[BruceZ]

Concerning the number I quoted above as .7734*sigma. I said this was how far above the average you are on average when you are above the average, or how far below the average you are when you are below the average. This is not quite accurate but it is very close. Actually this number is the "median" amount above or below the average. That is, when you are above the average, you will be at least this amount above exactly half the time. For some distributions the median and the average are the same, but in this case they are very slightly different. The actual average distance from the average turns out to be sigma*sqrt(2/pi) = .7979*sigma. This will make the tipping results a little worse. Remember awhile back we also talked about another type of average distance from the mean called the rms average which is exactly 1 sigma.

To illustrate why you will look like cheapskate even though you're not, consider in the above example that you could tip 10% of your expecation by tipping $20 per session only when you win over 2%. Since half the time that you tip you will win over $873, this will be a tip of less than 3% of your net win for the session, and you will likely hear "gee thanks" or some such thing.