StdDev/Probability question:

I was curious how to do the math for the following problem, which I am sure will help me with similar questions in the future.
I want to know:
At what number of hands will 1% of players with a theoretical (-1BB/100) and a standard deviation of 30BB/100 still be winning?

I know similar questions have been covered in the past, but I need more of a walk through on how to solve this.
Thank you, and Good luck.

[BruceZ]

[ QUOTE ]

I was curious how to do the math for the following problem, which I am sure will help me with similar questions in the future.
I want to know:
At what number of hands will 1% of players with a theoretical (-1BB/100) and a standard deviation of 30BB/100 still be winning?

[/ QUOTE ]

1% of players will have a win rate at least S standard errors above average, where from Excel, S =NORMSINV(99%) =~ 2.33. We need S standard errors to be > 1 bb/100 to be winning. The standard error is 30/sqrt(N/100), so

S*30/sqrt(N/100) > 1

N < 100*(S*30)^2 = 487,070 hands.

Thank you very much for the quick answer. Unfortunately, I didn't really understand it.
Is it possible to give a walk through?

[BruceZ]

[ QUOTE ]
Thank you very much for the quick answer. Unfortunately, I didn't really understand it.
Is it possible to give a walk through?

[/ QUOTE ]

That was a walk-through. I hardly know what else to write. I went back and made it an inequality, so that any number of hands less than this value will have at least 1% winners.

See the explanation of this similar problem for a walk- through of the thought process. Here is another one. Let me know if you have any questions.

That's exactly what I was looking for... Thanks!