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Old 04-07-2017, 02:27 PM   #1
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Am I doing this craps problem correctly?

Ignoring the underlying Don't Pass Bar bet for the moment, a $30 Don't Pass Odds bet has E[X]=0 and E[X^2] = $450, giving an SD of 21.22.

Throwing that into the poker variance calculator, and simulating 10,000 "hands," we get:

10,000 "hands" or bets, assuming 100 bets per hour at the table, implies 100 hours of craps play. The 95% confidence interval is +-424 bets, meaning after 10,000 bets, I will be within 424 bets up or down 95% of the time.

Ultimately I'd like to come up with a formula where I can dial in the SD of the bet, the bet amount, the acceptable risk of ruin, and the number of bets to be made, to get the required bankroll. I know this analysis doesn't quite do it because a line might cross the 95% CI threshold, then cross back inside, but I just wanted to get an estimate of the bankroll required for 10,000 bets or so.

So optically, from the graph, it looks like a bankroll of 500 bets (500*$30 = $15,000) would have a risk of ruin of less than 5% when betting $30 don't pass odds on 4,10 10,000 times. Additionally, $30 don't pass odds bets on 5,10 and 6,8, have lower variance, so this bankroll would be acceptable for those bets as well.

Anyone know how to explicitly calculate risk of ruin on even money propositions when truncating the number of bets that will be made?

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Old 04-07-2017, 09:43 PM   #2
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Re: Am I doing this craps problem correctly?

Here's an old thread discussing it, including a few ROR equations
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