Correlation coefficients & simulations

[bejammin075]

Suppose you are looking at 2 or more possible counting systems for the play of a particular hand with a proper index determined for each system under consideration. Each system has a correlation coefficient for the play, calculated using Don’s magnificent EoR tables.

Would it be possible for a simulation of a 2D or 6D game to show that a system with higher correlation performs worse for that play than a lower correlation system? For the sake of discussion, suppose the difference in correlation coefficients is greater than or equal to 5%.


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[DSchles]

Would it be possible for a simulation of a 2D or 6D game to show that a system with higher correlation performs worse for that play than a lower correlation system? For the sake of discussion, suppose the difference in correlation coefficients is greater than or equal to 5%.

That would surprise me. I don't see why that would happen. The work Gronbog and I are doing now will give the contribution of each index play to the overall SCORE, with rankings. Switching to a different system from Hi-Lo, the same values for the same play could be compared. You would have to specify if the plays would be isolated as the only index used, or if they would be allowed to interact with all the other indices, which is how we're doing it now.

Finally, you wrote above, "Would it be possible for a simulation of a 2D or 6D game to show that a system with higher correlation performs worse for that play than a lower correlation system?" Did you mean to compare the CC's of the entire systems (what would be the point?) as opposed to the individual CC's of the single play in question? I don't think you framed the question properly. Or else, I'm misunderstanding.

Don

[bejammin075]

Hi Don,

I’ll explain the motivation for my question: I developed a 2-parameter system where the second parameter is another balanced count. For a majority of plays, some multiple of the side count combined with the main count allows for the use of different tags with a higher correlation coefficient. The side count multiple for each individual play was chosen by maximizing the correlation coefficient. I am totally willing to accept that the effect on each individual play is probably a tiny EV gain, but something (I can’t remember what it was now) spooked me into thinking that there could be some unconsidered possibility that making my adjustments for some plays could be worse than using the main system tags.

What you said is reassuring to me.

Since you are working on the BJA 4^th edition, may I suggest one small update for the EoR tables: I think the splitting 8,8 v T numbers on page 515 are not quite the right ones. Those EoRs are for splitting versus hitting 8,8 v T, but really that decision is about splitting over standing. In a positive count with 8,8 v T, you either split or stand (assuming no late surrender).

[DSchles]

Since you are working on the BJA 4th edition, may I suggest one small update for the EoR tables: I think the splitting 8,8 v T numbers on page 515 are not quite the right ones. Those EoRs are for splitting versus hitting 8,8 v T, but really that decision is about splitting over standing. In a positive count with 8,8 v T, you either split or stand (assuming no late surrender).

That's a very interesting observation that no one has ever made before, and you are absolutely right! It isn't every day that someone finds a "mistake" in BJA3; it's been years since there has been anything pointed out at all, so thank you.

The problem is that I'm really not working on BJA4! What Gronbog and I are doing is unlikely to find its way into any possible fourth edition of the book, if there is one, although a very small sample of the work could potentially be construed as a new appendix. We'll have to discuss that.

So, I'm not altogether sure what can be done to remedy what you've pointed out. Note that Griffin doesn't even bother to have a line for 8,8 except against dealer upcards of 9 , T, and Ace, whereas we furnished them for all upcards (deemed unimportant by Griffin). So, a bit more work for me to correct them.

Don

[Freightman]

Bejammin said

Since you are working on the BJA 4^th edition, may I suggest one small update for the EoR tables: I think the splitting 8,8 v T numbers on page 515 are not quite the right ones. Those EoRs are for splitting versus hitting 8,8 v T, but really that decision is about splitting over standing. In a positive count with 8,8 v T, you either split or stand (assuming no late surrender).

Don said

That's a very interesting observation that no one has ever made before, and you are absolutely right! It isn't every day that someone finds a "mistake" in BJA3; it's been years since there has been anything pointed out at all, so thank you.

Then Bejammin saud

Since you are working on the BJA 4^th edition,

Well done - Mazel Tov
Two comments
1. Catching Don on a math point is a career enhancer. Best I’ve ever done is catch an egregiously outrageous spelling error
2. Be sure to catch the inclusion of the unknown regaled system both Basic and Advanced

[DSchles]

Catching Don on a math point is a career enhancer.

Don't get me wrong: I take responsibility for every comma in the book. But see p. 497, first paragraph. The EOR tables were done by Zenfighter and Cacarulo, with input from me as to format and other small points re the construction. I didn't do the math.

Don

[bejammin075]

it's been years since there has been anything pointed out at all, so thank you.

The problem is that I'm really not working on BJA4! What Gronbog and I are doing is unlikely to find its way into any possible fourth edition of the book, if there is one, although a very small sample of the work could potentially be construed as a new appendix. We'll have to discuss that.

Don

You're welcome. But...no BJA4?! In my industry, if you add any small thing such as a methyl group to your previous product, you can get a new patent & charge people a billion dollars for it. A new appendix with Gronbog is surly more substance than an extra methyl group.

Well done - Mazel Tov
Two comments
1. Catching Don on a math point is a career enhancer. Best I’ve ever done is catch an egregiously outrageous spelling error
2. Be sure to catch the inclusion

Toda! At one point in time I did spend a lot of quality time with the EoR tables.

The new word in Webster's Dictionary for 2022 is "auto-regalio".

[Freightman]

The new word in Webster's Dictionary for 2022 is "auto-regalio".

Certainly has a ring to it. I recently, as in today, used the English language adjective to said word responding to a post from 31forme.

For the life of me, I can’t seem to spot them.

Oh…..Toda has an h at the end, as in Todah.

[21forme]

Certainly has a ring to it. I recently, as in today, used the English language adjective to said word responding to a post from 31forme.

I prefer 21 to 31.

[Freightman]

Don't get me wrong: I take responsibility for every comma in the book. But see p. 497, first paragraph. The EOR tables were done by Zenfighter and Cacarulo, with input from me as to format and other small points re the construction. I didn't do the math.

Don

Oh shit!

[Freightman]

I prefer 21 to 31.

Sorry about that. The (accidental) elevation was in recognition of your experience level as well as your promotion of 4-2 blackjack.

I will backtrack to 21 for future commentary.

[aceside]

What are Zenfighter and Cacarulo doing today? Do they still login this forum? Some devoted players haven’t showed up here for a long long time.

[DSchles]

What are Zenfighter and Cacarulo doing today? Do they still login this forum? Some devoted players haven’t showed up here for a long long time.

I have lost contact with both of them. I have tried known email addresses, but to no avail. No, they don't read or participate in this forum or any other, to my knowledge. Two of the great minds of the game. Pity.

Don