Blackjack Deviations 18

Blackjack pros resort to using indices for their playing deviations. An index is a number that tells you at what true count you must diverge from the basic strategy. Let’s use hard 12 against a dealer with a deuce as an example just to give you a better idea of how playing deviations for hitting and standing work. 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. You may come across blackjack tables whose dealers are required to hit soft totals of 17. This gives the casino an extra 0.22% edge over you. Dealers who hit soft 17s have a higher probability of improving their totals to 18, 19, 20, or 21 as opposed to their colleagues who stand on all 17s.

History of an Important Blackjack Discovery

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

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

I would like to begin by addressing the history of thewell-known “Illustrious 18” index numbers. The Illustrious 18 are the “discovery” for which the blackjack writerDon 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 FromUsing Basic Strategy Variations for the Hi-Lo System in a 4-Deck Game,”Schlesinger claims credit for the seminal discovery that most index numberscontribute 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.

I will document in this article that Schlesinger should notreceive credit for this discovery, despite his claims in this article andelsewhere, because the discovery was made, and published, years beforeSchlesinger’s article.

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

This article is based upon a review of over one hundredpublished and unpublished documents related to the development of theIllustrious 18 and especially the original discovery that most index numbersrelate very little to actual player win rates.

TheHistory of the “Illustrious 18”

The first discussion of the relative potential gains fromthe different playing decisions was published in the first edition of PeterGriffin’s The Theory of Blackjack,(GBC, 1979). On p. 30 of his book, Griffin provided a chart titled “AverageGains for Varying Basic Strategy.” (The chart is available in more recenteditions 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 ofabout 0.28% over the house.

But Peter Griffin made no recommendations about how to usethis information in the real world of playing at the tables. The first authorto publish an interpretation of Griffin’s data and actual playingrecommendations based on it was Arnold Snyder in his 1980 paper “AlgebraicApproximations of Optimum Blackjack Strategy,” republished by the University ofNevada 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 immediatelyfollow 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 CarlCooper; 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 ZenCount, which was the first counting system designed to take into account theactual relative gain from using various index numbers with a real-world type ofcount. With his Zen count, Snyder included the “Zen 25” index numbers,explaining that most of the potential playing strategy gain available fromcard-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-deckgames he would revise the Zen list of 25 recommended indices to a smaller listof only 18 indices.

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

Top 18 Blackjack Deviations

Snyder responded: “This is a good point. There is no reason to learn strategy indices youwould never use, and there is rarely any reason to continue playing in a shoegame 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 18indices, 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 ofSchlesinger was not for any comments, public or private, that Schlesinger maderegarding the 18 most important indices, but for comments Schlesinger had madein private correspondence regarding the point Marvin L. Masters made aboutnegative 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 indicescaused great controversy. In the March 1982 BlackjackForum (Volume II #1), in the article JohnGwynn Tests the Zen Count, Snyder wrote (p. 3):

“Many of my subscribers have purchased the Zen Countstrategy from me, and Gwynn’s simulation answers the most frequently askedquestion I get from Zen Count players. Can the Zen Count really win with suchcondensed 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 hada win rate of about 0.03% greater than Hi-Opt I, while Uston’s APC, using all161 indices had a win rate about .03% greater than the Zen Count.

Blackjack Deviations 18 Game

Snyder wrote on p. 6:

“My advice for most players is to stick with a simple levelone counting system and to simplify your strategy tables. You are probablywasting 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 testthe 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 Griffinused to revise his “Average Gains for Varying Basic Strategy” chart, expressedsurprise at Snyder’s discoveries in the letter accompanying the data he hadsubmitted to Blackjack Forum.

Snyder’s correspondence continued to be packed withquestions from players regarding the importance of the index numbers beyond the25 Snyder recommended in the Zen Count for single deck, and the 18 herecommended for shoe games.

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

“First of all, insurance is the most important strategydecision. In single-deck games, assuming you are using a moderate bettingspread, insurance is almost as important as all other strategy decisionscombined…

'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 ofSchlesinger’s view of these recommendations at the time Snyder published them,initially six years prior to publication of Schlesinger’s “Attacking theShoe!”

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

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

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

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

…I think you have never quiteunderstood how important surrender is to a high-stakes player. And it is forthe very reason that you say to forget about making the play that I would neverforgive 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’tmatter. How can you sleep giving advice like that?”

Snyder had his typist prepare Schlesinger’s letter forpublication, with Snyder’s response. But Snyder told me he decided not to publish it atthe last minute because he felt that publishingthe 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 thisletter, 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 include8-8 v. X.

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

My simulations show that a player who uses Schlesinger’s 18rather than Snyder’s recommended 15 indices for shoe games, in a 6-deck shoegame dealt 75%, using a 1 to 12 spread, has an expectation of roughly anadditional three hundredths of a percent. In simulations of a single deck gamedealt 65%, with H17 and a 1 to 3 spread, Snyder’s 18 and Schlesinger’s 18 cameout 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 numberof decks in play, penetration, play-all versus tablehopping styles, otheradvanced techniques, and the spread you use, but will also change based on thecount system you use. The optimal set for the Hi Lo is not the same as theoptimal set for the Zen count, and so on.

Schlesinger deserves credit for pointing out that in shoegames 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 originatorof or even the first to publish the seminal discoveries about the relativevalue 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. ♠

Blackjack Deviations 18 Vs

Griffin’s1979 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; 12v. 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’s1981 Zen 25 for all numbers of decks:

Blackjack Deviations 18

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-Xv. 6; X-X v. 5

Snyder’s1982 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.

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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