I messed up my example a little, I meant a drawing of 1 billion tickets, where all tickets return $1, except for one that returned $1.7 million.
···
From: "Part Timer" <PartTimeVP@hotmail.com>
>From: bjaygold@aol.com
>
>I believe that the variance number can be used "directly" when calculating
>ROR (risk of ruin) bankrolls. That is, ROR bankroll is directly
>proportional to
> variance. Is this not so?This is not so.
If the possible outcomes for a game adhered perfectly to a normal
distribution, then you could use variance in the ROR calculation, but you'd
really be making a substitution.Since video poker hand outcomes do not follow a normal distribution, at best
what you get when you use variance in a ROR calculation is an approximation.An easy proof that variance cannot be used to determine ROR is to construct
a game where all hand outcomes are neutral or positive, but has a low %
return and high variance. For instance, create a game where you pay $1 for
a lottery ticket, there are 1.7 billion lottery tickets, and all tickets but
one return $1, and that one ticket returns $1 million. This game has a
return of 100.17%, and a high variance, but the risk of ruin playing this
game is 0% for any bankroll of 1 bet or more.
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