[TNixon]

In fact, given this:

[ QUOTE ]
P(bust in one month) + P(bust after first month ) = P( busting out)

[/ QUOTE ]

For some number of hands, P(having a 20BI drop) is certainly going to be greater than P(bust in one month). That number might be 10k, it might be 40 million, I don't know.

Whatever that number is is irrelevant, because it is quite obvious that the probability of dropping 20 buyins *can* be greater than the probability of going broke in the first month.

And if P(Drop 20BI) is greater than P(bust first month), then it follows that the chance of dropping 20BI over an infinite number of hands *has* to be greater than the chance of going broke when starting with 20BI. Because the chance of going broke per month has to decrease on average, but the chance of dropping 20 buyins per month can remain the same.

In fact, I'll go even a little further with this.

If our RoR is 1%, there is unquestionably *some* number X, where the chance of having a single 20BI downswing is greater than 1%. That 20BI downswing might happen after we've already won a thousand buyins, but if we play enough hands, there will eventually be a point where we're down 20 buyins from a previous point.

But since the chance of being down 20 buyins in a single month can possibly be higher than the chance of going broke sometime between now and the end of time (if we can just play enough hands in that first month), then this:

[ QUOTE ]
It should be obvious that it has to be lower .

[/ QUOTE ]

Is not "obvious" at all, since it's quite clear that it *can* be higher, for a sufficiently large number of hands.

The real question is how large "sufficiently large" is.