[TNixon]

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The probability of losing 20 buy-ins in a month must be lower than this number .

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Why?

You could lose 20 buyins after winning 1, and that situation would still not be part of the "ruin" percentage. In fact, I would think the chance of having a 20BI downswing over X hands (for a sufficiently large X) would have to be *higher* than the risk of ruin percentage, and pretty significantly so.

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No , this formula tells you the probability of busting if you play this game indefinitely . There is no simple formula to tell you the probability of busting in x hands .

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We don't care about the probability of busting in X hands. The question is the probability of losing 20 buyins in X hands.