matt21 said:
is that the right formula?...
That's fine - the denominator can be in whatever you want to be in - in your case you like "shoes" as the denomiator and choose to express things with a unit of a "shoe" lol.
Even simpler (for one game) is simply (22/0.63)^2=1219 shoes.
Using variance, as u do in your formula, is useful for "blending" alot of different games since it is additive.
I think you "gots it" lol.
As far as "Does it need to be looked at in conjunction with ROR?", not really in my mind anyway, as N0 will always occur after a specific period of time whether one's roll is 1000 units or 1000000 units. It's just that with more units in a roll, the chances of still being around when N0 occurs increases compared to a roll with fewer units.
I don't know, as far as BJ Avenger said, DI and SCORE seem to always be expressed in $'s rather than units. SCORE, being the square of DI, just makes it easier to compare how much better one game is vs another. It may not be immediately apparent that a game with DI of 7.07 is twice as good as a game with a DI of 5. (Whatever ratio=the square root of 2).
If betting optimally, N0 will be the lowest that N0 can be for that game (I think) and SCORE and DI will be the highest it can be. In effect, the ratio of SD/whatever to EV/whatever (units/hd/hour/shoe or even, maybe $'s) is maximized.
