Zenfighter: Answer to Mr. Lewis

[Zenfighter]

SD, 16 v T, three cards comp-dependence

 

Hand		hitting		standing     action	index		prob. occurrence  

 

T,5,A		-.549645	-.536044	s	-3.9		0.003546034 

T,4,2		-.549087	-.544808	s	-0.3		0.003546034 

T,3,3		-.544348	-.543884	s	 0.3		0.001329763 

9,6,A		-.511686	-.537348	h	 1.9		0.000945609 

9,5,2		-.559519	-.542159	s	-1.3		0.000945609	 

9,4,3		-.555709	-.541488	s	-0.8		0.000945609 

8,7,A		-.517238	-.511573	s	-2.9		0.000945609 

8,6,2		-.52146	        -.542529	h	 3.6		0.000945609 

8,5,3		-.566471	-.537241	s	-3.0		0.000945609 

8,4,4		-.56829	        -.537494	s	-3.2		0.000472805 

7,7,2		-.526452	-.515857	s	-1.4		0.000472805 

7,6,3		-.529144	-.537389	h	 2.1		0.000945609 

7,5,4		-.579651	-.532973	s	-5.6		0.000945609 

6,6,4		-.5368		-.559716	h	 4.5		0.000472805 

6,5,5		-.585888	-.556031	s	-2.0		0.000472805 

 

Basic strategy

Hit whenever a 6 is included except with 6,5,5; otherwise stand.

Average counting strategy

Weighted average index

Wi = (Sum Ii*Pi)/15 = -1.2

That?s: Stand on all your 3 cards 16s v T. Hit if TC < = -1.2 ( Hi-lo)

After the insurance bet, this index 16 v T is by far the most important in average gains for varying BS. If there is something worth in all this, it must be here. Disregard any attempt to employ this added complexity for the rest of indexes.

Sincerely

Z

[Don Schlesinger]

Thanks for some great work, Zen.

Actually, since you always do great work, I was most impressed that you spelled both "dependence" and "occurrence" correctly!! :-)

Don

[John Lewis]

Zenfighter

Interesting and useful data.

There are 9 non-6 containing indices. The average of these indices is -2.3. The index of 6,5,5 is -2.0. The average of these10 numbers is -2.27. Rounded index for this category: -2.

There are 5 3-card hands containing 6. 6,5,5 is excluded from this category; it is grouped with the first category of indices. The average index of the 4 remaining hands is +3.03, which is rounded to +3.

Conclusion:

Composition dependent 16 v 10 indices:

-- any 2 or 3 card 16 not containing 6(however containing 6,5,5): -2
-- any 2 or 3 card 16 containing 6 (excluding 6,5,5): +3
-- 9.7: 0

Use of these 3 index categories for 16 v 10 would considerably fine tune play of this very important hand.

I remain curious about the 4-card comp dependent indices.

Thanks, JL

[Cacarulo]

> SD, 16 v T, three cards comp-dependence
> Hand hitting standing action index
> prob. occurrence
> T,5,A -.549645 -.536044 s -3.9 0.003546034
> T,4,2 -.549087 -.544808 s -0.3 0.003546034
> T,3,3 -.544348 -.543884 s 0.3 0.001329763
> 9,6,A -.511686 -.537348 h 1.9 0.000945609
> 9,5,2 -.559519 -.542159 s -1.3 0.000945609
> 9,4,3 -.555709 -.541488 s -0.8 0.000945609
> 8,7,A -.517238 -.511573 s -2.9 0.000945609
> 8,6,2 -.52146 -.542529 h 3.6
> 0.000945609
> 8,5,3 -.566471 -.537241 s -3.0 0.000945609
> 8,4,4 -.56829 -.537494 s -3.2
> 0.000472805
> 7,7,2 -.526452 -.515857 s -1.4 0.000472805
> 7,6,3 -.529144 -.537389 h 2.1 0.000945609
> 7,5,4 -.579651 -.532973 s -5.6 0.000945609
> 6,6,4 -.5368 -.559716 h 4.5 0.000472805
> 6,5,5 -.585888 -.556031 s -2.0 0.000472805

See if you can fix this last line. Remember that 6,5,5 shouldn't occur (only 5,5,6). As you know this impacts on the prob. of ocurrence.

> Basic strategy
> Hit whenever a 6 is included except with
> 6,5,5; otherwise stand.

5,5,6

> Average counting strategy
> Weighted average index
> Wi = (Sum Ii*Pi)/15 = -1.2
> That?s: Stand on all your 3 cards 16s v T.
> Hit if TC After the insurance bet, this
> index 16 v T is by far the most important in
> average gains for varying BS. If there is
> something worth in all this, it must be
> here. Disregard any attempt to employ this
> added complexity for the rest of indexes.
> Sincerely
> Z

Excellent work ZF!

Sincerely,
Cacarulo

[Zenfighter]

[Zenfighter]

[John Lewis]

Thank you again for pointing out that a minority of hands containing two 5's and one 6 actually occur and contribute to the playing indices for the 16 v 10 hand.

Thus the importance of this hand's maverick index ("maverick" in the counting scheme I have proposed) is markedly diminished. My judgement is that this minor variation no longer merits its own caveat.

Based on this, I suggest that the comp dependent indices for the 16 vs 10 hand be simplified to the following three rules:

Composition dependent 16 v 10 indices:

-- any 2 or 3 card 16 not containing 6: -2
-- any 2 or 3 card 16 containing 6 : +3
-- 9.7: 0

Note that the accuracy of the count will be enhanced slightly by continuing to group 5,5 6 with the "not containing a 6" category. This is an easy to remember exception to the simplified rules if one analyses the cards functionally.

5's leaving the deck prior to one's play obviously make hitting the hand (thus placing it in the category of the not containing a 6 hands) much less attractive (16 plus 5 = 21) and standing on 16 much more attractive.

Thanks, JL

[Zenfighter]

 

 

T,5,A		0.002364023 

T,4,2		0.003546034 

T,3,3		0.001329763 

9,6,A		0.000630406 

9,5,2		0.000630406 

9,4,3		0.000945609 

8,7,A		0.000630406 

8,6,2		0.000945609 

8,5,3		0.000630406 

8,4,4		0.000354603 

7,7,2		0.000354603 

7,6,3		0.000945609 

7,5,4		0.000630406 

6,6,4		0.000354603 

5,5,6		0.000118201 

 

In the original column by taken short cuts using a generic i, j, k vs T, with i=\j=\k,
where total permutations are P (3, 3) = 3! = 6, I wrongly extrapolated this figure, so as to make inferences for the other ones, overlooking indeed the non realistic permutations, where
the player isn't going to hit, because he is either pat, or holding an 11 and striving for a
double. E.g. (7,4), (8,3),(6,5),(9,2).

Here we have

Wi = -0.86 as the average TC borderline, to change our Army Forces rule of thumb:

Joe, you should better stand on a 3 card 16 versus a dealer's ten, and hope for the best!

Happy New Year, America!!!!!

Best wishes

Z

[John Lewis]

Wow.

5,5,6 comprises approximately 1% -- only 1% -- of all 3 card 16's.

Yes, we can drop the caveat on the 3 card 16 v 10 indices!

Thanks Zen

JL

[John Lewis]

Zen

I hope you're happy about spreading all this between 2 Forums!

Substance:

Doing a quick and dirty (pen et paper and screw checking the results) frequency x index analysis using your data, it looks like the previously proposed rounded indices remain valid.

16 v 10 SD indices:

non 6 containing hands: -2
6 containing hands: +3
9,7: 0

Presumably these 3 rules will remain valid and continue to suffice even with more detailed (4 card hand) analysis.

-- fin (I hope)

Now what about double deck?

[Zenfighter]

I hope you're happy about spreading all this between 2 Forums!

I did the above 3 card comp-dependence article exclusively for your benefit. Even if you were the only person to find any degree of interest inside it, I would find that, more than a compensation, for the couple of hours it took to cycle around the whole stuff.

I have no interest whatsoever to let this modest article, to be watched at others BJ sites. Don?t forget also, that by cross posting an article, you always run the risk to enter into the ethical field.

P. Griffin?s quote:

For playing 16 v. Ten the remarkably elementary direction ?stand when there are more sixes than fives remaining, hit otherwise,? is more than 60% efficient.

God bless his soul!

Best wishes

Z

[John Lewis]

"I hope you're happy about spreading all this between 2 Forums!" -- JL

Zen --

This site titles it's various discussion categories "Forums." The initial question in this matter was posted on DD Main Forum. You responded to that inquiry in the Theory and Math Forum. Subsequent posts thus have been spread between these two Forums.

This resulted in some discontinuity in following the 2 separate threads which actually deal with the same subject. I was simply gently chiding you in fun over that. If it weren't for your computational work there would not have been threads in either location.

"I have no interest whatsoever to let this modest article, to be watched at others BJ sites. Don?t forget also, that by cross posting an article, you always run the risk to enter into the ethical field." -- Zenfighter

I was not suggesting that this material be posted to another site (such as bj21.) I understand that that is not the accepted protocol. Is this indeed what you thought was meant by my statement ("spreading . . . between 2 Forums")?

"I did the above 3 card comp-dependence article exclusively for your benefit. Even if you were the only person to find any degree of interest inside it, I would find that, more than a compensation, for the couple of hours it took to cycle around the whole stuff." -- Zenfighter

As I have told you many times, I appreciate the answers to computational questions that you have provided me now on several occasions. I hope you will be kind enough to do so again in the future.

Thanks, John

[Zenfighter]