bankroll concepts - risk of ruin

[ryanj247]

if i assume a given win rate and standard deviation, then the larger my bankroll, the lower my risk of ruin, correct?

by the same token, if i require a y% risk of ruin, then I need a $x bankroll.

now, let's say i run the calculation and fund a BR with the required $x for a y% risk of ruin, and head to the tables. suppose i lose money in the first month: is my risk of ruin now higher than it was when i started?

if so, then isn't a BR formula basically saying "you need a $x bankroll to have a y% RoR (given the WR and SD), unless you ever (i.e., initially) run bad enough that your BR drops below $x"? that is, if you lose in the first month, you should be prepared to replenish your bankroll to the starting amount to maintain a y% RoR going forward?

i'm having a hard time matching that line of thought to the idea that a BR calculation gives a definitive, "one time" amount that should be enough to withstand swings and avoid going broke all but y% of the time.