What kind of exceptions Dave?
What's your question? Covariance is used to calculate optimal bet sizes for multiple hands. Are you asking what that formula is and how the covariance enters into it? If not, what's the big deal about this?Originally Posted by davethebuilder
I swore I wouldn't get sucked into this again. 42 years and people still can't get enough of "should I bet one hand or two?" Kinda sad.
Don
It's probably because Modern BJ says two hands at all positive counts and says this is universally accepted as the answer, and BJA3 gives your table and explanation. It is seemingly contradictory and I think that's where this comes from in general.
As for me? I don't care anymore. I play one hand heads up unless I spread on the final hand for the extra cards. If I give up a tiny bit of EV or something I don't care.
Don,
My question is why my playing method as described in the Opening Post, which I believe is optimal for playing simultaneous hands, differed from the results of Norm's study. So I contacted him privately and asked for an explanation as to why playing two hands at all counts is superior and he suggested I create a post and discuss it on the forum, so I did and here we are. Since then I have been contacted by some members and others who read these pages supporting the thread so there is some interest in the subject. We don't need to go into detail about co-variance formulas, etc and I have recently read Chapter 2 of BJA3 which seems to support my method. Gronbog has explained that different study parameters were used and I accept that but their is still a question mark in my mind about the issue since new research can lead to changes in optimal betting and playing techniques. So I am just trying to understand the matter and if you can help then I'm listening.
Casino Enemy No.1
There is nothing more to be said that hasn't been said, oh, 5,000 times already -- mostly by me!
There is no question whatsoever as to what the correct bet sizing is for multiple hands, as a function of the one-hand optimal bet (73% on each of two hands). And, there is no question that, within a reasonable amount, the number of cards used by one player playing two hands alone against the dealer is approximately 50% more than the number used playing one hand alone (total of three hands instead of two). And yes, before Three writes six paragraphs on the subject, I'm well aware that the dealer isn't required to play out his hand as often against one hand instead of two, because of the player-bust frequency. But it isn't worth discussing.
So the only variable remaining is the game speed. If empirical studies (I haven't done them, but Wong did) show that overall profitability increases playing two hands because the time it takes to play two hands is not 50% more than the time it takes to play one hand, then maybe two hands can produce a higher SCORE. Maybe not.
Don
Don said
"So the only variable remaining is the game speed. If empirical studies (I haven't done them, but Wong did) show that overall profitability increases playing two hands because the time it takes to play two hands is not 50% more than the time it takes to play one hand, then maybe two hands can produce a higher SCORE. Maybe not."
Seems to me that most of the entire subject can be paraphrased to this sentence.
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