Standard Deviation, again.
 

I have been reading Malmuths "Gambling theory and other topics" last week and started to estimate my bankroll requirements and trying to understand how big a normal losing streak can be.

Malmuth in his book uses 3SD as the meassure. 2SD is with a confidence intervall of 95%. 3SD is 99.73002% (see: http://mathworld.wolfram.com/StandardDeviation.html )

I understand this - that it is 99.73% sure - if we got a finite number of hands, say 100 K hands. But when I play more and more hands (with same SD and same winrate) the risk of having a big losing streak should grow?

If I calculate my bankroll requirements to be 300BB, for how long is this 99.73% sure? As I understand it, this is only 99,73% true for the hands I already played? But my real interest is how big bankroll I need in the future not having to go broke, say, the coming year or the rest of my life as long as my SD and winrate stays stable.

One other problem is the winrate, after 800 hours with same SD and same winrate, my winrate i still WR+-38%, which have a huge impact on my bankroll requirements.