[pzhon]

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B = -(sigma^2/2u)ln(r)

r = exp(-2uB/sigma^2)

where u is your hourly rate
sigma is your hourly standard deviation
r is your desired risk of ruin
B is your bankroll

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If I look at this, it seems to indicate that the bankroll requirement to avoid ruin is independent of the level you're playing at.

This strikes something that cannot possibly be correct.

What am I missing?

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The main thing is that your win rate u is not a constant. It depends on the level you are playing. Slightly less importantly, your standard deviation sigma also depends on the level. For many people, the desired risk of ruin depends on their level, too: Losing your entire balance may be no big deal if you play for spare change at $1-$2, but it may be devastating if you are feeding a family at $15-$30.

Exactly how your win rate depends on the level would be interesting to determine. I've been assuming that there is a bit less than a 1 BB/100 drop for each step up, starting with $2-$4, but I don't have enough data to verify that.