MASTER CLASS – THE HI-LO CARD COUNTING SYSTEM
A complete guide to index play
By Don Schlesinger
As with so many of the ambitious blackjack projects I have directed over my career, the article that you are about to read summarizes the result—The Hi-Lo Card Counting System: A Complete Guide to Index Play—of an incredible amount of sophisticated computer programming and simulations by one of the most talented researchers in the game today. I came to know Dave “Gronbog” Brolley as a regular and valued contributor to Norm Wattenberger’s online website www.blackjacktheforum.com. When one of the discussions turned toward the extra advantage that advanced players might glean from learning an extremely complicated system employed by one of the more prominent forum members, Dave and I decided to see if we could evaluate this highly complex approach to the game and render an expert opinion as to its ultimate effectiveness.
It was through this daunting process, involving very challenging programming, that I came to admire the work ethic and extraordinary talents of this gifted member of the advantage-player community. And so, when yet another idea for a rather elaborate piece of blackjack research came to mind, Dave was a logical choice to share the adventure with me. Permit me to explain.
Ever since the appearance, in 1986, of the now iconic “Illustrious 18” in an article I wrote for Arnold Snyder’s Blackjack Forum magazine, players have asked if there could be more. Specifically, they wanted to know what strategy-departure index numbers lay beyond the 18, and ideally, in what order of importance they ought to be learned; that is, incrementally, as more indices would be added to one’s repertoire, for a given count system, they wondered how much extra advantage could be garnered in terms of what we now refer to as SCORE (my acronym for Standardized Comparison Of Risk and Expectation). The (somewhat limited) goals of the original article were clear: “1) To explore the actual gain available from using the Hi-Lo count in a multiple-deck situation, and 2) To rank, in order of contribution to that gain, each individual departure from basic [strategy].” Nonetheless, I left the door wide open, as I often do, for the possibility of future research in the area when I continued: “[I] hope to demonstrate … the adaptability of my approach for different counts, betting schemes, and rules.”
And to be sure, there were a few takers. First was Bryce Carlson, who, in 1995, published a study in Blackjack Forum, which I referenced on page 61 of Blackjack Attack, 3rd Edition (BJA3). In addition to the I18, he also examined an enlarged array, using a total of 68 indices for his Advanced Omega II count. As expected, the findings showed small incremental returns for the added indices with, quite naturally, larger gains for one- and two-deck games than for six-deck.
Next was Norm Wattenberger, who took me up on my suggestion to once again explore just the I18 (or, more accurately for Norm’s analysis, the “Sweet 16,” which omitted ten-splits) but for counts other than Hi-Lo, when, in 2009, he published a comprehensive “Super-SCORE” study, in volume 1
of Modern Blackjack. Using a variety of spreads for different numbers of decks, he investigated and compared 12 different counts in an impressive piece of work that expanded upon the findings of the SCORE chapter of BJA3.
Methodology
As previously stated, players were eager to know what lay beyond the original 18 indices (expanded subsequently to the “Catch 22”; see BJA3, pp. 374–375) and the Fab 4 surrender values, not only for Hi-Lo, but for other counts, as well. For decades, I had, somewhat stubbornly, resisted furnishing this information for a variety of reasons. First and foremost was my insistence, per the original premise, that adding more indices would have diminishing returns and that the bulk of all the advantage available through the use of strategy departures had already been furnished by the I18. I was convinced that establishing a more complete list of such indices would be tantamount to “spitting into the wind” and that the results would be disappointing. Not surprisingly, I was, more than once, roundly criticized, by players and researchers alike, for my apparent intransigence. They claimed that a) they wanted to be the judges of what the value of more indices could be, and b) there was a definite gap in the literature as to this potentially important area of research. Next was the sheer amount of work that such a venture would surely entail. Was I up to the task? Or was I too lazy or unmotivated to embark upon such a daunting piece of work, which, in my view, would simply not be worth the considerable effort?
I had always believed that if such a project were to be undertaken, it was going to have to be done in grand style. My grandfather taught me a precept that I have followed all of my life: Anything worth doing is worth doing well. I began to draw up the blueprint in my mind, consulting, of course, with Dave, who, after all, would be doing all of the heavy lifting.
And so (perhaps a bit later than was desired), with the new book and the anticipated entire series of such works encompassing a dozen of the most popular point-count systems, players are finally getting their wish—and then some!
To guarantee the integrity and accuracy of the indices, the most rigorous process imaginable was adopted for their generation. For every player holding versus each dealer upcard, sufficient simulations were undertaken to create a level of confidence of nearly 99.9% wherever feasible. That is, if a play turned out to be very close, and two indices were being considered, simulations continued until the comparison of their standard errors was so small that a “winner” for each play could be determined with virtual certainty. In short, the (floored) indices contained in the study are, without question, the most reliable ever produced.
It should be noted, nonetheless, that some plays simply defied an ultimate determination, no matter how large the simulations. In those cases, in the generating program, a percentage of confidence was furnished under the index in question, but for space considerations, we decided not to display those values in the final product. More often than not, for those thorny situations, we decided to err on the side of the more risk-averse play, delaying doubles and splits to the higher index of the two being considered, or surrendering at the lower of the two. In the end, the player can take solace in the fact that differences in SCOREs are virtually undetectable for the use of these “recalcitrant” indices.
Finally, it should be noted that the index charts represent the values associated with the 4.5/6 level of penetration for the six-deck game and the 62/104 level for the two-deck game. We tried, for the former, 4/6 and 5/6 and found only minor differences. We even generated 7/8 S17 DAS LS, because that game existed in Dave’s area, but still found no major differences as compared to 4.5/6. The same reasoning applied to the two-deck game and our decision to catalog only the 62/104 level for the current study.
Projects such as this one rarely end up as they were originally conceived. Always, along the way, ideas for enhancements and refinements pop up, and I thanked Dave for his infinite patience and flexibility, as I continued to ask for more features and more content. As readers are aware, the Hi-Lo point count is the standard-bearer when it comes to both blackjack research and popularity among players. So, it was natural to begin our quest for an expanded list of indices with the same Hi-Lo that had been the basis for the original I18 concept. But, I warned Dave that my appetite for such expanded lists would not stop with just this single system. No, if we were going to do it, we were going to do it in the aforementioned grand style! And so, now that this prototype monograph on Hi- Lo has been completed, many more companion pieces are envisioned, perhaps available as downloads, covering a majority of the most popular card-counting systems.
How to Read the Charts
The book contains charts with the long-desired expanded lists of indices to a now more robust 50, duly baptized the “Nifty 50” (or “Sporty 40,” for back-counting). There are eight columns: Line by line, the reader sees the rankings (column 1, Rank), the holdings (column 2, Hand) with the corresponding departure indices (column 3, Index) and playing decisions (column 4, Playing Decision), which are ranked by their contribution to the Max SCORE for the referenced game conditions (next-to-last row of column 6). Progressively, and starting with no index use at all (row 0, No Indices), one can, therefore, precisely determine the dollar value of adding each index to one’s play, both on an individual (column 5, SCORE Gain) and cumulative basis (column 6, Cumulative SCORE). Finally, once again on both an individual and cumulative basis, starting with the most important departure (row 1), one may reference the line-by-line percentage contribution of all the indices listed to that point to the Max SCORE available by using “all” the indices for a given system (column 7, Individual % of Total Gain, and column 8, Cumulative % of Total Gain). Thus, one can, with a simple glance, weigh the tradeoff between learning incrementally more indices and the added memorization and effort that are entailed by so doing. (Note: the bolded plays in column 2, Hand, highlight, in every chart, the original Illustrious 18 and, if surrender is offered, Fab 4.)
Next, in the manner of the well-known chapter 10 charts of Blackjack Attack, we would want to provide a wide variety of numbers of decks, rules, penetrations and bet spreads, so that the values of the various Nifty 50s cataloged would likely appeal to virtually all potential users, eager to find those conditions that most faithfully portray “their” personal approach(es) to the game. And so, the 306 tables contained in the book represent six- and two-deck games; eight different rules sets (dealer stands or hits on soft 17, double after splits is or is not permitted, and late surrender is or is not allowed); three levels of penetration; and six bet spreads, three each for the play-all and back- counting approaches.
The sample chart is intended to give the reader an idea of the vast amount of information that can be conveyed in a single tableau of this nature. And, if there is an enduring conclusion to be reached from our study, it has to be this: The original and seminal concepts of the Illustrious 18, Catch 22, and Fab 4 are as alive and vibrant today as they were more than 35 years ago, when first formulated. They continue to capture, across all games and rules sets, the great majority of all the gain available from the use of dozens of more indices. And while many will remain content to limit their index play to just these smaller subsets of the expanded lists, readers will now have the entirety of said lists at your disposal to do with as you see fit.
Enjoy!
Editor’s Note: The Hi-Lo Card Counting System: A Complete Guide to Index Play by Don Schlesinger and Dave Brolley is an invaluable resource for blackjack players looking to gain an advantage at the tables. With their extensive expertise in the field, the authors present a comprehensive exploration of the Hi-Lo card counting system, one of the most powerful and widely recognized methods in the realm of blackjack. With clear explanations, practical examples, and a wealth of tips and strategies, this guide equips readers with the knowledge and skills needed to excel in the game of blackjack and improve their chances of winning. The Hi-Lo Card Counting System: A Complete Guide to Index Play is available at www.amazon.com
