Risk of ruin formulas for kelly betting: Variance does not matter?

[ThodorisK]

http://74.6.239.67/search/cache?ei=U...icp=1&.intl=us

Check the formulas for risk of ruin for kelly betting (go down to the "Drawdown formulae" chapter of the above link) It says that variance and edge do not affect the risk of ruin probability to lose a times (where 0<a<1) your starting bankroll and that it depends only on k (i.e it depends only on whether you bet full or half or quarter etc kelly). Is this correct? I find it difficult to believe that blackjack (when card-counting) has the same risk of ruin with e.g. a +EV Jacks or Better game where the royal pays e.g. 1200 instead of 800.

Any links with risk of ruin formulas for kelly betting? Doesn't the wizard of odds give any?

[QFIT]

You can find many RoR formulae in Blackjack Attack. Or you can use the calculators at http://www.card-counting.com/blackjack-calculators.htm.

[ThodorisK]

Read chapter 2.1 and 2.2 only.

I cannot find any calculator in the link you gave me for kelly betting. I Think they all refer to flat betting.

[QFIT]

Chaptger 8.

All the calculators work for Kelly. The betting is built into the variance and EV numbers that you input.

[ThodorisK]

I got it now. The risk of ruin formulas for kelly betting which seemingly ignore variance, do not really ignore it, since variance is already included within the "k" factor, since: (kelly bet) = (kelly bet if variance was 1) / (variance), or (kelly bet)= ((payoff)(probability to win a bet)-1)/((payoff)-1), etc.

But now I want a link with the proof that:
(kelly bet) = (kelly bet if variance was 1) / (variance)
Because I doubt that this formula is absolutely accurate, and I fear that it is a rough approximation which just wants roughly to take in account variance, and thus I doubt that it is more accurate than the formula (kelly bet)= ((payoff)(probability to win a bet)-1)/((payoff)-1, and I even doubt that it is more accurate than the formula: (kelly bet) = (kelly bet if variance was 1).

I do not want the proof which shows that: (kelly bet)= ((payoff)(probability to win a bet)-1)/((payoff)-1).
I already have this proof, and it is obvious that this formula is more accurate than the (kelly bet) = (kelly bet if variance was 1), but it is not the perfectly accurate formula for the case of blackjack. Because the payoff is not the same for every won bet, as the won bets of doubles/splits/blackjacks have a different payoff than the rest of the won bets. I guess the perfectly accurate formula gives a smaller value for the kelly bet than the formula (kelly bet)= ((payoff)(probability to win a bet)-1)/((payoff)-1). Anybody knows the perfectly accurate formula and its proof?

[Sonny]

Originally Posted by ThodorisK

But now I want a link with the proof that:
(kelly bet) = (kelly bet if variance was 1) / (variance)

But it’s not. Kelly = Egde/Odds. The Edge is the average win, which includes all possible payouts. It does not assume that the variance is 1. Maybe this thread will help:

http://www.advantageplayer.com/black....cgi?read=6623

-Sonny-