What Is the Variance of Poker ?
May 30th, 2011 at 4:30:52 PM
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In Blackjack Appendix 4 we can get valuable information on standard deviation for the 6 deck blackjack shoe game. Did you make the same analysis for poker tournaments as well ?
My own research brought the following numbers:
1 Table Tournament with 9 players
EV = 0.1 Buy Ins (assumption for good player)
SDev= 1.7 Buy Ins
3 Table Tournament with 27 players
EV = 0.1 Buy Ins (assumption for good player)
SDev= 2.6 Buy Ins
Can you agree on the above numbers ? And what would be the standard deviation for a WSOP tournament with 1000 entrants ? Or even 8000 ?
mpower
My own research brought the following numbers:
1 Table Tournament with 9 players
EV = 0.1 Buy Ins (assumption for good player)
SDev= 1.7 Buy Ins
3 Table Tournament with 27 players
EV = 0.1 Buy Ins (assumption for good player)
SDev= 2.6 Buy Ins
Can you agree on the above numbers ? And what would be the standard deviation for a WSOP tournament with 1000 entrants ? Or even 8000 ?
mpower
May 30th, 2011 at 7:31:54 PM
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I'm using MGM Grand payout structure as a baseline. For both 9 and 27 players, the payout is 50% for 1st place, 30% for 2nd, and 20% for third. The buy in is $80, and 75% of the buy in money goes to the prize pool.
So the expected value is -0.25 buy ins in either case.
For the nine player tourney, the variance is 6/9*(-80)^2 + 1/9*(28)^2 + 1/9*(82)^2 + 1/9*(190)^2 = 9112. The standard deviation is the square root of the variance = $95, or 1.2 buy ins.
For the 27 player tourney, S2 = 24/27*(-80)^2 + 1/27*(244)^2 + 1/27*(406)^2 + 1/27*(730)^2 = 34202. Standard deviation = $185 = 2.3 buy ins.
So the expected value is -0.25 buy ins in either case.
For the nine player tourney, the variance is 6/9*(-80)^2 + 1/9*(28)^2 + 1/9*(82)^2 + 1/9*(190)^2 = 9112. The standard deviation is the square root of the variance = $95, or 1.2 buy ins.
For the 27 player tourney, S2 = 24/27*(-80)^2 + 1/27*(244)^2 + 1/27*(406)^2 + 1/27*(730)^2 = 34202. Standard deviation = $185 = 2.3 buy ins.
June 1st, 2011 at 4:39:53 AM
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Thanks PapaChubby ! Seems pretty easy to adapt the variance calculation for any size of poker tournaments.
My intention is to define kind of a luck factor for poker tournament players. So far, the ratio between net win and standard deviation serves quit well.
My intention is to define kind of a luck factor for poker tournament players. So far, the ratio between net win and standard deviation serves quit well.
June 1st, 2011 at 6:53:51 AM
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Yep, given the prize structure it's pretty straightforward to calculate the standard deviation. For a large tournament you'll probably want to use a spreadsheet.
I frequently use mean and standard deviation to determine the likelihood of being ahead or behind after a certain number of trials of a casino game. I use large bets and short gambling sessions to optimize standard deviation relative to expected loss. Based on the Central Limit Theorem, I assume a normal distribution for my analyses. You'll need to consider that the CLT does not apply to your poker problem, and the distribution is definitely not normal.
I frequently use mean and standard deviation to determine the likelihood of being ahead or behind after a certain number of trials of a casino game. I use large bets and short gambling sessions to optimize standard deviation relative to expected loss. Based on the Central Limit Theorem, I assume a normal distribution for my analyses. You'll need to consider that the CLT does not apply to your poker problem, and the distribution is definitely not normal.
