[irchans]

Standard deviation is a measure of how far numbers differ from average.

Examples.

1. Consider the list of numbers {17,17,17,17}. This rather boring list of numbers has an average of 17 and none of the numbers differ from 17. The standard deviation of this list is 0 because there is no variance in the list.

2. Consider the list of numbers {15,17,17,15}. This list has an average of 16. All of the numbers differ from the average by 1 so the standard deviation in this case is 1.

3. Consider the list {1,2,3,3,4,5}. Now the average is three. When I first learned the term standard deviation, I expected the standard deviation of this list to be one because, on average, the numbers differ from three by one. The actual standard deviation is 1.3 if you use the formula, so just notice that it is approximately, the average deviation from the average.

Applied to poker, standard deviation measures how much your hourly results differ from your average hourly results. So if you have a win rate of 1 BB per hour and a s.d. of 10 BB per hour, then typically, each hour you win between -9 and +11 Big Bets.

The nice thing about knowing your hourly standard deviation is that you can determine your bankroll requirements, risk of going broke, amount needed to play for a few hours, probability of being cheated, and size of draw downs with simple formulas all using standard deviation.

Hope that helps.