Podcast – listener emails

I’ve heard Bob compare the variance of different games in several different podcasts. This is misleading and a standard deviation would be better for his purposes. The standard deviation is just the square root of the variance, but it is the relevant number for comparing the volatility of different games.

Lets say I played a large number of hands in two different games, one with four times the variance of the other. but the same expectation The 95% confidence interval for the distribution of outcomes would be TWICE as wide for the higher variance game, the square root of four, not four. If I have approximately a five percent chance of being 10,000 or more dollars below expectation in the low variance game, then I have approximately a five percent chance of being 20,000 or more dollars below expectation in the high variance game, not 40,000 as implied by a variance four times as large.

In this podcast, Bob claimed that 100 hand quarter VP has 1/10 of the variance of 1 hand 25 dollar VP. This means the 100 hand game has sqrt(1/10) or about 1/3 the volatility of the single hand game.

I remember in another previous podcast Bob talked about comparing 9/6 Jack or Better which has a variance of about 20 to another more volatile game. I don’t remember which game that was but lets imagine it was Triple Double Bonus, which has a variance close to 100. The variance is different by a factor close to five but the volatility difference is just slightly above two.

The term “variance” is more useful as an ordinal concept, one game has more variance than another, while the standard deviation is more directly comparable between different games.