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# Thread: Don/other experts, How to find covariance of a game ?

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## Don/other experts, How to find covariance of a game ?

Hi Don/other experts,

How to find covariance of a game ?

There is an example how to find covariance of Blackjack at this link https://wizardofodds.com/games/blackjack/variance/

Firstly, find total variance of N hands per round, and use the formula,

Total variance of N hands per round= N* Variance of 1 hand per round+ N * (N-1) * covariance.

Fro example, variance of 1 hand per round = 1.31 and Total variance of 2 hands per round(through simulations) = 3.565, N = 2,

So, 3.565 = 2 * 1.31 + 2(1)* covariance

covariance = (3.565 - 2.62) /2 = 0.4725.

My question : Is simulations the only way to find total variance of N hands per round ?

Regards

James

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Of course not. You can also do a combinatorial analysis to find the exact covariance.

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Originally Posted by aceside
Of course not. You can also do a combinatorial analysis to find the exact covariance.
Are you sure ? I think it may need a massive computation for MULTIPLE HANDS.

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Originally Posted by James989
Are you sure ? I think it may need a massive computation for MULTIPLE HANDS.
I am not so sure because I am not a mathematician. If the covariance of two blackjack hands are well defined mathematically, it should have an exact value. You may ask Norm and Don about this.

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Originally Posted by aceside
I am not so sure because I am not a mathematician. If the covariance of two blackjack hands are well defined mathematically, it should have an exact value. You may ask Norm and Don about this.
If you are not so sure, why did you say that it can be done with combinatorial analysis ? No offense.

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Originally Posted by James989
If you are not so sure, why did you say that it can be done with combinatorial analysis ? No offense.
I responded to your post because I am an expert. There are two approaches to blackjack problems. If combinatorial analysis can not solve it, simulation might solve it. Clear?

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Originally Posted by aceside
There are two approaches to blackjack problems. If combinatorial analysis can not solve it, simulation might solve it. Clear?
You are not answering my question, we know it can be calculated with simulations but why you so sure it also can be done with combinatorial analysis in your first post ? And then you said not sure in your post #8.

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Originally Posted by James989
You are not answering my question, we know it can be calculated with simulations but why you so sure it also can be done with combinatorial analysis in your first post ? And then you said not sure in your post #8.
I was just being humble. Let me assure you now. It can be done with combinatorial analysis.

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Originally Posted by aceside
I was just being humble. Let me assure you now. It can be done with combinatorial analysis.
Thank you very much

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Originally Posted by James989
Thank you very much
There were some barbs questioning my expertise earlier.

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