Since some recent posters clearly understand the "mathematics" of VP,
I've got a idea regarding Variance numbers that I've never seen
anyone else mention. Am I correct?
Lets assume a VP game has a Variance of 25 and a Return of 100%. The
25 represents "25 squared betting units" and the 100% represents the
precent of 1 betting unit (each coin played or the dollar cost of
each game played) returned to the player in the long run, assuming
perfect play.
The square root of Variance is the Standard Deviation. Since the
square root of 25 is 5, the Standard Deviation represents "5 betting
units". The "squared" is dropped when you compute the square root.
In other words, the Return and SD are both directly related to the
same thing ... betting units. One can say that the Standard
Deviation of this game is 5 times the Return, or 500% of the 100%
return.
My point is I've never seen anyone mention the SD of a game can be
expressed as a percentage of the Return. The Variance and Return are
usually represented as two entirely separate things (one a number,
one a percentage), that are unrelated. I'm not talking about a
Normal Distribution here, I'm just playing with these numbers.
It seems to me there is a direct relationship between the Return of a
game and its Variance, if the Variance is expressed as a SD
percentage of the Return.