martidani: ROR equation for high % advantage games

[martidani]

Don -

Does the ROR equation found in BJA breakdown for games with high advantage? For example

BJ with 7% advantage
BJ with 10% advantage

Card games with 3.5% advantage
Card games with 17% advantage
Card games with 37% advantage

I used the BJA ROR formula for a card game with 3.5% advantage, and the numbers where almost identical to J Morgan's. So the question, would using that ROR equation be accurate for games with 10% advantage? What about 37% advantage?

thanks,

marti dani

[Don Schlesinger]

> Don -

> Does the ROR equation found in BJA breakdown
> for games with high advantage? For example

> BJ with 7% advantage
> BJ with 10% advantage

> Card games with 3.5% advantage
> Card games with 17% advantage
> Card games with 37% advantage

> I used the BJA ROR formula for a card game
> with 3.5% advantage, and the numbers where
> almost identical to J Morgan's. So the
> question, would using that ROR equation be
> accurate for games with 10% advantage? What
> about 37% advantage?

Interesting question -- one which I've never been asked before. Here's a quick test. I'm not sure if getting the right answer will confirm that the formula is good for any edge, but it might help: put in an advantage of 100% and see if it makes ROR zero. :-)

Don

[martidani]

> Interesting question -- one which I've never
> been asked before. Here's a quick test. I'm
> not sure if getting the right answer will
> confirm that the formula is good for any
> edge, but it might help: put in an advantage
> of 100% and see if it makes ROR zero. :-)

> Don

The equation is breaking down for any advantage over 30%. The excel spreadsheet just gives me an error, even if I put 1 unit as the bankroll. I don't have the equation in front of me, or else I could try and take the limit. I was mainly interested in BJ games with 7 to 10% advantage, so I am assuming the equation is still somewhat accurate for those advantages. I guess for games over 30% advantage I really shouldn't be worrying about ROR

marti dani

[Don Schlesinger]

> The equation is breaking down for any
> advantage over 30%. The excel spreadsheet
> just gives me an error, even if I put 1 unit
> as the bankroll. I don't have the equation
> in front of me, or else I could try and take
> the limit. I was mainly interested in BJ
> games with 7 to 10% advantage, so I am
> assuming the equation is still somewhat
> accurate for those advantages. I guess for
> games over 30% advantage I really shouldn't
> be worrying about ROR

Well, here's what seems to happen from a limit perspective. The ROR = 1/[e^(2EB/V)], where E is the EV, B is the bankroll, and V is the variance.

So, if your edge were 100%, the variance would be zero. If we allow the denominator of the exponent to which e is raised to tend to zero, that makes the power infintiely large, which in term makes the reciprocal (the ROR) tend to zero, which is correct.

Similarly, if we were to make the bank infinitely large, the same thing would happen.

Does this help at all?

Don