Re: Standard deviation
If you won or lost exactly the same amount every hand, your standard deviation would be zero. If your wins and losses fluctuated wildly, your standard deviation will be large.
DrVanNostrin gave you the mathematical formula for computing standard deviation. A somewhat simpler formula that is sometimes used instead of standard deviation is mean absolute deviation. If your average win rate is 2 BB/hour, the mean absolute deviation is the average amount your win rate deviates from 2 BB/hour. So if your results are +3, -4, +7; your average win rate is (3-4+7)/3 = 6/3 = 2. In the first hour you were 1 away from the mean, in the second hour you were 6, and in the third hour you were 5. (1+6+5)/3 = 12/3 = 4. So your mean absolute deviation is 4. This tells you what kinds of swings to expect; a result of -2 or +6 is the expected amount away from your mean. Anything outside that range is a larger swing than average, anything inside that range is smaller.
Standard deviation just squares the deviations before averaging them, then takes the square root of the result. In the example above (1^2+6^2+5^2)/3 = (1+36+25)/3 = 62/3 = 20.67. The square root of 20.67 is 4.55. So the standard deviation is a little different from the mean absolute deviation, but it's a similar idea.
There are two uses of standard deviation. First, it helps you decide how much to trust the average win rate. If you play for 100 hours with a win rate of 2 BB/hour and a standard deviation of 10 BB/hour, you're more confident that you are really a positive EV player than if your standard deviation were 40 BB/hour. In the second case, there's more chance that your win rate was due to luck. Standard deviation allows an exact calculation of that. It relies on some dubious assumptions, but the calculation works pretty well anyway.
The second use for standard deviation is predicting future results. The larger your standard deviation, the larger your expected swings (both good swings and bad ones). A high standard deviation player needs a larger bankroll than a low standard deviation player.
It's a pretty good rule that 2/3's of your results will be within one standard deviation of the mean, and 19/20 will be within two standard deviations.
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