poker as an investment: the math

[ryanj247]

i'm normally pretty good about figuring things out on my own. i could use a little kick-start here if anyone is inclined to be so helpful... to get to the final analysis i'm looking for here is going to require a sort of crash course in finance, i think. if you could help point me towards where to start educating myself, that's what i'm looking for.

assumptions (not real figures, just an example):

1) i have $1000 to "invest" (and i'm evaluating investing that $ in myself playing poker)
2) i've established my long-term winrate as 2BB/100
3) i've established my standard deviation as 15BB/100

so far, FWIW, i've determined how to calculate my risk of ruin. for example, playing 2 tables of 2/4 for 80 hours/month at 60 hands/hour/table, my RoR is approximately 1%. i can use that same formula to determine that my RoR would be ~25% if i started with only $300. just to confirm, this would mean that i have a 1 in 4 chance of losing ~$300 when i start with $1000 (or any amount), correct?

if so, then i've now determined that 1% of the time i will lose $1000, and 25% of the time i will lose $300. one problem here is that the RoR (i.e., bankroll) formula is independent of time. it says that my RoR at this moment in time is y%. but when we're looking at poker as an investment, we need to analyze it for a certain period of time, right? so how do i calculate the probability that i will win/lose $x in, say, 10,000 hands?

it seems to me that there must be a formula for this, and that the results of this formula would produce some kind of a curve that plots $won/lost against probability of said $win/loss. do i need some particular software to plot this?

once i have that curve, now how do i use that to evaluate the $1000 investment? that is, how do i compare this investment, with all of the probabilities of wins and losses, against any other investment?

[gull]

[ QUOTE ]
i can use that same formula to determine that my RoR would be ~25% if i started with only $300. just to confirm, this would mean that i have a 1 in 4 chance of losing ~$300 when i start with $1000 (or any amount), correct?

[/ QUOTE ]

Yes.



The risk of ruin formula assumes you play forever. time = infinity.

[SlowHabit]

People forget (or underestimate) how luck plays a HUGE role in poker in the short-run. You also have to take into account Hero's playing style. A formula with $1000 to "invest" doesn't really mean anything. The way to protect yourself from "risk of ruin" is have a lot of buy-ins.

Why do you need such formula again (I don't mean it in a consedencing tone but just out of curiousity)?

[ryanj247]

the reason i brought up the RoR/bankroll formula is to explain how that's as far as i've gotten so far in applying math to poker as an investment. it's not what i need because of its lack of a time component.

a little bit of a different angle on trying to clarify the questions i have:

1) with a given WR and SD, how do i calculate the probability (i'm assuming this would be with some margin of error??) that i will win/lose $X in a certain number of hands (or hours/days/weeks/etc)?

2) how do i (or is it even possible to) use the results of that calculation to calculate a ROI so that i can compare poker as an investment to any other investment?

maybe i'm making all of this too complicated. but i would like to be able to use math to quantitatively compare "investing" an amount of $ in poker for a certain period of time vs. some other investment. for example, suppose i can expect my $1000 investment in a goverment bond to be worth $1030 after one year. how does that compare to playing poker with that $ instead given the probabilities of the amounts i could possibly have after one year (ranging from x% probabilty of having $0 to y% probability of having $1030 to z% probability of having $4000)?

[SlowHabit]

Oh, so that's what you meant.

I think it is almost impossible to create such a formula because there's a lot of factors that need to be considered when calculating your winrate. Such factors can be tilt control, game selection, your edge against your opponents, etc. Perhaps an easier way to "create" this "formula" is take the averages of winrates of the top players at each limit and *formulate* your winrate by comparing yourself to these players.

I still feel like I haven't answer your question haha. And yes, you're making the math aspect of poker more difficult than it needs to be.

Side note: try messaging ZeeJustin. He's good with these kind of stuffs.

[ryanj247]

i'm almost certain i've seen calculations that say "if you've won $x in the past 100K hands, there is a y% probability that your winrate is between a and b". so it seems to me that we ought to also be able to calculate something like "if your winrate is x, there is a y% probability that you will win $x, a z% probability that you will lose $x, etc". for any given $ amount, positive or negative, we ought to be able to calculate the probability that at the end of, say, one year, a player with a given winrate would end up with that amount of $.

that would give us a "model" of this "investment". once we have that, isn't there a mathematical way to evaluate that against any other investment? aren't other investments analyzed with that same type of modeling? isn't an investment that has shown returns of {7%, 7%, 7%, 7%, 7%} a much different investment than one that has shown returns of {7%, 100%, 7%, -93%, 7%} in the past 5 years? (i understand the total ROI on those two investments is not the same for the past 5 years, but you get the idea...whatever the numbers in years 2 and 4 of the latter investment would have to be for its total ROI to have been equal to the former for the 5 year period) how do you compare and choose between those two investments when you're considering investing for a one year period? isn't there a way to take the returns for the past 5 years on the latter investment and be able to answer the question "what is the probability that the return next year will be 75%"? how would you use the answer to that question in deciding which investment was the better choice?

as for the poker "investment", i am assuming that the winrate is established and constant (same with the standard deviation). i understand that's a big assumption, but i'm trying to calculate probability of any given win/loss in a certain period of time given a certain winrate. once i can do that, then i can estimate best case/worse case with higher/lower winrates...

[ryanj247]

[ QUOTE ]

as for the poker "investment", i am assuming that the winrate is established and constant (same with the standard deviation). i understand that's a big assumption, but i'm trying to calculate probability of any given win/loss in a certain period of time given a certain winrate. once i can do that, then i can estimate best case/worse case with higher/lower winrates...

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just to reiterate, this is the same thing that is done in the RoR calculation. that calculation can tell me that with a given winrate and standard deviation, my RoR given $x bankroll is y%.

now, how do i get a time element into the probability equation? then i could determine the likely range of what my bankroll ("investment") will be one year from now. for example, starting with $1000, i'm looking for a mathematical way to determine that given a certain winrate and standard deviation there is a 10% probability that one year from now i will have $0, a much higher probability that i would have $700-$2000, and a 1% probability that i will have $4000. now, compare that to a CD where there is a 99.9% chance that i will have $1040 one year from now.

can't you compare those two investments mathematically, based on the probabilities of possible outcomes one year from now? how do you do the math?

[eastbay]

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compare that to a CD where there is a 99.9% chance that i will have $1040 one year from now.


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This is all apples and oranges. It'd be more sensible to compare the pros and cons of poker vs. working at the 7-11.

eastbay

[ryanj247]

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compare that to a CD where there is a 99.9% chance that i will have $1040 one year from now.


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This is all apples and oranges. It'd be more sensible to compare the pros and cons of poker vs. working at the 7-11.

eastbay

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i understand your point. i'm just trying to figure out if there's some way that i can compare the risk/reward of putting $ into a poker bankroll for a given period of time to the risk/reward of putting $ into an investment.

in a sense, comparing poker to 7/11 isn't really apples to apples either because you don't need a bankroll to start working at 7/11. the initial investment required for poker makes it somewhat more like...an investment...than a job...

[eastbay]

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compare that to a CD where there is a 99.9% chance that i will have $1040 one year from now.


[/ QUOTE ]

This is all apples and oranges. It'd be more sensible to compare the pros and cons of poker vs. working at the 7-11.

eastbay

[/ QUOTE ]

i understand your point. i'm just trying to figure out if there's some way that i can compare the risk/reward of putting $ into a poker bankroll for a given period of time to the risk/reward of putting $ into an investment.


[/ QUOTE ]

IMO not really, and it wouldn't tell you anything interesting anyway. And not only because poker is a job and not a passive investment.

First of all, poker will return ridiculously huge amounts compared to a CD if you are a winner with any reasonable bankroll. If your bankroll was huge, you could bring the %ages down to be comparable, but that wouldn't make sense either, because you could just take the excess bankroll and put it in the CD.

The main difference between poker and a CD is that one is passive and the other is a job. You can stop your comparison there and make your decision on that.

Or is this some kind of "I want to snow job my parents or my gf" kind of deal, where the point is not to be honest, but to sell a bill of goods?

eastbay