I`ve found this game where I have an advantage of 0.209% and planning to play 3 boxes 100 bucks each.
No card counting, they use a machine.
What bankroll do I need to take the ROR down to 5% or 2%?
What if the advantage was 0.4%?
Thanks for your time.
> I`ve found this game where I have an advantage of
> 0.209% and planning to play 3 boxes 100 bucks each.
>
> No card counting, they use a machine.
>
> What bankroll do I need to take the ROR down to 5% or
> 2%?
My estimations:
EV = $62.70 per hour
SD = 13.3 units per hour
$380,000 BR = 5.01% ROR
$500,000 BR = 1.95% ROR
> What if the advantage was 0.4%?
EV = $120.00 per hour
SD = 13.3 units per hour
$200,000 BR = 4.9% ROR
$260,000 BR = 1.98% ROR
-Sonny-
> My estimations:
> EV = $62.70 per hour
OK.
> SD = 13.3 units per hour
I got double that. What is your calculation?
> $380,000 BR = 5.01% ROR
Too high. I got about $163,000.
Before we go on, let's see why we diagree.
Don
>> SD = 13.3 units per hour
>
> I got double that. What is your calculation?
I just winged it. I figured that one hand of BJ is usually around 1.33 units, so 100 hands of BJ would be about 13.3 units (assuming a non-counting flat bettor). I didn?t take into account the rule changes for this game which give it a positive edge.
How?d you do it? We don?t know the win/loss ratio so we can?t use the EX^2 - (EX)^2 method, and we don?t know the rules of the game so we can?t simulate it or use the sqrt(x^2/N) for independent trials. I?m sure it?s probably something simple that I overlooked, so feel free to embarrass me. It?s the only way I seem to learn. =)
>> $380,000 BR = 5.01% ROR
>
> Too high. I got about $163,000.
Hmmm. How did you get a much higher SD but a much lower ROR given the same EV?
Thanks always for your help.
-Sonny-
> I just winged it. I figured that one hand of BJ is
> usually around 1.33 units, so 100 hands of BJ would be
> about 13.3 units (assuming a non-counting flat
> bettor). I didn?t take into account the rule changes
> for this game which give it a positive edge.
That's not the problem. The problem is that he said he was playing three simultaneous hands of $100.
See Griffin, p. 142 E. for the formula for variance with more than one hand.
> How?d you do it? We don?t know the win/loss ratio so
> we can?t use the EX^2 - (EX)^2 method, and we don?t
> know the rules of the game so we can?t simulate it or
> use the sqrt(x^2/N) for independent trials. I?m sure
> it?s probably something simple that I overlooked, so
> feel free to embarrass me. It?s the only way I seem to
> learn. =)
The advantage of the game has no bearing on the variance, provided that it's very small, compared to the average squared result, as is the case for BJ. So, we do'nt need to know any of the above.
> Hmmm. How did you get a much higher SD but a much
> lower ROR given the same EV?
Don't know what you used for calculating ROR, but in the online calculators that Norm makes available and that are part of BJRM, as well, I just plugged in 0.62 units for Ev, 26 for s.d. and fiddled with BR until ROR was 5%.
Don
> That's not the problem. The problem is that he said he
> was playing three simultaneous hands of $100.
Yup, that's exactly where I messed up. I forgot about the covariance. Using Griffin?s formula we get variance of 6.78 (or 6.99 since I used 1.33 per hand instead of 1.26) and an hourly SD of 26.04 (26.44 for mine).
>?I just plugged in 0.62 units for Ev, 26 for s.d. and
> fiddled with BR until ROR was 5%.
I was using the right ROR formula, just the wrong EV and SD. I was still thinking of 1 hand of $300 so my EV was set to 0.209 and my hourly SD was 11.53. The reason my RORs were so much higher than yours is because I was using a $300 unit instead of a $100 unit.
Rookie mistake. =) At least he knows what to expect if he plays one hand instead of three.
-Sonny-
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