Poker Bankroll Management – Variance and Standard Deviations (2 of 5)
Variance, according to Wikipedia is: In probability theory and statistics, the variance of a random variable or distribution is the expected, or mean, value of the square of the deviation of that variable from its expected value or mean.
I know most people are probably saying, “WHAT???” or “Come again?” But I will explain why you need to know this technical jargon, and its importance at the poker tables. The answer is quite simple; as a poker player, formulating your bankroll requirements hinges on your understanding of variance, and standard deviation.
Variance: In poker variance is the distribution of your results over a set period of time –sessions, hours, weeks, hands, or years. Variance will also show your swings, both good and bad. The less of an edge you have, the higher the variance: The higher your edge the closer the results will be to your average. By taking the extreme high and low mark you will get your variance.
The most basic example of variance is the coin flip: If you were to flip a coin 20 times the odds say you will get 10 heads and 10 tails. However, this is the average over a large sample size, over the course of any 20 flips you could get any number of results: The actual odds of getting precisely 10 heads and 10 tails is only 17.6%! However, it’s possible to have 20 heads or 20 tails in a row!
Standard Deviation: Standard deviation is a way to measure the likelihood of possible outcomes based on certain data. Standard deviation measures how widespread your results can be considering what your average results are. The standard deviation is the simply the square root of your variance: If your variance is 100, your standard deviation is 10.
Suppose you play $.50/$1 NLHE: If you were to chart your win-rate over 10 online poker sessions of 300 hands –where you won a total of $330– from best to worst it would look something like this:
poker variance
Your average win is $33.00 per session, but your wins and losses are all over the place, in fact your variance is $300 (a low mark of -$100 and a high mark of $200). Based on your results, over the course of 10 sessions you could win as much as $200 or lose up to $100. Obviously, 10 sessions isn’t a large sample size, but suppose each bar of the graph represented 100 sessions. Now suppose you want to know your chances of maintaining your $11/100 win-rate with a 95% accuracy.
With these numbers your win rate could fluctuate between $15/100 and $8/100 over any 100 sessions, but over 1,000 sessions will be between $10 and $12/100, and over 5,000 sessions will be between $10.50 and $11.50/100.
Basically, the higher your variance, and standard deviation, the higher your bankroll requirements will be. This is why many players will give up some smaller edges, or play in a less risky game that offers less profit, in order to cut down on their variance. For more on what types of games, styles, and other factors play into variance continue on to Part 3 of this series.
Author: Alex Galin
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