[ryanj247]

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Nobody? Well I was thinking about it.

Let's say you have to play 5,000 hands to clear the bonus, which would mean for you to not clear it your WR would have to be -5 BB/100 hands for you to not comlete it.

SO then the question becomes, what are the chances that a player with a WR of 1.5 BBs/100 hands and a sd of 17 BBs/100 hands runs at -5BBs/100 hands or worse in 5,000 hands.

Now that I think about it I think I have to find the chance that I will never be down 250 BBs during any block of X hands.

Thoughts? Links? Anybody?

Thanks,
Ben

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As a rule of thumb, your risk of going broke sometime during the 5000 hand interval is a little more than twice the probability of being broke at the end of the 5000 hand interval, assuming that you always play that long. On average you should be up 75 BB at the end of the 5000 hands, so being down 250 BB is 325 BB below average. The standard deviation for 5000 hands is 17*sqrt(50), so the probability of being down 325/(17*sqrt(50)) standard deviations is given by the Excel function =NORMSDIST(350/(17*SQRT(50))) =~ 0.34%. So your probability of going broke sometime in the 5000 hands interval is a little more than twice this or a little more than 0.68%. The short term risk of ruin formula from Blackjack Attack by Don Schlesinger gives 0.89%.

NORMSDIST[(-250-1.5*50)/(17*SQRT(50))] +
EXP[-2*1.5*50*250/(17^2*50)]*NORMSDIST[(-250+1.5*50)/(17*SQRT(50))] =~ 0.89%.

So both methods agree that your risk of ruin is a little less than 1%.

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bruce, i'm having some problems here. i'm probably just tired and missing something obvious...

when i run the first formula in excel, i get a different result (i get 99.8%). to get .34%, i have to change "350" to "-325". "-325" seems more logical to me...is that just a typo??

i went ahead with the assumption that it was. i was able to run the 2nd (schlesinger) formula in excel and get the same result of ~.89%.

then i wanted to see what would happen if we kept everything the same except the number of hands. instead of 5000 hands, i wanted to use 50,000 hands.

at the end of 50,000 hands, you should be up 750BB. so being down 250BB is 1000BB below average. so the excel function should be NORMSDIST(-1000/(17*SQRT(500)))*2 = ~.85%. sounds about right.

i tried using the same scenario for the schlesinger formula. it ended up looking like this:

NORMSDIST((-250-1.5*500)/(17*SQRT(500))) + EXP(-2*1.5*500*250/(17^2*500))*NORMSDIST((-250+1.5*500)/(17*SQRT(500))) = ~7.19%.

did i make a mistake somewhere? why such a big difference between the two formulas for a larger number of hands?