Playing the Pros’ Way Don Schlesinger Huntington Press Las Vegas, Nevada Table of Contents List of Tables ix Foreword by Stanford Wong xiii Introduction by Arnold Snyder xv Publisher’s Introduction by Viktor Nacht xvii Acknowledgments xix Prefaces by Don Schlesinger xxiii 11 Back-Counting the Shoe Game 1 12 Betting Techniques and Win Rates 15 13 Evaluating the New Rules and Bonuses 29 14 Some Statistical Insights 43 15 The “Illustrious 18” 55 16 The “Floating Advantage” 67 17 Camouflage for the Basic Strategist and the Card Counter 91 18 Risk of Ruin 111 19 Before You Play, Know the SCORE! 151 viii Table of Contents 10 The “World’s Greatest Blackjack Simulation” 185 11 Team Play 287 12 More on Team Play: A Random Walk Down the Strip 303 13 New Answers to Old Questions 343 14 Some Final “Words of Wisdom” from Cyberspace 379 Appendix A: Complete Basic Strategy EVs for the 1-, 2-, 4-, 6-, and 8-Deck Games 387 Appendix B: Basic Strategy Charts for the 1-, 2-, and Multi-Deck Games 475 Appendix C: The Effect of Rules Variations on Basic Strategy Expectations 491 Appendix D: Effects of Removal for the 1-, 2-, 6-, and 8-Deck Games 495 Epilogue 523 Selected References 525 Index 529 List of Tables 1.1 Back-Counting with Spotters 13 2.1 Standard Deviation by Number of Decks 20 2.2 Probability of Being Ahead after n Hours of Play 21 2.3 Analysis of Win Rates and Standard Deviation for Various Blackjack Games 23 2.4 Optimal Number of Simultaneous Hands 26 2.5 Expectation as a Function of “Spread” 27 3.1 Summary of New Rules 39 4.1 Final-Hand Probabilities (in %) 50 5.1 The “Illustrious 18” and the “Fab 4” 62 6.1–6.4A Single-Deck “Floating Advantage” 72–74 6.5–6.9A Double-Deck “Floating Advantage” 75–77 6.10–6.11 6 Deck/Deal 5.5 “Floating Advantage” 78 6.12–6.15A 6 Deck/Deal 4.5 “Floating Advantage” 84–85 6.16–6.19A 6 Deck/Deal 5 “Floating Advantage” 86–87 6.20–6.24A 6 Deck/Deal 5.5 “Floating Advantage” 87–89 7.1 Hand Frequencies Based on 100,000 Playable Hands 97 7.2 Conditional Penalty, in Percent, for Deviating from Basic Strategy 98 7.3 Absolute Penalty, in Cents per $100 Bet, for Deviating from Basic Strategy 99 7.4 2-Deck, Play All 109 7.5 6-Deck, Play All 109 7.6 6-Deck, Back-Counting 109 8.1 Risk of Ruin 116–18 8.2 Bankroll Requirements 119–21 8.3 Trip Bankroll Requirements (Preliminary) 127 8.4 Trip Bankroll Requirements (Final Results) 131 8.5 Lifetime ROR Comparisons 141 8.6 Trip ROR Comparisons 142 8.7 Reach Goal or ROR, with Time Constraints Comparisons 144 x List of Tables 8.8 Reach Goal, with No Time Constraints Comparisons 144 8.9 Cumulative Normal Probability Distribution (-3.09 to 0) 147 8.10 Cumulative Normal Probability Distribution (0 to 3.09) 148 8.11 Exponential Functions 149 9.1 Hi-Lo 1-Deck SCORE 156 9.2 Hi-Lo 2-Deck SCORE 156 9.3 Hi-Lo 6-Deck Play-All SCORE 157 9.4 Hi-Lo 6-Deck Back-Count SCORE 157 9.5 Hi-Lo 8-Deck Play-All SCORE 158 9.6 Hi-Lo 8-Deck Back-Count SCORE 158 9.7 Hi-Lo 1-Deck SCORE 159 9.8 Hi-Lo 2-Deck SCORE 160 9.9 Hi-Lo 2-Deck SCORE 160 9.10 Hi-Lo 6-Deck SCORE 161 9.11 4.5/6 Back-Count SCORE 165 9.12 5/6 S17 DAS LS SCORE 166 9.13 5/6 S17 DAS LS SCORE 167 9.14 5/6 S17 DAS LS Play-All SCORE 168 9.15 31/52 S17 SCORE 168 9.16 39/52 H17 D10 SCORE 169 9.17 31/52 S17 SCORE 171 9.18 39/52 H17 D10 SCORE 171 9.19 62/104 S17 DAS SCORE 171 9.20 62/104 H17 DAS SCORE 171 9.21 5/6 S17 DAS LS SCORE 172 9.22 K-O (P) 1-Deck SCORE 173 9.23 K-O (P) 2-Deck SCORE 173 9.24 K-O (P) 6-Deck Play-All SCORE 174 9.25 K-O (P) 6-Deck Back-Count SCORE 174 9.26 K-O (P) 8-Deck Play-All SCORE 175 9.27 K-O (P) 8-Deck Back-Count SCORE 175 9.28 Hi-Lo v. Red Seven v. K-O SCORE 176 10.1 The Simulation Indices 213 10.2 8-Deck Play-All SCORE Summary 214 10.3 8-Deck Back-Count SCORE Summary 215 10.4–10.35 8-Deck Simulation Results 216–31 List of Tables xi 10.36 6-Deck Play-All SCORE Summary 232 10.37 6-Deck Back-Count SCORE Summary 233 10.38–10.69 6-Deck Simulation Results 234–49 10.70 2-Deck Play-All SCORE Summary 250 10.71 2-Deck Back-Count SCORE Summary 251 10.72–10.103 2-Deck Simulation Results 252–67 10.104 1-Deck SCORE Summary 268 10.105–10.140 1-Deck Simulation Results 269–86 12.1 The Simulation Settings 304 12.2 The Team’s Year 1 Results 305 12.3 Al’s Year 1 6-Month Results 308 12.4 Al’s Year 1 Third Quarter Results 309 12.5 Al’s Year 1 Fourth Quarter Results 310 12.6 Bob’s Year 1 First Weekend Results 311 12.7–12.10 Bob’s Year 1 Quarterly Results 312–15 12.11 Cal’s Year 1 First Weekend Results 316 12.12 Cal’s Year 1 Results after Hour 47 317 12.13–12.16 Cal’s Year 1 Quarterly Results 318–21 12.17–12.18 Don’s Year 1 First Two Weekend Results 322–23 12.19 Don’s Year 1 Results after 86 Hours 324 12.20–12.23 Don’s Year 1 Quarterly Results 325–28 12.24–12.27 Ed’s Year 1 Quarterly Results 329–32 12.28 The Team’s 5-Year Results 333 12.29 Hi-Opt II Simulation Results (Lance) 336 12.30 Lance’s First Two Weekends Results 337 12.31–12.34 Lance’s Quarterly Results 338–41 13.1–13.4 Optimal Departure 6-Deck 360–63 13.5–13.8 Optimal Departure 8-Deck 364–67 13.9 Hourly 6-Deck Entry and Departure Data 368 13.10 Hourly 8-Deck Entry and Departure Data 369 13.11 The “Catch 22” Indices 375 13.12 Comparative Study of EV-Maximizing and Risk-Averse Approaches 375 13.13–13.15 Risk-Averse Analyses 378 A1 Summary of Basic Strategy EVs for the 1-, 2-, 4-, 6-, and 8-Deck Games 394 A2–A17 Basic Strategy EVs for the 1-Deck Game 395–410 A18–A33 Basic Strategy EVs for the 2-Deck Game 411–26 xii List of Tables A34–A49 Basic Strategy EVs for the 4-Deck Game 427–42 A50–A65 Basic Strategy EVs for the 6-Deck Game 443–58 A66–A81 Basic Strategy EVs for the 8-Deck Game 459–74 B1 Basic Strategy for 1-Deck S17 NDAS 478 B2 Basic Strategy for 1-Deck S17 DAS 479 B3 Basic Strategy for 1-Deck H17 NDAS 480 B4 Basic Strategy for 1-Deck H17 DAS 481 B5 Basic Strategy for 2-Deck S17 NDAS 482 B6 Basic Strategy for 2-Deck S17 DAS 483 B7 Basic Strategy for 2-Deck H17 NDAS 484 B8 Basic Strategy for 2-Deck H17 DAS 485 B9 Basic Strategy for Multi-Deck S17 NDAS 486 B10 Basic Strategy for Multi-Deck S17 DAS 487 B11 Basic Strategy for Multi-Deck H17 NDAS 488 B12 Basic Strategy for Multi-Deck H17 DAS 489 B13 Basic Strategy for Early Surrender 490 B14 Basic Strategy for European No Hole Card 490 C1 The Effect of Rules Variations on Basic Strategy Expectations (in percent) 492–93 D1 Effects of Removal for Dealer’s Upcard A (S17) 506 D2 Effects of Removal for Dealer’s Upcard 2 (S17) 507 D3 Effects of Removal for Dealer’s Upcard 3 (S17) 508 D4 Effects of Removal for Dealer’s Upcard 4 (S17) 509 D5 Effects of Removal for Dealer’s Upcard 5 (S17) 510 D6 Effects of Removal for Dealer’s Upcard 6 (S17) 511 D7 Effects of Removal for Dealer’s Upcard 7 (S17) 512 D8 Effects of Removal for Dealer’s Upcard 8 (S17) 513 D9 Effects of Removal for Dealer’s Upcard 9 (S17) 514 D10 Effects of Removal for Dealer’s Upcard T (S17) 515 D11 Effects of Removal for Dealer’s Upcard A (H17) 516 D12 Effects of Removal for Dealer’s Upcard 2 (H17) 517 D13 Effects of Removal for Dealer’s Upcard 3 (H17) 518 D14 Effects of Removal for Dealer’s Upcard 4 (H17) 519 D15 Effects of Removal for Dealer’s Upcard 5 (H17) 520 D16 Effects of Removal for Dealer’s Upcard 6 (H17) 521 D17 Betting and Insurance Effects of Removal 522 D18 Betting and Insurance Correlations 522 Chapter 1 December 1984 Cover Art by Jesse Hover Back-Counting the Shoe Game “Enjoyed Don Schlesinger’s fine article.” — Ken Uston, legendary player, and famed author of many blackjack books, including Million Dollar Blackjack “I can provide an assurance that Don Schlesinger really is as good, as successful and as disciplined as he claims.” — Stanford Wong, noted blackjack author of several landmark works, including Professional Blackjack “Schlesinger’s article is the best that has ever appeared re: ‘Casino Comportment.’” — Peter Griffin, author of The Theory of Blackjack 2 Blackjack Attack: Playing the Pros’ Way As the saying goes, “This is where it all began.” I had been, for several years prior, a steady contributor and letter-writer to both Stanford Wong’s blackjack newsletters and Arnold Snyder’s quarterly magazine, Blackjack Forum.