Quote from: a1choi on June 05, 2014, 09:04:05 AM

makes lots of sense. i guess the best way to calculate risk of ruin is to go through a bernoulli process then. Assuming a reasonal bankruptcy point > 0. maybe 30-40% of original bankroll. since going to 0 would be infinite time.

Maybe consider the risk of losing half the bankroll - a kind of a 'half life' thing.

Also, what if someone came with enough coins to bet the maximum at 98% over and over. Each time they have a very good chance of winning 0.5% of the house bankroll.

If they win 138 times in a row, they've won half the bankroll, and they can do so with 6% chance:

>>> 0.995 ** 138 = 0.5007
>>> 0.98 ** 138 = 0.06154

If the max profit per roll was a full 1% of the bankroll, they only need to win 69 times in a row, and they can do so with 25% chance:

>>> 0.99 ** 69 = 0.4998
>>> 0.98 ** 69 = 0.24808

So by cutting the max profit from 1% to 0.5% we've made it ~4 times harder to win half the bankroll by max-betting at 98%.