i dont think that your method of using a target of doubling the BR is bad, however, but i feel like that gives somewhat of a skewed result.
i think my version of ROR is.
it all has to do with hands played. The Standard deviation will be higher for MORE HANDS played than for LESS hands played. obviously the standard deviaton across infinity hands will be infinity, so using your target of doubling BR is a good way to make this problem finite.
i will walk you through my math so that you know where im coming from.
assume your bankroll is $10,000 and your average bet is 50 dollars. As an AP you have a "general" advantage of 1%, so for each hand we play, we have an expectation of profit of 50 cents. Therefore we need to play 20,000 hands to achieve an expected profit of $10,000.
20,000 hands in a year is about 6.5 hours of play per week (at 60 hands/hour)
This 10,000 will be the MEAN point of a normal distribution chart (that we will talk about later). Please remember that the more hands you play, the higher this mean is. If you play zero hands, your Mean will be Zero. If you play 100 hands your mean will be 5 bucks.
the next step is calculating a standard deviation for this particular player with bankroll $10,000. this is where you mix a little bit of art with science.
The equation i use to calculate STDEV is (square root of hands played) x (average bet) x 1.1
i use 1.1 becuase that is what Don Schlesinger says is the standard devation in units per hand of blackjack.
to find average bet, i assume something between TC 1 and TC2 bet. (note, i still assume a small bet for TC 1, like 1 or 2 units, because there's not actually player edge at those levels)
the STDEV for the player above should be $7,778.175 ~~ $8,000. so after 20,000 hands, if he has 1 standard devation of negative variance he should have a bankroll of $10,000 + (10,000-8000) = 12,000. Two standard devations of negative variance and he would have a expected remaining bankroll of $4,000.
Now if you start with an expectation of zero (i.e. zero is the mean, not 10k) it would only take about 1.25 standard deviations of negative variance (across 20,000 hands) to wipe out the original 10k. 1.25 stdev on the normal distribution chart covers about 75% of the probability (accounting for positive AND negative variance). So accounting for only negative variance, that means that a 10k bankroll with this kind of stdev has a 12.5% ROR.
