This Blackjack Forum article on the history of blackjack card counting shows the roles of Arnold Snyder, Peter Griffin, and Don Schlesinger in the discovery of the Illustrious 18 playing strategy rules for blackjack card counters.
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Peter Griffin, Arnold Snyder, Don Schlesinger and the History of the "IIlustrious 18"

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History of an Important Blackjack Discovery

By Blackjack Historian
(From Blackjack Forum Vol. XXIV #1, Winter 2004/05)
© 2004 Blackjack Forum

Most players do not have access to the journals where the important blackjack discoveries were first published, and they do not have access to the materials that led to these discoveries. Most players therefore do not have a good sense of the history of many of the important blackjack discoveries, and tend to credit those who have been most aggressive about claiming credit, whether or not these people actually deserve this credit.

This article will provide a documented history of one of the most important blackjack discoveries, and seek to restore proper credit to the people who made the real original contributions to the game.

I would like to begin by addressing the history of the well-known “Illustrious 18” index numbers. The Illustrious 18 are the “discovery” for which the blackjack writer Don Schlesinger is perhaps best known and most respected.

In his September 1986 article on the Illustrious 18 (Blackjack Forum Vol. VI #3), titled “Attacking the Shoe!: A Revealing Study of the Relative Gain Available From Using Basic Strategy Variations for the Hi-Lo System in a 4-Deck Game,” Schlesinger claims credit for the seminal discovery that most index numbers contribute very little to player win rates. Specifically, he states:

“More than ten years ago, when I taught myself to count cards using Lawrence Revere’s text, I had no one to consult with for learning the index numbers. Over the years, as I grew more expert in the subject I suspected that most of the numbers I had learned (some 165) contributed very little, if anything to the overall gain available from the Point Count.

Furthermore, despite hundreds of books and articles published on blackjack, I have not to this day seen a study which would tell a player which index numbers are most important to learn based on the amount of total gain which can be obtained by their use. In this respect, I believe that the chart presented near the end of this article contains information which has never been published before and which should provide some revealing facts for consideration by the blackjack playing community.

“Note that the insurance play all by itself is worth over one-third of all the gain. The ‘Big 3,’ insurance, 16 V. 10, and 15 v. 10, account for nearly 60% of the total gain available while the top 6 plays contribute almost 75% of the advantage. The first half of the chart (9 plays) garners over 83% of the edge and the ‘even dozen’ (top 12 plays) provides more than 90% of the total gain. I believe this is the first time that such information has been accurately quantified in a published article.

“Of course, the ramifications of this study are quite clear. If you are a practicing hi-lo player and have diligently committed to memory 150 to 200 index numbers, you may be interested to learn that for this particular game and style of play, you might just as well throw 90% of your numbers away and keep the ‘Illustrious 18’ for further play.”

I will document in this article that Schlesinger should not receive credit for this discovery, despite his claims in this article and elsewhere, because the discovery was made, and published, years before Schlesinger’s article.

In this article I will show that Schlesinger was aware of this published information, though he failed to acknowledge these prior researchers and authors.

This article is based upon a review of over one hundred published and unpublished documents related to the development of the Illustrious 18 and especially the original discovery that most index numbers relate very little to actual player win rates.

The History of the “Illustrious 18”

The first discussion of the relative potential gains from the different playing decisions was published in the first edition of Peter Griffin’s The Theory of Blackjack , (GBC, 1979). On p. 30 of his book, Griffin provided a chart titled “Average Gains for Varying Basic Strategy.” (The chart is available in more recent editions as well.)

The chart shows, in thousandths of a percent, the perfect gain a computer, with a perfect count of all cards in a 75%-dealt single-deck game, could get from making a strategy departure from basic strategy based on his count information. You can get an idea for yourself of which play variations are most valuable by looking for the biggest numbers in Griffin’s chart.

The very biggest number—186 (or 0.186%)--is for the insurance decision. The second biggest, 95 (or 0.095%), is for the 16 v. 10 decision. To show you the value of these decisions, as indicated by this chart, imagine yourself playing in this game, except that the only play variations you are allowed to make are the insurance and 16 v. 10 decisions. In a game with no house edge, these two decisions alone, if based on perfect count information, would gain you an edge of about 0.28% over the house.

But Peter Griffin made no recommendations about how to use this information in the real world of playing at the tables. The first author to publish an interpretation of Griffin’s data and actual playing recommendations based on it was Arnold Snyder in his 1980 paper “Algebraic Approximations of Optimum Blackjack Strategy,” republished by the University of Nevada in 1981. In this article, he states:

“From Griffin’s table of ‘Average Gains for Varying Basic Strategy,’ note that some hit-stand decisions alone are worth more than all pair-splitting decisions combined…

From the practical point of view, the only pair-splitting indices worth learning at all are splitting X-X vs. 4, 5, and 6. Of the doubling indices, only 10 and 11 vs. X, and 11 vs. ace are worth varying basic strategy for.

A sophisticated player would memorize strategy indices according to potential profitability… [T]he recommendations of most systems developers to learn and utilize strategy tables for pair-splitting, surrender, and most double-down decisions are ill-considered, since the potential gains from such strategies are so negligible that most players should not chance making errors by attempting to employ such indices.

The information provided in Theory of Blackjack, in conjunction with the formula presented in this paper, is more than sufficient to develop a count strategy for any balanced count system as complete as any player could practically apply at the tables. Until system sellers analyze and incorporate into their systems the wealth of information in Griffin’s Theory of Blackjack, serious players should study this book themselves.”

Unfortunately, count system developers did not immediately follow up on this information.

In the June 1981 issue of Blackjack Forum (Volume I #2), in reviews of The World’s Greatest Blackjack Book by Lance Humble and Carl Cooper; Professional Blackjack (revised), by Stanford Wong; and Ken Uston’s Million Dollar Blackjack, Snyder wrote (p. 17):

All three of these books also provide strategy tables for pair splitting, hard and soft doubling, and both early and late surrender. Most players should ignore these tables. As systems developers analyze and incorporate the wealth of information from Griffin’s Theory of Blackjack into their systems, players will be advised to use count information primarily for betting, insurance, and hit-stand decisions only.

Basic strategy should always be followed for most other decisions. Griffin has shown that, other than for the splitting of tens, no pair splitting variation from basic strategy is worth more than one-thousandth of one percent. This means that for every $1000 of action, you may potentially gain 1 cent if you make this decision with computer accuracy. And this is in a single-deck game, head-on, dealt out 75% with Vegas Strip rules.

In multi-deck games, each pair-splitting index you memorize and apply perfectly will be worth only a fraction of a penny for every $1000 of your action. My advice is don’t waste your time.

Hard and soft doubling indices are likewise relatively worthless. I queried Griffin on his estimates for the value of early surrender and pair-splitting changes when doubling after splits is allowed. He informed me that the average gains from varying from basic strategy for these rules are negligible.

Doubling after splits indices are not worth much simply because of the rarity of occurrence. Early surrender decisions are a waste of time because early surrender is available in multi-deck games only. Don’t chance making errors to potentially increase your profits by a few cents per hour. Simplify your strategy. Basic strategy will take the majority of the potential gain from these decisions.

The insurance decision is worth 200 times as much as any pair splitting decision in a single-deck game. The hit-stand decision for 16 vs. 10 is worth almost 100 times as much.

The only pair splitting indices you may want to learn are for splitting 10’s vs. 5 or 6. The only double-down decisions of minor value are for 10 and 11 vs. ace, and 10 vs. 10. These are the only double and split changes which would pay more than a dime per $1000 bet in a single-deck game. Again, I urge you to get Griffin’s Theory of Blackjack so you can see where the money is.

Then, on September 30, 1981, Snyder published his own Zen Count, which was the first counting system designed to take into account the actual relative gain from using various index numbers with a real-world type of count. With his Zen count, Snyder included the “Zen 25” index numbers, explaining that most of the potential playing strategy gain available from card-counting was provided by these 25 index numbers.

The Zen 25 were selected for use in any number of decks, including single deck. Snyder wrote (Blackjack Forum Vol. 1 #3, September 198, p. 8) “The [Zen] tables are condensed to include only those strategy decisions which are of significant value, based on Griffin’s ‘average gains’ table (Theory of Blackjack page 30) as proposed in Blackjack Forum #2, (p. 18-19).”

A year later, in the September 1982 issue of Blackjack Forum, Volume II #3, Snyder, responding to a letter from Marvin L. Masters, wrote that in multiple-deck games he would revise the Zen list of 25 recommended indices to a smaller list of only 18 indices.

Marvin L. Masters wrote: “The major strategy changes worth learning (Blackjack Forum Vol. II, #2, p. 7)… are for single deck. Shoe strategy changes at, say –3 or less are of no interest to me: I’ve left the table at –2.”

Snyder responded: “This is a good point. There is no reason to learn strategy indices you would never use, and there is rarely any reason to continue playing in a shoe game when the true count goes down to –2. For shoe players, table-hoppers etc., I would revise the list of 25 recommended indices to a smaller list of only 18 indices, if I were using the Zen Count and assuming I leave the table at –2.

"Of course, if you have no trouble with the memory work you might also add a few more positive indices since playing these hands accurately will become more important to your win rate as your bet size increases. I’d like to thank Don Schlesinger also for pointing this out.”

I think it important to note that the acknowledgement of Schlesinger was not for any comments, public or private, that Schlesinger made regarding the 18 most important indices, but for comments Schlesinger had made in private correspondence regarding the point Marvin L. Masters made about negative indices being unimportant to table-hoppers.

Technically, this was not a “discovery” of either Marvin L. Masters’ or Don Schlesinger’s, however—credit for that belongs to Stanford Wong. In his first edition of Professional Blackjack (Pi-Yee Press, 1975), Wong advised table-hopping players to ignore index numbers below –2. Marvin L. Masters was simply pointing out the obvious and Snyder acknowledged that Schlesinger had sent a letter to Blackjack Forum with a similar comment.

Snyder’s recommendation of such a short list of indices caused great controversy. In the March 1982 Blackjack Forum (Volume II #1), in the article John Gwynn Tests the Zen Count, Snyder wrote (p. 3):

“Many of my subscribers have purchased the Zen Count strategy from me, and Gwynn’s simulation answers the most frequently asked question I get from Zen Count players. Can the Zen Count really win with such condensed strategy tables?

"The Zen Count has by far the simplest set of strategy tables ever published for a count which claims to be an 'advanced' higher-level system. Many players who receive the strategy from me immediately write and request “the complete” tables. If you want to know how simple the Zen Count tables are, keep in mind that Gwynn simulated the Zen Count exactly as I have published it. There are a total of only 25 indices: 18 hit/stand, 3 doubling, 3 splitting and 1 for insurance.

"By comparison Uston’s APC was simulated exactly as Uston published it in his book Million Dollar Blackjack, using a total of 161 indices (43 hit/stand, 76 doubling, 41 splitting, 1 insurance.) Hi-Opt I was simulated in its complete form, as available from International Gaming, with 202 indices (62 hit/stand, 94 doubling, 45 splitting, 1 insurance). After simulating the Zen Count, Gwynn wrote to me: ‘It really is amazing that Zen with only 24 [indices, plus insurance] is so good.’”

On p. 4 of the article, Snyder shows that the Zen Count had a win rate of about 0.03% greater than Hi-Opt I, while Uston’s APC, using all 161 indices had a win rate about .03% greater than the Zen Count.

Snyder wrote on p. 6:

“My advice for most players is to stick with a simple level one counting system and to simplify your strategy tables. You are probably wasting your time if you are trying to employ more than a few dozen indices.”

And on p. 30, regarding Dr. John Gwynn’s simulations to test the effect of pair-splitting on a player’s win rate:

Some sample results, assuming Northern Nevada rules in a single-deck game, using the Hi-Opt I counting system: If flat-betting, the gain from splitting pairs according to the Hi-Opt I indices, instead of basic strategy only, is about .06%. Of this total gain approximately .05% is realized from applying the indices for splitting tens.

The other .01% gain is due to all other pair splits. Likewise, if playing basic strategy for all decisions other than splitting pairs, and betting nothing any time the true count is less than +0.5 and betting one unit any time the true count is equal to or greater than +0.5, Gwynn’s simulations result in the following per-hand win rates:

1. Splitting all pairs as per Hi-Opt I indices: +0.65%

2. Splitting only tens as per Hi-Opt I indices, other pairs according to basic strategy: +0.65%.

3. Splitting all pairs according to basic strategy only: +0.60%.

As Gwynn commented in his letter to me which accompanied his results: ‘All of this bears out your contention that only splitting tens is really worthwhile using indices; basic strategy is adequate for all other pairs.’

Even Gwynn, who had run the simulations that Peter Griffin used to revise his “Average Gains for Varying Basic Strategy” chart, expressed surprise at Snyder’s discoveries in the letter accompanying the data he had submitted to Blackjack Forum.

Snyder’s correspondence continued to be packed with questions from players regarding the importance of the index numbers beyond the 25 Snyder recommended in the Zen Count for single deck, and the 18 he recommended for shoe games.

In 1983, in the first edition of Blackbelt in Blackjack, in his discussion of the Red Seven Count on p. 42, Snyder wrote:

“First of all, insurance is the most important strategy decision. In single-deck games, assuming you are using a moderate betting spread, insurance is almost as important as all other strategy decisions combined…

"As for other playing decisions, there are only a few to remember. Any time you are at your pivot or higher stand on 16 vs. 10 and stand on 12 vs. 3. In single-deck games, the 16 vs. 10 decision is the second most important strategy decision for a card counter—insurance being first. The 16 vs. 10 decision is more important than all pair splitting indices combined!

"After you find these few strategy changes easy, there are a couple of others you can add which will increase your advantage. At your pivot plus 2, or higher, with any number of decks, stand on 12 vs. 2; stand on 15 vs. 10; and double down on 10 vs. X. In multi-deck games, you will be taking advantage of about 80% of all possible gains from card counting by using this strategy…”

I think it interesting to record at this point something of Schlesinger’s view of these recommendations at the time Snyder published them, initially six years prior to publication of Schlesinger’s “Attacking the Shoe!”

In the March 1984 Blackjack Forum Vol. IV #1 (p. 36), the following letter from a reader was published:

“Letter from California: ‘With 8-8 vs. 10, do I split instead of surrender even when the deck is rich?’”

Snyder’s published reply to this reader: “You would be playing more accurately if you surrendered 8-8 vs. 10 when the count was high enough, but your expected difference in win rate from learning and applying an accurate count strategy on this play would be measurable in pennies per year, even for a high stakes pro. The situation is rare and the gain is negligible. Forget about it. It’s a waste of time to consider it.”

Schlesinger sent a letter, dated June 24, 1984, for publication in Blackjack Forum, regarding Snyder’s answer:

…I think you have never quite understood how important surrender is to a high-stakes player. And it is for the very reason that you say to forget about making the play that I would never forgive myself if I had $500 out and failed to make the play.

The point is that we don’t get hundreds of thousands of chances at this 8-8 v. 10 surrender in our lives. We get perhaps one or two in a lifetime, as you suggest. Thus, the negligible difference never has a chance to be negligible!

If I split those 8’s (at Caesars, for example) and then double and/or split after, I might wind up with $2000 on the table. And I might lose it all, instead of losing $250 by surrendering.

Now please don’t lecture me about expectation. I know all about how I could also win the $2000 and that when you multiply by the probability of each, it comes to pennies or dollars. Well, you go ask the dealer for your pennies when he sweeps away the $2000!

Maybe five years later, when the hand comes up again, you’ll have another chance to get your money back. As for me, it is a cop-out to claim that you would purposely and knowingly play a hand incorrectly because you were too lazy to ‘clutter your brain with worthless strategy indices’ when you could, instead, cultivate your act and seek better table conditions.

You know what, Arnold, some of us can actually walk and chew gum at the same time! Would you believe that I can really roam a casino back-counting, look natural doing it, and miraculously remember the number for 8-8 v. 10 all at the same time! Amazing, huh?

…In any event, Arnold, stop telling people to play incorrectly, particularly when they play for thousands of dollars, because playing wrong doesn’t matter. How can you sleep giving advice like that?” [This was a hand-written letter and the underlining is his.]

Snyder had his typist prepare Schlesinger’s letter for publication, with Snyder’s response. But Snyder told me he decided not to publish it at the last minute because he felt that publishing the letter would cause Schlesinger public embarrassment.

The response that Snyder had prepared for publication pointed out that if, in fact, we should all learn the index number for 8-8 v. X because this hand might occur at a time when we had a big bet on the table, then we should, in fact, simply learn the full 150-200 index numbers for all decisions. Any of them might occur some time when we have a big bet on the table.

Schlesinger didn’t understand, at this point, the logic of reducing the number of indices based on actual dollar value. The reason for reducing the number of indices wasn’t because they had no value. It was because a simpler set of indices would allow players to play longer, with less mental fatigue, little actual dollar cost, and fewer errors.

It is amusing to me that, in 1986, three years after this letter, Schlesinger included no surrender numbers in his “Illustrious 18.” Moreover, his “Fab 4” surrender indices, published 11 years after his letter to Snyder, in December of 1995, did NOT include 8-8 v. X.

Don Schlesinger’s article on the “Illustrious 18” (“Attacking the Shoe!”) takes the work of Griffin, Snyder, and Gwynn regarding the most important indices in terms of gain, and works out precise numbers for one particular situation: a player using the Hi-Lo count with a particular 1-12 spread in a 75%-dealt four-deck game.

My simulations show that a player who uses Schlesinger’s 18 rather than Snyder’s recommended 15 indices for shoe games, in a 6-deck shoe game dealt 75%, using a 1 to 12 spread, has an expectation of roughly an additional three hundredths of a percent. In simulations of a single deck game dealt 65%, with H17 and a 1 to 3 spread, Snyder’s 18 and Schlesinger’s 18 came out exactly the same, at a .99% win rate (100 million hands, standard error .02%).

Using the full 25 indices Snyder recommended for single deck, the sims for the single-deck game show a win rate for Snyder of 1.01%, versus Schlesinger’s .99% (100 million hands, standard error .02%).

The optimal set of indices changes not only with the number of decks in play, penetration, play-all versus tablehopping styles, other advanced techniques, and the spread you use, but will also change based on the count system you use. The optimal set for the Hi Lo is not the same as the optimal set for the Zen count, and so on.

Schlesinger deserves credit for pointing out that in shoe games where card counters must use large spreads, the doubling indices for 9 v. 2, 9 v. 7, and X v. A gain in value. However, his claim of being the originator of or even the first to publish the seminal discoveries about the relative value of various index plays is false.

He was not the first to tell players “which index numbers are most important to learn based on the amount of total gain which can be obtained by their use.” He was not the first to quantify and write about the relative value of the insurance play or 16 v. 10 or 15 v. 10, or other important plays, as he claimed in “Attacking the Shoe!”, or to write about the total gain available from a small number of the most important indices.

He was not the first to discover or recommend that players might just as well throw 90% of their numbers away. He just failed to acknowledge the contributions of the real originators of condensed strategy tables. ♠

Griffin’s 1979 play variation ranking, for 1-Deck (top 18 plays):

Insurance; 16 v. X; 14 v. X; 15 v. X; 13 v. X; 13 v. 2; 12 v. 4; 12 v. 3; 13 v. 3; X-X v. 6; X-X v. 5; 11 v. X; 13 v. 4; 16 v. 7; 12 v. X; 16 v. 9; 14 v. 2; 10 v. X

Snyder’s 1981 Zen 25 for all numbers of decks:

Insurance; 16 v. X; 16 v. 9; 15 v. X; 15 v. 2; 14 v. 2, 3, 4; 13 v. 2, 3, 4, 5, 6; 12 vs. 2, 3, 4, 5, 6; 11 v. A; 11 v. X; 10 vs. X; X-X v. 6; X-X v. 5

Snyder’s 1982 recommended Zen 18 for table hoppers who leave at –2:

Insurance; 16 v. X; 16 v. 9; 15 v. X; 14 v. 2; 14 v. 3; 14 v. 4; 13 v. 2; 13 v. 3;; 12 vs. 2; 12 v. 3; 12 v. 4; 12 v. 5; 12 v. 6; 11 v. A; 10 vs. X; X-X v. 6; X-X v. 5

Schlesinger’s 1986 recommended indices for a 4-deck, 75%-dealt game, for a Hi-Lo player using a specific 1-12 spread.

Insurance; 16 v. X; 16 v. 9; 15 v. X; 13 v. 2; 13 v. 3; 12 v. 2; 12 v. 3; ; 12 v. 4; 12 v. 5; 12 v. 6; 11 v. A; 10 v. X; 10 v. A; 9 v. 2; 9 v. 7; X-X v. 6; X-X v. 5

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  The History of Blackjack's Illustrious 18 Card Counting Indices
The simplification of playing and betting strategy in blackjack card counting was one of the most important developments in professional blackjack play. This blackjack history article focuses on the roles of Arnold Snyder, Peter Griffin, and Don Schlesinger in this card counting development.