N would be the number of hands and the “variance of the sum” would be the sum of the variances of all the outcomes.įor example the variance for a single fair coin flip is 0.25. Variance of the mean result after N hands = (1/(N squared)) * Variance of the sum What youre looking for is the standard deviation for the mean. The standard deviation for a single outcome is always constant. StdDev(evBB/100) is at most 28BB/100 lower than StdDev(BB/100), on average not more than 19BB/100 lower. Meaning: We can compare this with the numbers above for Games with 6 players.
Median Standard Deviation for hands without an all in & showdown: 67. Hands without all in & showdown: 3,058,874 Only 29k of those (0.9%) had an all in before the river and a showdown.Īgain I filtered for all player with at least 1k hands and removed all hands with all in before the river & showdown. In my database I have 3.06 Million hands (NL100) with 5 or 6 players. At least this will show the maximum impact all in hands have on the standard deviation. Unfortunately, PokerTracker doesn’t have a StdDev(evBB/100) readily available.īut I think we can get a decent approximation when we just remove all hands with an all-in and call before the river when calculating the standard deviation. Go into detail regarding the standard deviation when looking at evBB/100 is a bit tricky. Those are the standard deviations the players in my database had:ĩ5% Interval means that 95% of all players had a standard deviation between those two values.Īs you can see, standard deviation doesn’t change much between 9 player games and 6 player games.Įdit : This didn’t really answer your question though. (Regular cash game, not fast fold.) I filtered for number of players and removed all players with less than 1000 hands. I just went through my database with a couple of million cash game hands to get some detailed numbers about the standard deviation of all players in the database. More aggressive players tend to have much higher SD/100 than super tight players. Standard Deviation heavily depends on your play style. Should you have any questions, encounter any errors or have ideas for improvements, please let me know. In general these simulations underestimate the extent of downswings, but the numbers should still give you a decent idea of the vastness of downswings you should expect. Meaning, by this definition a downswing is not over until the player has fully recovered its losses. For the purpose of these calculations a downswing is defined as any period where the current total winnings are below the maximum previous total winnings. For example (50000+ Hands – 15.81%) means the simulated player was in a downswing over at least 50,000 hands 15.81 percent of the time. For example (1000+ BB – 31.77%) means the player was in the middle of a downswing of at least 1,000 big blinds 31.77 percent of the time.The second table shows how long downswings last on average. It shows how often the simulated player was stuck in a downswing of at least X big blinds. Therefor 100 million hands are simulated and all downswings over this simulation are tracked.The first table shows the extents of downswings. Minimum bankroll for less than 5% risk of ruin: the bankroll needed to have a risk of ruin of less than 5%ĭownswings in numbers The last section of the Variance Calculator sheds some more light on potential downswings. 
Probability of running below observed win rate …: Same as above – probability that you will experience a run below the observed winrate over the amount of hands.Probability of running at or above observed win rate …: If you entered an observed winrate, this number will show you the probability that you will experience a run at or above this winrate over the amount of hands.Probability of loss after X hands: probability that you will experience negative winnings (meaning: losses) over the amount of hands.Meaning: 19 out 20 times your actual winnings will be within this interval.
95% confidence interval: Same as the above with 95% certainty.The first interval shows absolute numbers, the second translates those into BB/100, showing the 70% confidence interval for your winrate. 70% confidence interval: Your actual results over the simulated amount of hands will be within this interval 70% of the time.The first number shows the absolute value, the second translates this number into BB/100, showing the impact on your winrate.
Standard deviation after X hands: This number shows by how much your actual results will differ from the expected results on average. Expected winnings: estimated winnings over the simulated amount of hands. 
Standard deviation: standard deviation entered above.Variance in numbers Below the first chart the Variance Calculator compiles a neat list of additional information:
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