Bankroll Considerations

[uphigh_downlow]

I'm just trying to seek confirmation on this.

Wonder if there is more to the picture. I think an example might illustrate my question better.

Lets say I place a bet 'b' on a game repeatedly.

And as per my average returns and variance(unknown at this stage), I have somehow magically determined that an appropriate bankroll for this kind of venture is 'BR'

However I dont have enough money to meet the bankroll requirement.(Again meeting the bankroll requirement is a pretty hazy term in itself). But hopefully we can take it at face value. And assume that it is a meaningful statement. Lets say, its something that gives me a 99% chance of not going broke ever.


Anyway my dilemna is that I only have an amount X, which is below BR

However I decide to take a chance that I wont go broke before I can turn a profit and decide to gamble anyway.

A few fine days later, I have managed to turn a profit and I now have the exact amount to meet the bankroll requirement.

Can I now feel better, assuming that I'm safe, as if I never played that game before and am making a fresh start with the appropriate bankroll.

Does the fact that I have had good days not mean that I'm probably going to have bad days soon, which would mean that I cannot really feel safe?

Now if we replace this "game" with
a) SNGs
a) Ring game at $blah buyin

etc etc

Does the independence of the result of each bet still hold??
Is independence a safe assumption, or are there reasons to believe there might be corelation.

Also assuming that I started with X, what is the probability that I bust out before I reach BR?