John Lewis: Contribution to PE of ace side count with Hi-Lo

[John Lewis]

> Wong's old edition of PBJ had the indices for using a side of aces with hi-lo. He discarded the whole idea in the 1994 revised edition, because, frankly, it isn't worth the time or effort. < --Don Schlesinger

Wong did indeed cover ace side counts to High-Low (and halves) in his orginal (1977) edition of Professional Blackjack (thank you Howard Schwartz at Gambler's Bookstore for finding that edition for me.) Wong concludes that the contribution to playing strategy of the ace side count adds only 0.1 bet per hour. Yes, insignificant.

Wong states only that "for purposes of playing strategy, aces are neutral." There is no elaboration on how this conclusion was reached. His playing efficiency calculations are based on this principle.

Griffin in Theory of Blackjack states the same. He does give his method for this conclusion, however. It is that all of the good players he talked to agreed on that! No mathematical exploration of the question whatsoever.

If Wong used a different technique to come to his conclusion he does not state it in his book.

Are aces truely neutral in all playing decisions? Is the ace neutral in splitting 9's against a dealer 8, or would it be best considered a large card in this decision? Is the ace neutral in splitting aces vs. a dealer ace, or should it be considered a small card?

What is needed is a formal mathematical analysis of the value of an ace on each playing decision. Numbers obtained can then be rounded into appropriate indicies. The observation of the net effect of aces on every playing decision lumped together (been done) does not answer questions such as those posed in the preceding paragraph. I have reviewed every significant blackjack text (with the exception of Beyond Counting -- unavailability, and Cellini's book -- cost) and have not found a description of or reference to such an analysis.

In the absence of this needed analysis I have formulated the following conjecture.

There are 3 classes of ace valuation for stragegy decisions (High-Low):

ace = 0 (neutral):
hit/stand 12-15 v dealer 2-5
hit/stand 15 v ace
double A5 v 6
split 22, 33; 66 v 6

ace = +1 (small card):
hit/stand 6 v dealer 2-5
hit/stand 16 v ace
double on 11
soft doubles A2-4
split aces
insurance (per Wong in referenced text)
LS 14-16 v dealer ace

ace = -1 (10 card):
hit/stand 12-15 v dealer 6
hit/stand 15, 16 v dealer 7-10
double 8,9,10
double A5-A9 (except A5 v 6)
split 66 (except 66 v 6),77,88,99,10?10
LS 14-16 v dealer 7-10

High-Low indicies were developed for decks in which the aces have an approximately normal (1/14) distribution. Decks which have a skewed proportion of aces give skewed index decisions if this ace maldistribution is not factored in instances where strategically ace is not equal to 10 in standard High-Low. This situation would also give skewed decisions in instances where ace is not equal to 0 using Wong's High-Low with ace side count strategy.

To accomplish this adjustment one should ideally make the adjustment in 1/4 deck increments. Extra aces dealt or undealt should be adjusted to the running count appropriate to the particular strategic decision.

One would accomplish this adjustment as follows to appropriately utilize ace information with a standard High-Low count. For ace neutral (ace=0) plays, +1 would be subtracted from the running count for each extra ace undealt. For ace=small card (ace=+1) plays, +2 would be subtracted from the RC for each undealt ace. The opposite adjustment (adding +1 and +2 respectively) would be applied in instances of extra aces dealt. For ace equals 10 (-1) (traditional value) plays, no adjustment would be necessary.

I do not have the ablity to do the necessary calculations, so I do not know if this conjecture is an improvement over ace=0 (Wong's ace side count strategy) for all playing decisions or not.

However, if it is even partially valid, then betting efficiency gain from an ace side count would be underestimated by Wong.

Griffin didn't run the numbers. Did Wong? Has anyone?

I will conclude by saying that if I have made some ridiculous, egregious error in this post, making a complete ass out of myself, it will not be the first time.

[Norm Wattenberger]

> Wong did indeed cover ace side counts to
> High-Low (and halves) in his orginal (1977)
> edition of Professional Blackjack (thank you
> Howard Schwartz at Gambler's Bookstore for
> finding that edition for me.) Wong concludes
> that the contribution to playing strategy of
> the ace side count adds only 0.1 bet per
> hour. Yes, insignificant.

Did you get the hard-cover version?

> Wong states only that "for purposes of
> playing strategy, aces are neutral."
> There is no elaboration on how this
> conclusion was reached. His playing
> efficiency calculations are based on this
> principle.

Well, neutral may have been meant as a relative term.

> Griffin in Theory of Blackjack states the
> same. He does give his method for this
> conclusion, however. It is that all of the
> good players he talked to agreed on that! No
> mathematical exploration of the question
> whatsoever.

Griffin had a habit of skimping on the math when something was inherently obvious to him. I doubt his conclusion was based on the observations of others.

> If Wong used a different technique to come
> to his conclusion he does not state it in
> his book.

> Are aces truely neutral in all playing
> decisions? Is the ace neutral in splitting
> 9's against a dealer 8, or would it be best
> considered a large card in this decision? Is
> the ace neutral in splitting aces vs. a
> dealer ace, or should it be considered a
> small card?

Of course it is not neutral. No card is. That's the point of multi-parameter play. And Hi-Opt II was first published in '76.

> What is needed is a formal mathematical
> analysis of the value of an ace on each
> playing decision. Numbers obtained can then
> be rounded into appropriate indicies. The
> observation of the net effect of aces on
> every playing decision lumped together (been
> done) does not answer questions such as
> those posed in the preceding paragraph. I
> have reviewed every significant blackjack
> text (with the exception of Beyond Counting
> -- unavailability, and Cellini's book --
> cost) and have not found a description of or
> reference to such an analysis.

This is an intractable math problem. Formulaic analysis is not adequate in this case. Only simulation.

> In the absence of this needed analysis I
> have formulated the following conjecture.

> There are 3 classes of ace valuation for
> stragegy decisions (High-Low):

> ace = 0 (neutral):
> hit/stand 12-15 v dealer 2-5
> hit/stand 15 v ace
> double A5 v 6
> split 22, 33; 66 v 6

> ace = +1 (small card):
> hit/stand 6 v dealer 2-5
> hit/stand 16 v ace
> double on 11
> soft doubles A2-4
> split aces
> insurance (per Wong in referenced text)
> LS 14-16 v dealer ace

> ace = -1 (10 card):
> hit/stand 12-15 v dealer 6
> hit/stand 15, 16 v dealer 7-10
> double 8,9,10
> double A5-A9 (except A5 v 6)
> split 66 (except 66 v 6),77,88,99,10?10
> LS 14-16 v dealer 7-10

> High-Low indicies were developed for decks
> in which the aces have an approximately
> normal (1/14) distribution. Decks which have
> a skewed proportion of aces give skewed
> index decisions if this ace maldistribution
> is not factored in instances where
> strategically ace is not equal to 10 in
> standard High-Low. This situation would also
> give skewed decisions in instances where ace
> is not equal to 0 using Wong's High-Low with
> ace side count strategy.

Hence the 70% max PE without side counts.

> To accomplish this adjustment one should
> ideally make the adjustment in 1/4 deck
> increments. Extra aces dealt or undealt
> should be adjusted to the running count
> appropriate to the particular strategic
> decision.

> One would accomplish this adjustment as
> follows to appropriately utilize ace
> information with a standard High-Low count.
> For ace neutral (ace=0) plays, +1 would be
> subtracted from the running count for each
> extra ace undealt. For ace=small card
> (ace=+1) plays, +2 would be subtracted from
> the RC for each undealt ace. The opposite
> adjustment (adding +1 and +2 respectively)
> would be applied in instances of extra aces
> dealt. For ace equals 10 (-1) (traditional
> value) plays, no adjustment would be
> necessary.

> I do not have the ablity to do the necessary
> calculations, so I do not know if this
> conjecture is an improvement over ace=0
> (Wong's ace side count strategy) for all
> playing decisions or not.

> However, if it is even partially valid, then
> betting efficiency gain from an ace side
> count would be underestimated by Wong.

> Griffin didn't run the numbers. Did Wong?
> Has anyone?

The numbers must come from sims. I have not seen any numbers on this since Stanford's - and they are very old and probably based on sims that were too small.

> I will conclude by saying that if I have
> made some ridiculous, egregious error in
> this post, making a complete ass out of
> myself, it will not be the first time.

I also will conclude by saying that if I have made some ridiculous, egregious error in my post, making a complete ass out of myself, it will not be the first time

[John Lewis]

< Did you get the hard-cover version (of the 1977 Professional Blackjack)? >

No, the softcover was the one available. But it was new (i.e., unused)! I was extremly pleased to obtain it. They didn't have it in the front, but Mr. Schwartz had some in the back of the store. And Mr. Schwartz made it a memorable experience. He gave us a tour of the blackjack greats photo display he has in the store. Very nice man, great store.

< Griffin had a habit of skimping on the math when something was inherently obvious to him. I doubt his conclusion was based on the observations of others. >

I don't have the book with me, so I can't give you the exact quote at this time. But he states only that ace is unanimously considered neutral in playing decisions by "blackjack gurus." That's his entire statement on the subject.

> Hence the 70% max PE without side counts. <

It is my understanding that simple High-Low has a PE of just 51%. Is 70% the max possible with any count without the use of side counts?

Thanks, JL

[Norm Wattenberger]

> No, the softcover was the one available.
> But it was new (i.e., unused)! I was
> extremly pleased to obtain it. They didn't
> have it in the front, but Mr. Schwartz had
> some in the back of the store.

I think he could find the Magna-Carta if he poked around in the back long enough.

> I don't have the book with me, so I can't
> give you the exact quote at this time. But
> he states only that ace is unanimously
> considered neutral in playing decisions by
> "blackjack gurus." That's his
> entire statement on the subject.

> It is my understanding that simple High-Low
> has a PE of just 51%.

Yes, probably why Stanford first looked at an Ace SC.

> Is 70% the max
> possible with any count without the use of
> side counts?

Yes. Griffin shows 70.3% with a 180 level count. This is based on single deck and an absurd number of indexes. Don't know what the PEs would be in shoes with a more reasonable number of indexes.

[John Lewis]

> Of course (ace) is not neutral. No card is. That's the point of
multi-parameter play. And Hi-Opt II was first published in '76. <

High-Opt II does indeed treat aces differently depending on decision. It treats aces uniformly as equal to 10's for all betting decisions, as does Wong. It assigns them a neutral value (0) for the large majority of playing decisions (this is uniform in Wong's ace side count strategy.)

It escaped my attention until you prompted a review, but this count does indeed assign yet a different value to 5 individual categories of playing decisions (3 doubles and 2 splits.) I shouldn't present this in more detail for fear of a "fine, jail sentence, or both." All 5 are instances of significant departure from Wong's technique of valuing all aces as 0, and 4 of the 5 represent incremental changes in the values I assigned in my post (the 5th is identical to the post's assigned value.) As such these indices presumably represent refinement of those values suggested in the post. None are interger values (converted to High-Low) different from those values in the post, however. Thus they probably do not represent a change from those presented.

Hubble and Braun's work, in it's perhaps more limited approach to the issue of varying ace playing value, is therefore supportive of the post's central conjecture. And this well established count (Hi-Opt II) does thus assert that Wong's playing efficiency strategy for utilization of the ace side count is indeed suboptimal.

I continue to assert that aces do have significantly varied effects on individual playing decisions, and that these variations are much more extensive than those presented by Hubble and Braun. And I continue to assert that structuring these values into a count and utilizing this for playing decisions would appreciably enhance the gain from an ace side count.

I have found no evidence that ace playing values for the full range of playing decisions has been explored to date. Do you or any other Domain members have such information?

[Norm Wattenberger]

I may be missing something here. Do you have Humble's four page MP addition to his original Hi-Opt II doc? It contains 58 Ace associated index adjustments.

[John Lewis]

> I may be missing something here. < --NW

Norm

You're not missing anything, but I am. A loop of cerebral cortex, evidently.

Yes, the multiparameter tables addendum is indeed included in my Hi-Opt II document. I missed it. I'm glad facial photos are not included in our posts. Anonymity is especially valuable in instances like this.

And these tables certainly answer all my questions. Thank you.

Aces are individually valued per playing decision, and I'm sure the values are well done and valid. They should apply directly to High-Low with appropriate adjustment.

But of more significance is Hubble's statement that using these ace values correctly will add only 0.2% to one's advantage. At 100 hands/hour that is only 0.2 bets, correct? This is double the efficiency of Wong's ace always = 0 strategy, but STILL quite insignificant compared to the extra work involved.

So Schlesinger (and Wong) were right. The ace side count, even with Hubble's optimal technique, "isn't worth the effort."

So I'll retract as irrelevant my entire original post with the exception of the all too prophetic last paragraph:

"I will conclude by saying that if I have made some ridiculous, egregious error in this post, making a complete ass out of myself, it will not be the first time."

[Norm Wattenberger]

Actually, I think the .2% improvement is a bit high. I received permission from Humble many years back to include these tables in CV but never got around to it. The sample MP tables currently included are for Hi-Opt I. Perhaps I'll add them.

Serious Blackjack Software

[Don Schlesinger]

> So Schlesinger (and Wong) were right.

It isn't nice to fool with Mother nature! :-)

> The ace side count, even with Hubble's optimal
> technique, "isn't worth the effort."

HuMble!

> "I will conclude by saying that if I
> have made some ridiculous, egregious error
> in this post, making a complete ass out of
> myself it will not be the first time."

You're forgiven.

We value your insightful posts. Keep 'em coming.

Don

[John Lewis]

Well the guy will never get far in the field of astronomy with a name like that.

Thank you for your comments.

[Don Schlesinger]

> Well the guy will never get far in the field
> of astronomy with a name like that.

Actually, you should see his real name!!

> Thank you for your comments.

My pleasure.

Don

[Cacarulo]

I don't know what you consider significant or insignificant but I believe that a 5% of increase in SCORE is not insignificant. Below is part of the analysis I did a long time ago:

The game is 2D,S17,DOA,DAS,SPA1,SPL3,NS,Catch-22,5 billion rounds.
We'll see how much worth is the use of an ace side count for two different penetrations (50% and 75%).

A) Penetration 50%

1) Hi-Lo

 play-all | rounds played = 100.00% 

 spread   ev/h   sd/h   ror%      n0    di  score      ekb   avb    unit  kelly 

------------------------------------------------------------------------------ 

 1 -  1 -0.138 11.609 100.00       0  0.00   0.00 10000.00 1.000   1.000  0.000 

 1 -  2  0.283 15.750  13.53  308783  1.80   3.24   875.19 1.281  11.426  1.000 

 1 -  3  0.705 20.901  13.53   87973  3.37  11.37   619.94 1.561  16.131  1.000 

 1 -  4  1.034 23.986  13.53   53761  4.31  18.60   556.15 1.702  17.981  1.000 

 1 -  5  1.389 28.083  13.53   40892  4.95  24.46   567.89 1.880  17.609  1.000 

 1 -  6  1.671 30.974  13.53   34351  5.40  29.11   574.06 1.997  17.420  1.000 

 1 -  7  1.963 34.192  13.53   30354  5.74  32.95   595.70 2.126  16.787  1.000 

 1 -  8  2.265 37.708  13.53   27712  6.01  36.09   627.72 2.266  15.931  1.000 

 1 -  9  2.517 40.468  13.53   25841  6.22  38.70   650.51 2.373  15.373  1.000 

 1 - 10  2.760 43.136  13.53   24422  6.40  40.95   674.10 2.475  14.835  1.000

2) Hi-Lo/A

 play-all | rounds played = 100.00% 

 spread   ev/h   sd/h   ror%      n0    di  score      ekb   avb    unit  kelly 

------------------------------------------------------------------------------ 

 1 -  1 -0.118 11.605 100.00       0  0.00   0.00 10000.00 1.000   1.000  0.000 

 1 -  2  0.311 15.740  13.53  256353  1.98   3.90   796.92 1.281  12.548  1.000 

 1 -  3  0.740 20.885  13.53   79696  3.54  12.55   589.58 1.561  16.961  1.000 

 1 -  4  1.075 24.002  13.53   49866  4.48  20.05   535.98 1.704  18.657  1.000 

 1 -  5  1.435 28.115  13.53   38379  5.10  26.06   550.79 1.884  18.156  1.000 

 1 -  6  1.727 31.130  13.53   32484  5.55  30.78   561.06 2.008  17.823  1.000 

 1 -  7  2.024 34.383  13.53   28857  5.89  34.65   584.07 2.139  17.121  1.000 

 1 -  8  2.332 37.927  13.53   26447  6.15  37.81   616.78 2.282  16.213  1.000 

 1 -  9  2.619 41.191  13.53   24744  6.36  40.41   647.94 2.411  15.434  1.000 

 1 - 10  2.868 43.918  13.53   23457  6.53  42.63   672.63 2.517  14.867  1.000

Gain of Hi-Lo/A over Hi-Lo

+--------+---------+ 

| 1 -  2 |  20.37% | 

+--------+---------+ 

| 1 -  3 |  10.38% | 

+--------+---------+ 

| 1 -  4 |   7.80% | 

+--------+---------+ 

| 1 -  5 |   6.54% | 

+--------+---------+ 

| 1 -  6 |   5.74% | 

+--------+---------+ 

| 1 -  7 |   5.16% | 

+--------+---------+ 

| 1 -  8 |   4.77% | 

+--------+---------+ 

| 1 -  9 |   4.42% | 

+--------+---------+ 

| 1 - 10 |   4.10% | 

+--------+---------+

B) Penetration 75%

1) Hi-Lo

 play-all | rounds played = 100.00% 

 spread   ev/h   sd/h   ror%      n0    di  score      ekb   avb    unit  kelly 

------------------------------------------------------------------------------ 

 1 -  1 -0.018 11.633 100.00       0  0.00   0.00 10000.00 1.000   1.000  0.000 

 1 -  2  0.713 16.438  13.53   53219  4.33  18.79   379.20 1.334  26.371  1.000 

 1 -  3  1.339 20.239  13.53   22864  6.61  43.74   306.03 1.536  32.677  1.000 

 1 -  4  1.895 23.655  13.53   15591  8.01  64.14   295.36 1.691  33.857  1.000 

 1 -  5  2.403 26.885  13.53   12514  8.94  79.91   300.75 1.830  33.251  1.000 

 1 -  6  2.891 30.090  13.53   10834  9.61  92.30   313.19 1.964  31.929  1.000 

 1 -  7  3.339 33.019  13.53    9778 10.11 102.28   326.50 2.084  30.628  1.000 

 1 -  8  3.809 36.254  13.53    9059 10.51 110.40   345.05 2.216  28.981  1.000 

 1 -  9  4.227 39.066  13.53    8540 10.82 117.10   361.01 2.329  27.700  1.000 

 1 - 10  4.646 41.926  13.53    8146 11.08 122.77   378.39 2.443  26.428  1.000

2) Hi-Lo/A

 play-all | rounds played = 100.00% 

 spread   ev/h   sd/h   ror%      n0    di  score      ekb   avb    unit  kelly 

----------------------------------------------------------------------------- 

 1 -  1  0.015 11.635  13.5364132650  0.12   0.02  9317.24 1.000   1.073  1.000 

 1 -  2  0.759 16.439  13.53   46871  4.62  21.34   355.90 1.334  28.097  1.000 

 1 -  3  1.396 20.266  13.53   21089  6.89  47.42   294.30 1.538  33.979  1.000 

 1 -  4  1.963 23.742  13.53   14634  8.27  68.34   287.20 1.696  34.819  1.000 

 1 -  5  2.486 27.081  13.53   11862  9.18  84.31   294.94 1.841  33.905  1.000 

 1 -  6  2.983 30.329  13.53   10336  9.84  96.75   308.34 1.978  32.432  1.000 

 1 -  7  3.442 33.320  13.53    9371 10.33 106.72   322.54 2.101  31.004  1.000 

 1 -  8  3.908 36.478  13.53    8711 10.71 114.80   340.45 2.230  29.373  1.000 

 1 -  9  4.318 39.167  13.53    8230 11.02 121.52   355.30 2.338  28.145  1.000 

 1 - 10  4.744 42.068  13.53    7863 11.28 127.19   373.01 2.455  26.809  1.000

Gain of Hi-Lo/A over Hi-Lo

+--------+---------+ 

| 1 -  2 |  13.57% | 

+--------+---------+ 

| 1 -  3 |   8.41% | 

+--------+---------+ 

| 1 -  4 |   6.55% | 

+--------+---------+ 

| 1 -  5 |   5.50% | 

+--------+---------+ 

| 1 -  6 |   4.82% | 

+--------+---------+ 

| 1 -  7 |   4.34% | 

+--------+---------+ 

| 1 -  8 |   3.99% | 

+--------+---------+ 

| 1 -  9 |   3.75% | 

+--------+---------+ 

| 1 - 10 |   3.60% | 

+--------+---------+

One thing I find very important is that with poor penetration the gain is even bigger. A similar analysis applies to the 6D game.

Sincerely,
Cacarulo

[Zenfighter]

Visit us more often! Well that's Don, not me.

Don't you have no mercy at all, for all your fans round here or what? :-)

I know,I know, you have been very busy doing.....

Now serious, I didn't have any idea, you having performed such an interesting comparison.

Best wishes

Z