Quantifying the profitability of the short-stack strategy - Page 2

Troll_Inc · #11 12-11-2006, 10:13 PM

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You are talking about standard deviation, right?

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Variance is simply standard deviation squared.

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That's funny...you mean variance is like some math term?

As a mean increases (winrate for example), the variance will almost always increase.

What you should really be talking about is comparing winrate to stdev(or variance). That would be an interesting metric to investigate.

And lastly, in agreement with the OP, Rolf pretty much says the same thing ...shortstack strategy is less profitable than a good full stack player at the same level.

But another point to consider, which I haven't seen addressed here, is that say I don't have 40 buyins for playing full stacked PLO200. I will buyin short and use a modified Rolf strategy. If some maniac LAG doubles me up, then I sure am not hitting and running.

pete fabrizio · #12 12-11-2006, 10:25 PM

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What you should really be talking about is comparing winrate to stdev(or variance). That would be an interesting metric to investigate.

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This isn't an "interesting metric to investigate," this is the central metric to bankroll management and other long-term variance considerations. Even if you win a ton of money, if your winrate/SD ratio lower than .05, you will occasionally have losing years. With a winrate/SD ratio higher than .20, you're unlikely to ever have a losing month.

Silent A · #13 12-11-2006, 11:00 PM

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You are talking about standard deviation, right?

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Variance is simply standard deviation squared.

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and a lower winrate means a larger standard deviation right?

so they have more variance.

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No. Win rate and standard deviation have virtually no co-relation with each other.

Now, if we're talking specifically about the "coefficient of variation" then maybe.

CV is the std devation divided by the win rate, and as Pete alluded to, this is the fundamental measure of how likely you are to go broke.

Even if we agree that a short stacker's winrate is lower, since their standard deviation is lower too it's far from clear who is morelikely to go broke.

Troll_Inc · #14 12-11-2006, 11:17 PM

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What you should really be talking about is comparing winrate to stdev(or variance). That would be an interesting metric to investigate.

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This isn't an "interesting metric to investigate," this is the central metric to bankroll management and other long-term variance considerations. Even if you win a ton of money, if your winrate/SD ratio lower than .05, you will occasionally have losing years. With a winrate/SD ratio higher than .20, you're unlikely to ever have a losing month.

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Exactly.

So what's the answer.

antistuff · #15 12-11-2006, 11:32 PM

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You are talking about standard deviation, right?

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Variance is simply standard deviation squared.

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and a lower winrate means a larger standard deviation right?

so they have more variance.

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No. Win rate and standard deviation have virtually no co-relation with each other.

Now, if we're talking specifically about the "coefficient of variation" then maybe.

CV is the std devation divided by the win rate, and as Pete alluded to, this is the fundamental measure of how likely you are to go broke.

Even if we agree that a short stacker's winrate is lower, since their standard deviation is lower too it's far from clear who is morelikely to go broke.

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i dont understand the math behind this at all

but with that said ive always heard that if you are a lets say 1bb/100 winner you will have bigger swings than if you are a 3bb/100 winner.

maybe ive heard wrong or there is something im not understanding. i think ive been playing poker long and seriously enough where i should learn about all this properly. any suggestions on a good book?

Troll_Inc · #16 12-11-2006, 11:57 PM

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maybe ive heard wrong or there is something im not understanding. i think ive been playing poker long and seriously enough where i should learn about all this properly. any suggestions on a good book?

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Anywhere near college age? Easiest thing would be to take a basic Probability/Statistics class.

I don't know of any poker books that teach this adequately assuming no previous knowledge.

Silent A · #17 12-12-2006, 12:39 AM

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i dont understand the math behind this at all

but with that said ive always heard that if you are a lets say 1bb/100 winner you will have bigger swings than if you are a 3bb/100 winner.

maybe ive heard wrong or there is something im not understanding. i think ive been playing poker long and seriously enough where i should learn about all this properly. any suggestions on a good book?

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It's not that a 1bb/100 winner has bigger swings, it's that his win rate is lower so he has less of a cushion to absorb the inevitable downswing, so he is far more likely to go broke.

For example, take two players that play 100K hands a year. One has a win rate of 1BB/100, while the other has a win rate of 3bb/100 (let's just assume for a minute that these are their real long term win rates - keeping in mind that an argument can be made that there's no such thing as a real long term win rate). Each player starts with a 40 buy-in bankroll (i.e. 4000BB) and has a style of play that gives them a 75BB/100 standard deviation. The odds that the first player will go bankrupt before the end of the year are roughly 1 in 10, while for the second player it's closer to 1 in 100.

If you want to know how to do these calculations all you need is a basic statistics textbook. It's all based on a normal probability distribution theory. It would also be a good idea to get a solid understanding about what a z-score is.

Bartholow · #18 12-12-2006, 12:54 AM

Just to clarify, the "swings" are the same size relative to where you "would" be given your earn.

So in your example, let's say after 1000 hands, they'd have the same chance of being down 100bb from where they should be at, but that means the weaker player will be down 90 big bets, whereas the stronger player would be down 70 big bets with equivalent likelihood. So the "swings" in a non-technical sense are certainly "bigger" for the player with a lower winrate, even though his std. dev. is the same. I think this may be what confuses people.

Silent A · #19 12-12-2006, 01:00 AM

If you want to save yourself the trouble of looking it up, here are some useful equations that summarize the theory:

WR = your win rate in PTBB/100 hands
SD = your standard deviation in PTBB/100 hands

A PTBB = a Poker Tracker Big Bet = 2 Big blinds

To absorb a 1 in 10000 downswing, you need a bankroll with BI buyins (i.e. 100BB or 50 PTBB):

BI = 0.06*SD^2/WR

To survive a 1 in 1000 downswing:

BI = 0.05*SD^2/WR

To survive a 1 in 100 downswing:

BI = 0.027*SD^2/WR

To survive a 1 in 10 downswing:

BI = 0.0085*SD^2/WR

Note: these calculations give you the number of FULL buyins. This still applies even if you're playing shortstacked.

pete fabrizio · #20 12-12-2006, 02:54 AM

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maybe ive heard wrong or there is something im not understanding. i think ive been playing poker long and seriously enough where i should learn about all this properly. any suggestions on a good book?

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Anywhere near college age? Easiest thing would be to take a basic Probability/Statistics class.

I don't know of any poker books that teach this adequately assuming no previous knowledge.

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