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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
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