Expectation and Variance

Statistics — Third Secondary

Expectation in games and decisions

Expectation is used to find the expected gain or loss in the long run.
If the expected gain of the player is positive, the game favours the player.
If it is negative, the game favours the organiser.
If it is zero, the game is fair.
Note that a negative expectation does not mean that the player loses every time; it is the long-run average.
The standard deviation in such cases tells us how much the gain fluctuates around its average, that is, how risky the game is.

Expectation and Variance · 4 / 7