Question re: heads-up NL winning %ages

[cognito20]

Hello:

I was wondering how to go about doing the following calculation. I have been playing a lot of heads-up no-limit SNGs recently and have a record so far of 69-40 (.633 winning percentage). What I would like to know how to calculate, to get a better grip on where I really am, is the probability that a certain winning percentage, achieved over a given number of trials, is the result of chance. In my particular case, for example, what is the probability that a .525 player (break-even) can have a .633 winning percentage over 109 matches? Do I need more information, such as the standard deviation for these matches, or can I do the calculation with what I have? Thanks for your help.

--Scott

[jay_shark]

The probability that a .525 player can have 69 wins in 109 matches is 0.525^69*0.475^40*109C69 = .00593...

All this means is that it's unlikely you win exactly 52.5% of your matches . You may still be a losing player but there is a decent chance you're also a profitable player .

Here is a useful rule to remember .

If you wish to be within x% of your sample win rate at a 95% confidence level after n games , then you need n=(1/x)^2 number of games .
So if you wish to be within 5% of your sample win rate , you need (1/0.05)^2=400 games .

If you wish to be within 2% of your sample win rate , then you need (1/0.02)^2=2500 games .

[pzhon]

[ QUOTE ]
In my particular case, for example, what is the probability that a .525 player (break-even) can have a .633 winning percentage over 109 matches? Do I need more information, such as the standard deviation for these matches, or can I do the calculation with what I have?


[/ QUOTE ]
If your true win rate is exactly 60%, the probability that you would win precisely 60% out of a million matches would still be very low, although it would be higher than the probability that you would win precisely 600,001.

The usual question to ask is what the probability is that you would see a result that extreme or more, which in this case can be interpreted as winning 69 or more matches out of 109. If your true win rate is 10/19 = 52.6%, and your results are independent (no tilting or learning, for you or your opponents), then the probability you win 69 or more matches out of 109 is about 1.6%. The usual interpretation would be that you have strong evidence that you are not a losing player.

You have to be careful that this may be biased by the decision to carry out the analysis now. If you chose to play for a month, and then analyze your results, that is different from tracking your results continuously and analyzing them when they seem extreme. If you look at your results after 10 matches, after 100 matches, after 1000 matches, etc., then these are almost independent opportunities to see a rare event, which means the event is not as rare as it appears.