ToAnyOne: Co-variance when playing multiple hands

[ToAnyOne]

Does the co-variance factor fluctuate with the count? If so, to what extent? If I spread to multiple hands in negative counts, can I expect a similar co-variance as spreading to multiple hands in positive counts?
Thanks in advance,
TAO

[Magician]

> Does the co-variance factor fluctuate with the count?
> If so, to what extent? If I spread to multiple hands
> in negative counts, can I expect a similar co-variance
> as spreading to multiple hands in positive counts?
> Thanks in advance,
> TAO

I would think that the co-variance would tend to increase with the count since the dealer is more likely to bust, making all your unbusted hands winners. But that's just a guess really.

[ToAnyOne]

[Don Schlesinger]

> I would think that the co-variance would tend to
> increase with the count since the dealer is more
> likely to bust,

The dealer is slightly less likely to bust as the count increases. He's more likely to bust if he shows 2-6, but, since the count is high, he's less likely to show 2-6, in the first place. :-)

On the other hand, as the count gets very high, there is a large increase in the number of 20-20 pushes, and this increases the correlation coefficient.

So, the answer is that the correlation increases as the count rises, but I don't think it's for the reason you state.

Don

[ES]

Were there any good blackjack games in France?

[Don Schlesinger]

> Were there any good blackjack games in France?

I didn't have the time to check things out. But, the games are pretty standard in France. s17, das, double on 9, 10, 11 only, and usually 4.5/6 or 5/6. No surrender. And, usually no ability to play at uncrowded tables, as, if a table is empty, they rarely allow you to play by yourself.

Don

[zugszwang]

Sorry Don, completely untrue. I recently played 90% of the casinos in France and nearly all I played on my own (however they do insist you play 2 boxes).

[Magician]

> The dealer is slightly less likely to bust as the
> count increases.

Even if you ignore pushes? I didn't know that.

> On the other hand, as the count gets very high, there
> is a large increase in the number of 20-20 pushes, and
> this increases the correlation coefficient.

That would have been my next guess. :-) Also more dealer blackjacks I suppose.

> So, the answer is that the correlation increases as
> the count rises, but I don't think it's for the reason
> you state.

This is where my stats get a bit rusty. Is correlation coefficient the same thing as co-variance?

A graph of count vs co-variance would be fantastic but I don't think any of the available simulators can generate the data?

[Don Schlesinger]

> Sorry Don, completely untrue. I recently played 90% of
> the casinos in France and nearly all I played on my
> own (however they do insist you play 2 boxes).

Glad to hear this. When last I played (many years ago), dealers would open a table and then wait for enough people to sit down to make it "worth their while" to deal, which, of course, was asinine. Nice to know they've joined the 21st century!

Don

[Don Schlesinger]

> Even if you ignore pushes? I didn't know that.

Not sure what pushes would have to do with it. You deal 100 hands in a neutral count. Then, you deal 100 hands in a higher count. The dealer breaks less frequently (ever so slightly) in the higher-count situation.

> That would have been my next guess. :-) Also more
> dealer blackjacks I suppose.

> This is where my stats get a bit rusty. Is correlation
> coefficient the same thing as co-variance?

It's directly proportional. If cc = correlation coefficient, cv = covariance, anc v = variance, then:
cc = cv/v. So, if, say, cv = 0.50 for two simultaneous hands, and v = 1.33 for a single hand, then cc = 0.50/1.33 = 0.375.

> A graph of count vs co-variance would be fantastic but
> I don't think any of the available simulators can
> generate the data?

I don't think it changes enough to get too worried about it.

Don

[Magician]

> Not sure what pushes would have to do with it. You
> deal 100 hands in a neutral count. Then, you deal 100
> hands in a higher count. The dealer breaks less
> frequently (ever so slightly) in the higher-count
> situation.

I was confusing the probability of a dealer bust with the probability of a winning hand (which also decreases with the count, unless you ignore pushes). But the latter isn't as relevant to a discussion about correlation.

> It's directly proportional. If cc = correlation
> coefficient, cv = covariance, anc v = variance, then:
> cc = cv/v. So, if, say, cv = 0.50 for two simultaneous
> hands, and v = 1.33 for a single hand, then cc =
> 0.50/1.33 = 0.375.

Makes sense. Thanks for that.

> I don't think it changes enough to get too worried
> about it.

I guess that's the answer the original poster wanted to hear.