[TNixon]

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You need to focus on a reference point . The formula tells you the probability of dropping 20 buy-ins if you start off with 20 buy-ins .

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You need to STOP focusing on the reference point. The reference point is moving, and the effects are cumulative per hand.

I start with 20 buyins and a winrate/std dev sufficient for a 1% RoR. From the first hand on, my chances of ever going broke are 1%. If I win the first hand, then my chance of going broke from that point on is smaller than 1%, but my chance of losing 20 buyins at some point is still 1%. If I win the second hand, my total RoR drops, but my chance of losing 20 buyins from that point is still 1%. RoR drops over time, but the chance of dropping 20 buyins remains the same.

You're trying to compare two values that have absolutely no relationship whatsoever, and say that one "has" to be lower than the other. It doesn't have to be lower at all.

If you were able to play an infinite number of hands in one month, there is a 100% chance that at some point, you would have a 20BI downswing that would not bust you. For *some* number of hands less than infinite, there's a 50% chance that you will have a 20BI downswing that doesn't bust you in a single month.

A 50% chance of having a 20BI downswing in a single month is clearly a whole lot bigger than our entire 1% probability of going broke from now until the end of time.