Definition of standard deviation
When we talk about standard deviation in poker, we are mostly talking about variance. The variance is basically. the deviations from the mean. For example, when you roll a six-sided die, you have a one-in-six chance of getting any number, and each number will come up one in six times. But out of six rolls, you will not necessarily get 1-2-3-4-5-6. You may well get 2-2-5-5-5. Here, the 2 and 5 are over-represented and the numbers 1-2-4 and 6 are under-represented. This is called variance. The more often you roll the die, the less variance you will have.
Standard deviation and variance in poker
Variance in poker manifests itself in many ways. It can be the frequency with which we receive preflop aces that are too low on a good sample of hands, it can be the frequency with which our opponents hit brelans when we have a pair of aces, it can be the over-representation of unplayable hands like 27o, variance has many faces. It is part of the game, it is the beauty of the game for better or for worse. But remember that the average will always be respected in the long run. Variance is an illusion to which human beings are sensitive, but it is not rational to make a big deal out of it when it hits us head on.