Blackjack Math

[Guynoire]

I was trying to calculate the standard deviation of multihand play, when I realized that the two hands are not independent events, which complicates things.

Does anyone know the covariance between two hands at the same blackjack table or how to approximate it?

 

[nightspirit]

This post of Sonny will help you.

 

[Kasi]

I was trying to calculate the standard deviation of multihand play, when I realized that the two hands are not independent events, which complicates things.

Does anyone know the covariance between two hands at the same blackjack table or how to approximate it?

Recognize that the variance and co-variance will change based upon different rule sets.

That being said, for a standard 6D,S17,DAS,DA2 game the standard deviation for one hand is 1.155. For 2 hands, 1.35. For 3 hands, 1.52.

So, when betting $10 for one hand, the standard deviation is $10*1.155=$11.55

When playing 2 hands at the same time of $5 each, the total standard deviation would be $10*the square root of 2*1.35=$9.54

For 3 hands of 3.33, it would be 3.33*square root of 3*1.52=$8.76 etc

Hope that helps a little anyway.

To determine the variance and co-variance of a given game in the first place, I'd guess u need software and know what u r doing lol. I lack both requirements.

But if u know the variance and co-variance of a given game, there are formulae out there that you could apply. If u look hard enough, u may very likely be able to find these numbers for the game u have in mind.

I don't think using these numbers would be hugely off in most circumstances in that the variance for BJ doesn't vary that much. The co-variance might have a wider range of values depending on specific rule sets.

 

[EyeHeartHalves]

You could just do what I do?

I used to bet two circles (boxes, whatever) when the Halves TC was at least +1 but that was a long time ago. My computer simulations could not do two card counting hands so I had to break out the old college textbook and the Peter Griffin and then do all that ish...

until...

I came to rethink the whole concept. Don't mostly all CC'rs bet spread to at least two at times??? Oh, they do? Well, I'll just never ever do it then. Think about it.

RETHINK EVERYTHING YOU THOUGHT YOU KNEW