John Lewis: 3-card compostion dependent indices for 16 v 9?

[John Lewis]

Signifant composition dependent index variation has been demonstrated for the hand 16 v 10 at the 3-card level of analysis (this page.) The existence of this 3-card CD variation was suggested by the discrepancy between the 2-card indices and the mean index for the hand.

Such a discrepancy also exists for the hand 16 v 9. Wong gives a mean index for this hand (SD) of +5. Yet he gives CD indices (2-card) of +8 and +9 for 10,6 and 9,7, respectively. Zenfighter, in recent calculations which may have more modern parameters gave indices of +7 for both of these hands (+6.9 and +7.1, again respectively.)

16 v 9, while less frequent than 16 v 10, is nonetheless a very significant hand, at 0.96% of all hands (multideck, Schlesinger BJA.)

I believe a 3-card CD analysis of 16 v 9 would be interesting, and possibly even worthwhile for SD players.

Do you agree, Zen?

[Zenfighter]

16 v 9, while less frequent than 16 v 10, is nonetheless a very significant hand, at 0.96% of all hands (multideck, Schlesinger BJA.)

Your generic floored index for this hand is 4. Therefore to make a BS departure on this particular hand you will need to multiply both probabilities of occurrences. You do have frequencies in PBJ, 1994 Edition, page 288.

Read again the introduction to The Illustrious 18, BJA 2nd Edition, page 63.

After that I?m sure you?ll realize that a 3 card CD analysis of 16 vs 9 is definitely not worth it. In the final paragraph of the main article, you do have my opinion regarding these complexities, anyway.

Sincerely

Z

[John Lewis]

Zenfighter

Thanks for your response. Comments as follows.

"Your generic floored index for this hand is 4"--Z

And, again, your (Zenfighter) 2-card comp dependent indices are +7. Therefore other (3 and more-card) indices must at net be significantly less than +4 to create an average index of +4. And the index x frequency must be substantial to have such a marked effect on the average index.

This is the same effect seen in examination of the 3-card indices for 16 v 10.

"Read again the introduction to The Illustrious 18, BJA 2nd Edition, page 63. After that I?m sure you?ll realize that a 3 card CD analysis of 16 vs 9 is definitely not worth it." -- Z

Your assertion is that this hand is not significant enough to warrant a detailed analysis of comp dependent indices. I feel BJA argues precisely the opposite. This is one of the most common hands. It is, in fact, the 4th most common hand, surpassed only by 16 v 10, 15 v 10, and 10 v 10 (BJA.)

"you do have my opinion regarding these complexities, anyway." -- Z

Yes, I have asked you to examine this before, and the response was the same. I continue to feel the hand is worth examining, however, so we disagree on that. Certainly learning each 3-card index would be impractical. But if the indices are grouped in a way that a single average index can be utilized, as we saw with 16 v 10, then this discovered index would be a worthwhile one.

Hopefully someone with the requisite mathmatical expertise will share my interest.

Thanks, JL

[Zenfighter]

along with 10 v. A is the poorest in Hi-lo average gains (1000ths of a pct.) as per column 9 of table 5.1 page 70, BJA 2nd.

For Hi-lo actual gains it ranks between 12 and 15.(column 10).

What do you expect to gain then, by further refinements of this less than mediocre index?

More clear now?

Regards

Z

[Cacarulo]

> Signifant composition dependent index
> variation has been demonstrated for the hand
> 16 v 10 at the 3-card level of analysis
> (this page.) The existence of this 3-card CD
> variation was suggested by the discrepancy
> between the 2-card indices and the mean
> index for the hand.

> Such a discrepancy also exists for the hand
> 16 v 9. Wong gives a mean index for this
> hand (SD) of +5. Yet he gives CD indices
> (2-card) of +8 and +9 for 10,6 and 9,7,
> respectively. Zenfighter, in recent
> calculations which may have more modern
> parameters gave indices of +7 for both of
> these hands (+6.9 and +7.1, again
> respectively.)

Precise floored indices are:

16 vs 9 = +4 

T6 vs 9 = +7 

97 vs 9 = +7

in agreement with ZF.

> 16 v 9, while less frequent than 16 v 10, is
> nonetheless a very significant hand, at
> 0.96% of all hands (multideck, Schlesinger
> BJA.)

I've got 0.896% for 6D and 0.904% for 1D without considering 16s generated after splits.

> I believe a 3-card CD analysis of 16 v 9
> would be interesting, and possibly even
> worthwhile for SD players.

3+ = 0.45% 

4+ = 0.11% 

5+ = 0.02% 

6+ = 0.00% 

7+ = 0.00% 

8+ = 0.00% 

9  = 0.00%

The correct BS for this hand is to HIT but further CA refinements say to STAND with 5 or more cards (only in 1D). You can use this variation although I don't know if it's worth learning more indices as in 16vT.

Sincerely,
Cacarulo

[John Lewis]

"What do you expect to gain then, by further refinements of this less than mediocre index? "

Zen -- you left out the descriptor "execrable."

This execrable little hand is ranked 12th on Schlesinger's Illustrious 18 in actual gain from index utilization. Perhaps we should change his categorization to the Illustrious 11 and the Shit 7.

[John Lewis]

Cacarulo

Thank you very much for your post, and thank you for the data you provided. This data has allowed calculation of the solution to my inquiry.

3-or more-card 16's comprise about 65% (2/3) of the 16 v 9 hand (thank you.)

We know that 2-card indices, 35% (1/3) of the total (slightly less when 8-8 is excluded), average +7. The average index for all card totals is +4. Thus the average index for 3 or more-card hands is as follows:

(7 x 1/3) + (Index x 2/3) = 4

Index = +2.5

Taking 8-8 into account would lower this index fractionally, yielding a rounded index of +2.

.:. Indices for 16 v 9, SD High-Low:

2-card hand: +7
3 or more-card hand: +2

This is an Illustrious 18 hand; i.e., one of the 18 hands that produces the largest actual gains from index use of all blackjack hands. Significant index improvements in any of these 18 hands is indeed worthwhile, in my opinion.

This pronounced divergence in this dichotomous index (16 v 9) makes recognition of this dual index worthwhile, in my opinion. I certainly will use it myself.

Thank you for your interest and feedback.

JL

[Cacarulo]