double the bankroll

How many hands do you have to play(6 deck, Hi/Lo,75%pen,s17)to double your bankroll?(1-15spread). I want to be sure for 95%.

And 100,000 hands for 66% probability.

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.

--Mayor

As you say, the figure you give is for a 5% RoR

Steve actually wanted a 95% chance of doubling his bankroll (as far as I understand), which is somewhat more difficult than just avoiding ruin.

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!

You are not going to make a living playing BJ at that game.

It sounds like you are playing at full tables at a crappy game.

If you want to make a living at BJ, you will have to find much better games... which is not even the beginning of the story.

--Mayor

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.

what else can you suggest. I want to point out, that I can not play another game.

... not even given consideration to making BJ your primary source of income if this is the only game available.

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.

on this board are pipe dreamers. No harm in that, unless you actually play the game.

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.

The more time I spend reading the board, the more correct I think you are :-).

Under the conditions described and optimal Kelly betting, I find the returns to follow a normal (gaussian) law with a mean of 2 (on the 1-15 scale) and a stdev of 46 for one shoe (approx. 65 hands).

For 95% confidence you need (EV - 2 x Stdev) > initial bankroll.

This happens after 3000 shoes, i.e. 200,000 hands.

Note: I assumed no resizing of bets when the bankroll varies, which is sub-optimal. You could probably do a bit better.

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.