Peter Griffin, Arnold Snyder, Don Schlesinger and the History of the "IIlustrious 18"
From ET Fan:
History of an Important Blackjack DiscoveryBy 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:
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This article is based upon a review of over one hundred published and unpublished documents related to the development of the Illustrious 18 and especially the original discovery that most index numbers relate very little to actual player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:
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):
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:
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:
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.