Poker Variance

by Jesse Knight


Poker Variance
Variance - The difference between your short term results and long term expectation.

Using probability calculations, statisticians can predict with some degree of accuracy the probability of events occurring over the long run. Consider this: If you play poker regularly, at the end of your life you will have flopped tens of thousands of flush draws (possibly more). Given the sample size (10,000’s of hands), we can say that it is extremely likely that you will have completed slightly less than 40% of the draws you have taken to the river. We can also say, with some degree of confidence, that other players with a similar sample size will have a completion rate that is almost identical to yours. Notice that I used the terms “extremely likely,” and “some degree of confidence.” I cannot be 100% sure about your lifetime flush completion rate, because I am making a prediction about the future. Would it be possible to take 100,000 flush draws and miss them all? Sure! But the odds against it are so long that it would be unlikely to occur once over a period of trillions of lifetimes. You can see that probabilities can be used to accurately predict expectation over the long run. And you can use this information to make more effective decisions. For example, if we project our flush draw calculation forward in time, probabilities can tell us that if a player flops a flush draw, and they draw to it until the river, their completion percentage will be slightly less than 40%.

This is all well and good, but when it comes to predicting the results of specific outcomes, statistical analysis is useless. If I flop a flush draw, the laws of probability tell me my probable completion rate over the long run. But they also tell me nothing about what will happen on this specific occasion. I may make the flush or I may miss it. In fact I may miss five flush draws in a row for a short term completion rate of 0%. Or I may make five flush draws in a row for a short term completion rate of 100%. The difference between my long term expectation and the results that I realize in the short run (in this case 0% or 100% completion), is called variance.

Variance is natural and unavoidable, and is more prevalent with smaller sample sizes. If my sample size is only one flush draw, I must either make it (100% completion) or miss it (0% completion). As the sample size grows, variation tends to diminish. If I take 100 flush draws, I will make some and miss some others, but my variance will be less extreme than it was when my sample size was only one. So, the larger the sample size, the less variance you will tend to experience.

What does this all mean? It means that if you are a poker player, you must be prepared to deal with variance. If the variance is favorable, and you experience a winning streak, it is no problem. However, if the variance is unfavorable, and causes a losing streak, its impact can be profound. This is why you must have a proper bankroll in order to stay in action. It is protection against unfavorable variance.

If you experience unfavorable variance, you can do one of two things. First, you can ignore it and play your way through it. You can be confident that in the long run you will encounter favorable variance that will offset the current unfavorable variance you have been experiencing. This is your best option, provided your bankroll is large enough. Your second option is to attempt to mitigate unfavorable variance through risk management. This means that you avoid marginally profitable situations if they are too risky, so long as you are on short money. Be forewarned, this strategy will have a negative impact on your expectation. It should only be used to protect a short bankroll.

Related definitions: Equity, Expectation

Usage: Poker Variance

Previous Poker Term: Value Bet
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