[ QUOTE ]
Read
Gambling Theory and Other Topics by Mason Malmuth, particularly the section titled "How Much Do You Need?"
Mason doesn't give this formula outright but if you know a bit of algebra you can pull it out of what he wrote. If
S is your hourly standard deviation -- the square root of the variance your play records show you experience in one hour's play -- and
W is how much you expect to win in one hour's play, then the minimum bankroll you need to play with negligible risk of going broke is:
BR = 9/4 *
S*
S/
W
[/ QUOTE ]
This formula will give a 1.1% risk of going broke due to an issue with the GTAOT derivation (see footnote in new version), and the 9/4 needs to be replaced by -ln(ror)/2 for a general risk of ruin ror. See
Bankroll formulas for an explanation and the correct formulas. Also,
Derivation of bankroll formulas
Tool for bankroll and risk of ruin