Statisticians: Bankroll and Certainty

[Abbaddabba]

As I understand it, the number of BB's you have in a bankroll represents a given level of N whereby there is an associated level of certainty that a (typical) winning player won't go broke on account of chance. It's basically a simple issue of confidence intervals, where you need to know the standard deviation of limit poker in order to evaluate certainty for given levels of N (big bets in this case).

I'm aware of the commonly cited figure of 300BB's being an adequate bankroll for limit poker. What I'd like to know is what level of certainty that represents. I want to know precisely how risky it is to play beyond a limit where i have 300BB's (or rather, that im willing to lose).

Im not sure the question is entirely clear or how you would apply the information to the standard confidence interval scheme. If anyone could help it would be appreciated.

[pzhon]

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What I'd like to know is what level of certainty that represents. I want to know precisely how risky it is to play beyond a limit where i have 300BB's (or rather, that im willing to lose).

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risk of ruin = exp(-2*winrate*bankroll / stddev^2)

The 300 BB rule of thumb is (mis)applied to contexts with different win rates, so it does not represent a particular risk of ruin. Someone playing unraked microlimits with casual players may win 10 BB/100. A marginally winning player may win 0.5 BB/100. A bankroll of 300 BB may represent a very low risk of ruin for the former and a high risk of ruin to the latter.

The standard deviation in limit Hold'em seems to be about 15 BB/100 in full games and about 17 BB/100 in short-handed games.