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#41
08-09-2007, 03:25 AM
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Re: Ribbit\'s Edits
In the 50-70 ptBB/100 range, bankroll isn't that sensitive to SD. But I never imagined a case with a SD over 100. I am truly impressed. [img]/images/graemlins/smile.gif[/img]
The required bankroll is proportional to SD^2/WR. The exact equation is: BR = -ln(ROR)*SD^2/(2*WR) Where, WR = win rate in ptBB/100 hands BR = bankroll in ptBB SD = your standard deviation in ptBB/100 hands ROR = risk of ruin (as a fraction of 1, e.g. 0.01 for 1%) 1 ptBB = one Poker Tracker big bet = 2 big blinds With a SD = 105 ptBB/100 hands, Rempel needs a bankroll of 500/WR (measured in buy-ins) for a 1% ROR. So, if his expected winrate at 2/4 is about 5 ptBB/100 hands, he needs about 100 buy-ins. This stuff needs to be in the FAQ. 
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#42
08-09-2007, 05:29 AM
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Re: Ribbit\'s Edits
On Stars I would probably be very comfortable with 60BI on Stars but I find the game selection there to be generally very poor. Unfortunately party's games tend to have a mix of very aggro solid players, very aggro bad players, and gigantic call stations. 2/4 on there really does play more like 0.05/0.10 with a few more good players at the table. 4 way flop all ins are fairly common in these games. Also I would estimate based on my EV I have probably won 70-80% of what I should have over like 50k hands in the last year or so.
Suprisingly my SD at HU 2/4 is only like 80 and I have a higher WR so my BR with a 1% ROI is only like like 50BI. Keep in mind that poker is my sole income and without the buffer of 3-4K rakeback on a monthly basis I can't really afford to screw around anymore.
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#44
08-09-2007, 09:15 AM
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Re: Ribbit\'s Edits
[ QUOTE ]
In the 50-70 ptBB/100 range, bankroll isn't that sensitive to SD. But I never imagined a case with a SD over 100. I am truly impressed. [img]/images/graemlins/smile.gif[/img] The required bankroll is proportional to SD^2/WR. The exact equation is: BR = -ln(ROR)*SD^2/(2*WR) Where, WR = win rate in ptBB/100 hands BR = bankroll in ptBB SD = your standard deviation in ptBB/100 hands ROR = risk of ruin (as a fraction of 1, e.g. 0.01 for 1%) 1 ptBB = one Poker Tracker big bet = 2 big blinds With a SD = 105 ptBB/100 hands, Rempel needs a bankroll of 500/WR (measured in buy-ins) for a 1% ROR. So, if his expected winrate at 2/4 is about 5 ptBB/100 hands, he needs about 100 buy-ins. This stuff needs to be in the FAQ. [/ QUOTE ] I think your (accepted) analysis is pretty wrong. It would be like a cop standing by the side of a 16 lane highway during rush hour watching 2,000 cars go by an hour and trying to guess what the average speed of the cars will be on Sunday at 2pm. The distribution of hand results is far from normal. You have essentially three major sets of results. Big net wins, big net losses, and a lot of results around zero. (A finer point would be to make it 5 groups, adding in medium losing and winnings hands.) Just using a basic stat test for poker results just isn't that helpful for determing the population mean.
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#45
08-09-2007, 11:54 AM
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Re: Ribbit\'s Edits
You are correct that real poker results aren't normally distributed, so this theory is approximate. However, this doesn't change the fact that bankroll would still be proportional to SD^2/WR. You'd just have a slightly different coefficient out front.
Feel free to do the math by incorporating skew. But if Bill Chen et al. don't feel it's worth the trouble I'm probably not going to look into it until I have a lot more spare time.
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#46
08-09-2007, 12:11 PM
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Re: Ribbit\'s Edits
I just did a quick check of my last 25k PLO 50 results. I have a skew of about 2.1, which is significant (normal should be zero) but not so bad that it makes the above theory terrible.
Pearson distribution!
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#47
08-09-2007, 12:35 PM
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Re: Ribbit\'s Edits
[ QUOTE ]
I just did a quick check of my last 25k PLO 50 results. I have a skew of about 2.1, which is significant (normal should be zero) but not so bad that it makes the above theory terrible. [/ QUOTE ] I disagree. The approximation and standard winrate analysis is so terrible so as to not be useful at all, especially for winning (or losing) players.
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#48
08-09-2007, 01:04 PM
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Re: Ribbit\'s Edits
[ QUOTE ]
I think your (accepted) analysis is pretty wrong. It would be like a cop standing by the side of a 16 lane highway during rush hour watching 2,000 cars go by an hour and trying to guess what the average speed of the cars will be on Sunday at 2pm. The distribution of hand results is far from normal. You have essentially three major sets of results. Big net wins, big net losses, and a lot of results around zero. [/ QUOTE ] This is true but I have a theory that is very useful and accurate for statistical analysis of all sorts, it says that all random distributions are normal or should be treated as so.
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#50
08-09-2007, 02:54 PM
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Re: Ribbit\'s Edits
I still think it's not as bad as you're suggesting Troll.
The big swings we're worried about will happen when we get into a bad run losing a lot of big pots in coin flip type situations. If we just focus on these big pots, we should see something approximating the binomial distribution, which is well approximated by the normal. So the question for me is, does the SD calculated for every hand accurately model the SD of the big pots? It should be fairly obvious that the SD in poker is highly dependent on the frequency and size of large pot events. As such, I think it's a reasonable parameter to use. Furthermore, it's fairly well established that SD is relatively easy to estimate. Not exactly a rigorous argument, I know. Later on tonight I will go over my last 25k PLO 50 hands and see if the big pots match up with a binomial distribution well.
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