Risk Of Ruin

Hello to everyone at BJ Info....

I have a math question that I am struggling to work out regarding risk of ruin (ROR).

I can work out the ROR when playing ONE BOX using this formula:

exp(-2*edge*bank/sigma^2)

But my question is, knowing what the ROR is playing on ONE BOX, how do I then work out the ROR playing TWO BOXES?

Any help would be greatly appreciated.

Sp1N-D1zZy

The Easy Way

Not commenting on the formula you are using.

However, if you bet approximately 73% or 75% for ease of use of your one bet on each of 2 spots you will have the same ror. An example, if your one hand bet is $100 then for 2 bets it should be $73 or $75. If you bet more your ror is higher and if you bet less your ror is lower.

:joker::whip:

Thanks so much for your help!

I have another question:

If I know the risk of ruin for betting, say, max bet $100 on a single box with BR of $20,000 is 0.8%, then how can I work out the risk of ruin for betting $100 on two boxes with BR of $20,000.

If 0.73% is the figure for two boxes, what is the figure for three boxes? And four?

I believe it is 57% for 3 hands. I'm not sure for 4.

Use the following equation:

1.32 / (1.32 + 0.48 * (n-1) )

You can change 1.32 to whatever the variance is for 1 hand at the given count. You can change the 0.48 to whatever the covariance is for your game. n is how many hands you are playing.

If n = 1, it's 100%. If n = 2, it's 73%. etc. etc.

Here's how to derive it:

Optimal Bet Per Round = Bankroll (BR) * Advantage (Adv) / Variance (Var)
Optimal Bet Per Hand = Bet_n = BR * Adv / Var_n / n

Bet_n / Bet_1 = (BR * Adv / Var_n / n) / (BR * Adv / Var_1)
Bet_n / Bet_1 = n * Var_1 / Var_n
Bet_n / Bet_1 = (1.32 * n ) / (1.32 * n + 0.48 * n * (n - 1))
Bet_n / Bet_1 = 1.32 / (1.32 + 0.48 * (n-1) )

Thanks Assume R,

I have another question, as you seem to be the man to ask these things to:

If I have unlimited bankroll, will I make the maximum possible amount of money long term by playing table minimum when I have a negative advantage, and playing table maximum when I a positive advantage? (even if that positive advantage is very slight?

Cheers.

Yes, but there is a big difference between a very large bankroll and an "unlimited" bankroll.

I can't think of a bankroll large enough that would warrant this strategy, but small enough that you would want to be sitting in the casino in order to make more money.

If you have a big enough bankroll relative to the table max, you can certainly do this. It's not that unusual, especially when table maximums are $500 or so, and/or your advantage is big enough.

This will indeed give you the maximum expected return, but your variance and risk will be very high. Thus the huge bankroll.

(Slightly better to bet $0 when there's no advantage, but hey..)

Yes, what the others said.

Also remember that when you bet optimally (not just Min or Max, but values in between), your bankroll will grow fastest.

When you only have a 0.5% advantage, and theres a lot of variance, you don't want to be betting the table max, because if you hit negative variance you will lose table max, whereas if you bet optimally, you won't have lost that much.

If the edge at TC of +4 is pretty high, but there's a huge variance, you don't want to bet your max bet.

Also the more negative hands you play (even at table minimum), the more you have to bet when you have an advantage to compensate.

So optimal bet theory is designed specifically to grow your bankroll at the fastest rate.

Hope that helps.

This is because you are balancing the EV of each bet with the risk of going on a downswing (due to over-betting) and having to lower your bets and hence your EV on future hands.

If your bankroll is infinite, but you are constrained by the table limits, then the "optimal" bet will always be zero/min or the max.

Let's say you do have a large bankroll. Would there be much heat for spreading from the table min at all counts <2 to table max at all counts >=2? They would just see you arbitrarily changing your bet from min to max and not following a progression.

On Large Bets

Large bets draw attention.
Table max bets draw attention.
There is still a pattern in your idea.

:joker::whip:

Sorry to be a pest, but I have another math question I am struggling to solve.

Lets say I work out my optimal staking sizes for each count value for any given bankroll size using the Kelly Criterion for optimal long-term growth. If I want to play 2 boxes instead of 1, what forumla do I use to adjust the optimal staking amounts based on the fact that I want to play 2 boxes instead of 1.

For example, say for a 20k bankroll my stake size based on Kelly for count x is $100 (for one box). For the same 20k bankroll, how do I adjust the stake size ($100) to play 2 boxes, but at the same time achieving optimal llong term growth of the BR?

Thanks in advance.
Spin.

I've solved this now.... Thanks to everyone for their help...

Very good program

http://www.bjrm2000.com/software/one_second_simulator.html