Definition of standard deviation
When we talk about standard deviation in poker, we'll talk mostly 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 once out of six. But out of 6 rolls, you may not necessarily get 1-2-3-4-5-6. You might very well get 2-2-5-5-5-5-5. Here, 2 and 5 are over-represented and 1-2-4 and 6 are under-represented. This is called variance. The more often you roll the dice, the less variance there will be.
Standard deviation and variance in poker
Variance in poker manifests itself in several ways. It can be the frequency at which we receive preflop aces that is too low on a good sample of hands, it can be the frequency at which our opponents hit three of a kind when we have a pair of aces, it can be the over-representation of unplayable hands like 27o, variance has many faces. It's part of the game, it makes it beautiful for better or worse. But tell yourself 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 hard.