The game you describe: (6 deck, Hi/Lo,75%pen,s17) is very weak, look elsewhere for greener pastures.
You do not say what your BR is in units, nor the type of betting you are using.
From page 200 of Blackjack Attack:
If you have a 800 unit bankroll, spreading 12-1, your risk of Ruin is about 13.5%. Your win per 100 hands is 1.06 units. Thus, to win 800 units will require about 75,000 hands. For a 15-1 spread, the number may be in the 70,000 range, since 15-1 is not that much better than 12-1. But let's stick with 12-1, since I have that number at hand.
Note, this is only a 800 unit bankroll with a large ROR. For a practical bankroll so that your ROR is 5% (which is the number you indicated), you will need a bankroll of about 1200 units, so... (drumroll) this will take about 110,000 hands.
6times a day. So thats 240 hands/day. Assuming it requires 75,000 hands to double a BR of 800 Units, I have to play 312 days. It is
important for me to know this. Because of making a living of it, you should make at least 20,000 dollar a year!
There's a distinct problem with the formula presented. If I am reading it correctly, you are basing the final figure of 110,000 hands on a 12-1 spread.
There is very little to no chance of spreading 12-1 without getting barred from every good game in town (or every game) long before you get anywhere near 110,000 hands. On paper, this sounds all fine and well, but the reality is that consistently spreading 12-1 is a pipe dream.
With an 800 unit bank and using a 1-15 spread it is impossible to be 95% certain you will ever double your bank. The reason being is you are at a high risk of ruin (about 25%), therefore the best you can do is have an 80% chance of hitting your target after 300,000 hands. Even if you play infinitely your 80% chance of doubling the bank will remain constant. You simply do not have enough units in the bank to achieve a 95% assurance.
I was just beginning to think about the equation when I read the other answers. The Mayor's answer basically gives N0, which is when you have an 84% probability of being on the plus side of zero. This is a far cry from a 95% probability of doubling the bank or better. If the number the Mayor gives is correct then he will have a 50% chance of doubling the bank after that number of rounds. BJRM can answer this question given the w/rnd and SD/rnd. If it doesn't answer it directly it would take only a few iterations of guesses to zero in on the correct figure in the trip stats section.
resizing of bets is only "growth" optimal. It is not optimal for minimizing the long run index and actually increases it. Instantaneous resizing of bets perfectly would require you to play 4X as many hands to reach the same confidence level.
Your sim shows a win of 2 per 65 hands or .0308, and an SD per 65 of 46/sqrt(65)=5.076. So you get a DI of .0308/5.076*1000=6.06. Not very good.
For 95% confidence you need (EV - 2 x Stdev) > initial bankroll.
That looks right and with your sim information someone should be able to solve it directly. It is not actually 2SD confidence you are looking for, though, which would be about 97.5% confidence. 2SDs take in 95% of the distribution with 2.5% falling on either side. I belive you want about 1.65 SD certainty.