little specious, I think. The idea is maximum ROI, so when going after your R, you have to worry about your I.

[/ QUOTE ]

EV matters. Variance matters. Bankroll matters. Return on investment is irrelevant. When you're playing poker, the large majority of your bankroll is NOT working. Most of it is sitting in your pocket, your lockbox, or your bank account, waiting there in case you lose tonight and need to go get it. Thus, who cares how much return you're getting on your current poker investment (that is, the game you're in right now)? Would you rather buy into a 1-3 stud game for $100, earn an expected $5 per hour for 5% ROI; or, would you rather buy into the 10-20 game for $500, earn an expected $20 over the same hour, and only have a 4% ROI?

If your bankroll can afford the variance, you generally want to play in the game that offers you the highest EV per hour. At least in my opinion.

Same thing for tourneys and tourney chips. If the play is one that offers +EV, then who cares about ROI? If a play is going to bust you out when you lose, that's poker. It doesn't become correct to fold just because you will survive longer in this event (without cashing), and thereby put off investing into another tourney right away.

Even if ROI is what matters, you need R to make this number positive, and folding when you've got the best of it does not lead to long-term R.

Later, Greg Raymer (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).

[SossMan]

[ 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. 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]

[ QUOTE ]
[ 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.

[drewjustdrew]

This is a case of Net Present Value method vs. Internal Rate of Return method (ROI) as a measurement of investments. Greg advocates the NPV which indicates which investment will yield the greatest return in the long run, regardless of total up front capital. This is also favored by most financial analysts. Internal Rate of Return would be used if you only had a certain amount to invest, and planned to invest the entire amount, so bankroll considerations are irrelevant.