References and Bibliography

Transcription

1 References and Bibliography Anonymous, Ashley, Elizabeth, and Maria, The Secret Diary of an All-Girl Blackjack Team, CreateSpace Publishing, (2015) Baldwin, Roger, Wilbert E. Cantey, Herbert Maisel, and James P. McDermott, The Optimum Strategy in Blackjack, Journal of the American Statistical Association 51, (1956) Black, Fischer and Myron Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81, (1973) Braun, Julian H., How to Play Winning Blackjack, Data House Publishing, Chicago, (1980) Carlson, Bryce, Blackjack for Blood, Ingram Publishing, 3rd edition, (2017) Cox, J.C., S.A. Ross, and M. Rubenstein, Option Pricing: a Simplified Approach, Journal of Financial Economics 7, (1979) Epstein, Richard A., The Theory of Gambling and Statistical Logic, Academic Press, New York, revised edition (1995) Epstein, Richard A., The Theory of Gambling and Statistical Logic, Academic Press, New York, 2nd edition (2009) Ethier, S.N., The Kelly System Maximizes Median Fortune, Journal of Applied Probability 41, (2004) Griffin, Peter A., The Theory of Blackjack, Huntington Press, Las Vegas, 6th edition (1999) Grosjean, James, Beyond Counting, RGE Publishing, Oakland (2000) Harris, B., The Theory of Optimal Betting Spreads ; Janacek, K., Theory of Optimal Betting ; Yamashita, W., Optimal Betting Strategy : all at (1997) Hull, J.C., Options, Futures and Other Derivatives, Prentice Hall, Englewood Cliffs, NJ (2002) Ingersoll, J. E., Jr., Theory of Financial Decision Making, Rowman & Littlefield, New York (1987) Ito, C., On Stochastic Differential Equations, Memoirs of the American Mathematical Society 4, 1 51 (1951) Kelly, John L., Jr., A New Interpretation of Information Rate, System Technical Journal 35, (1956) MacLean, Leonard C., Edward O. Thorp and William T. Ziemba, The Kelly Capital Growth Investment Criterion: Theory and Practice, World Scientific (2010) Manson, A.R., A.J. Barr, and J.H. Goodnight, Optimum Zero-Memory Strategy and Exact Probabilities for 4-Deck Blackjack, The American Statistician 29, (1975) Marcus, H.I., New Blackjack Strategy for Players who Modify their Bets Based on the Count, in Ethier, S.N. and W.R. Eadington (eds.), Optimal Play: Mathematical Studies of Games and Gambling, Institute for the Study of Gambling and Commercial Gaming, University of Nevada, Reno (2007) Marsden, Jerrold E. and Anthony J. Tromba, Vector Calculus, Freeman, 5th edition (2007) Springer International Publishing AG, part of Springer Nature 2018 N. R. Werthamer, Risk and Reward, 145

2 146 References and Bibliography Maslov, Sergei and Y.-C. Zhang, Optimal Investment Strategy for Risky Assets, International Journal of Theoretical and Applied Finance 1, (1998); Matteo Marsili, Sergei Maslov and Y.-C. Zhang, Physica A 253, (1998) Merton, Robert C., Theory of Rational Option Pricing, Bell Journal of Economics & Management Science 4, 141 (1973) Mezrich, Ben, Bringing Down the House, Free Press, New York (2002) Mezrich, Ben, Busting Vegas, William Morrow, New York (2006) Morse, P.M., H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York (1953) Nersesian, Robert A., The Law for Gamblers: A Legal Guide to the Casino Environment, Huntington Press (2016) Poundstone, William, Fortune s Formula, Hill and Wang, New York (2005) Revere, Lawrence, Playing Blackjack as a Business, Carol Publishing, Secaucus NJ, revised edition (1980) Samuelson, Paul A., Proof that Properly Anticipated Prices Fluctuate Randomly, Industrial Management Review 6, 41 (1965) Scarne, John, Scarne s Complete Guide to Gambling, Simon & Schuster, New York (1961) Schlesinger, Don, Blackjack Attack: Playing the Pros Way, RGE Publishing, North Las Vegas, 3rd edition (2005) Scott, Jean, The Frugal Gambler, Huntington Press, Las Vegas, 2nd edition (2005) Shores, Thomas S., Applied Linear Algebra and Matrix Analysis, Springer, Berlin (2007) Sileo, Patrick, The Evaluation of Blackjack Games Using a Combined Expectation and Risk Measure, in Eadington, W.R. and J.A. Cornelius (eds.), Gambling and Commercial Gaming, University of Nevada, Reno (1992) Snyder, Arnold, Blackbelt in Blackjack, Cardoza Publishing, Las Vegas, 3rd edition (2005) Snyder, Arnold, The Big Book of Blackjack, Cardoza Publishing, Las Vegas (2006) Thorp, Edward O., Beat the Dealer, Blaisdell, New York, revised edition (1966) Thorp, Edward O., Does Basic Strategy Have the Same Expectation for Each Round?, in Vancura, O., J.A. Cornelius, and W.R. Eadington (eds.), Finding the Edge: Mathematical Analysis of Casino Games, University of Nevada, Reno (2000) Tilton, Nathaniel, The Blackjack Life, Huntington Press, Las Vegas (2012); for other memoirs see Scoblete, Frank, I Am a Card Counter: Inside the World of Advantage Play Blackjack, (2014); Anonymous, The Secret Diary of an All - Girl Blackjack Team, (2015) Vancura, Olaf, and Ken Fuchs, Knock-Out Blackjack, Huntington Press, Las Vegas, 3rd edition (2016) Werthamer, N. Richard, Optimal Betting in Casino Blackjack, International Gambling Studies 5, 253 (2005) Werthamer, N. Richard, Optimal Betting in Casino Blackjack II: Back-counting, International Gambling Studies 6, 111 (2006) Werthamer, N. Richard, Basic Strategy for Card Counters: An Analytic Approach, in Ethier, S.N. and W.R. Eadington (eds.), Optimal Play: Mathematical Studies of Games and Gambling, Institute for the Study of Gambling and Commercial Gaming, University of Nevada, Reno (2007) Werthamer, N. Richard, Optimal Betting in Casino Blackjack III: Table-hopping, International Gambling Studies 8, 63 (2008) Wong, Stanford, Professional Blackjack, Pi Yee Press, Las Vegas, 5th edition (1994); Blackjack Secrets, Pi Yee Press, Las Vegas (1994) Zender, Bill, Casino-ology: The Art of Managing Casino Games, Huntington Press, Las Vegas (2008)

3 Index A Aces, effects of, 38 Analogous relation, 56 Anti-counter table practices, 50 Asymptotic distribution, Auxiliary functions, 57 B Back-counting, Basic strategies composition-dependent, 12, 14 count-dependent strategy, 12 definition, 9 expected return vs. return on investment, generic strategy, 9 10 optimal basic strategy, 9 10 pair splitting, 10, 12 variant rules and procedures, 13 Bet staircase, 45 Bet strategies back-counting and table-hopping, chain rule convolution, 130 cumulative ruin probability, 102 current capital Invariance Theorem, 113 Kelly bet size, 111 Kelly betting, win/loss probabilities, 113 distribution of capital, 101 effective yield vs. risk curves, 107 expected capital and risk, fixed return, risk in capital distribution, 93, 95 conditional probability, 92 conservation of probability, 93 error functions, 94 expected capital and risk of ruin, 94 Player s trip capital, 92 ruin probability, 93, 96 sequence of rounds, 91 warm-up exercise, 91 Gaussian distribution, 105 generic strategy, 106 HJY point, 109 Lagrange multiplier, 104 lifetimer parameters, 106 mixed additive and multiplicative betting, 115, 116 multiple simultaneous hands, player s capital, distribution of, ramp modification, 110 risk and expected capital expressions, 102 slope parameter, 106 staircase vs. ramp performance, true count, 105 upper and lower bet bounds, 108 Wong bet function, 111 Wong s Benchmark bet staircase, 110 Betting back-counting and table-hopping, bet size bet ramp steepness, choice of parameters, 31 parameter values, 30 risk of ruin, 30 computation, 25 continuum of optimal curves, 27 doubling/pair splitting, 23 expected return, 23 jagged staircase, 24 Springer International Publishing AG, part of Springer Nature 2018 N. R. Werthamer, Risk and Reward, 147

4 148 Index Betting (cont.) lifetimer, 25, 26 negative return rounds, 24 optimal strategy, 24 overriding determinants, 24 parameters, 28 performance factors, player s capital, 24 player s current capital, player s yield, 23 playing multiple hands, return on investment, 31 risk of ruin, 26 shallow ramp, 24, 25 steep ramp, 24, 25 substantial losses, risk of, 24 Black-Scholes formula, 100 C Card counting procedure analytical framework asymptotic distribution, expected return; invariance theorem, Hermite series, back-counter, 46 basic strategy procedure, bet adjustment, 16 bet staircase, 45 counting vector, 44 expected return at nonzero depth, Kelly betting, 46 money management, 48 number of rounds playing, 48 optimal betting, 47 optimize player s performance, pack composition, 16 player s favor, 15 predict the return, 16 ruin protection, 48 running count, 44 table-hopping, 46 true count, 45 unbalanced counts, yield reduction factor, 48 Casino Blackjack history of American Indian tribes, 3 card-counting method, 5 computational methods, 4 counting scheme, 5 craps, 4 Internet chat-room, 5 in Las Vegas and Reno, 3 player decisions, 4 roulette, 3 slot machine, 3 table games, 3 recreation vs. a profession anti-counter table practices, 50 competitive non-professional, 50 non-counting player, 50 non-playing investors, 51 team-members time, 50 rules, procedures, and terminology chip units, 6 dealer, 5 6 doubling down, 7 equal-valued cards, 7 hard hand, 7 hitting, 7 performance implications, 8 player options, 7 Player s judgment, 6 soft hand, 7 spot cards, value of, 6 standing sticking, 7 surrender, 8 Composition-dependent play, 12, 14 Conditional probabilities, 55, 57 Count-dependent playing strategy, 12 computer simulation approach, 133 counting vector, counting vector optimal, insurance, with variable betting, Counter basic strategy (CBS), 41 42, Counting vector, 38 39, 44 Halves vectors, 18 Hi-Lo and Hi-Opt, integer half-integer, 18 Cox, Ross, and Rubenstein (CRR) approach, D Dealer reshuffles, 28 6-Deck pack, 40 Doubling pair splitting, 23 E Eigenmodes, 89 Expected return, 23 coefficient of proportionality, 20 computation of derivatives, linearity of return, 21 linear relationship of, 20

5 Index 149 at nonzero depth count-dependent, 83 count-independent optimal basic curve, 82 Invariance Theorem, 81 low-order polynomial, 83 polynomial fits, 83 reshuffle return, 82 yield and functions, 81 vs. return on investment, single-deck games, 21 vs. true count, 20 vs. true count, reshuffle round, six decks, 81 M Markov process, 100 Money management, 48 N Nonzero depth, expected return of count-dependent, 83 count-independent optimal basic curve, 82 Invariance Theorem, 81 low-order polynomial, 83 polynomial fits, 83 reshuffle return, 82 yield and functions, 81 G Gaussian distribution, 105 O Optimal betting, 47 Overriding determinants, 24 H Hermite series, Hi-Opt counting vector, 38 I Initial Running Count (IRC), 87 Insurance bet, Intuition, 62 Invariance Theorem, 81, 113 J Jagged staircase, 24 K Kelly betting, 32, 46, Kronecker delta functions, 57 L Lagrange multiplier, 104 Lifetimer bet strategies, 106 HJY bet point, operating parameters, Linear counts running count, six-deck shoe, 17 true count, 17 P Pair splitting, 62 63, 73 Performance factors bet spread, 29 counting strategy, 30 degradation in, 29 pack s composition, 28 player s capitalization, 29 player s financial performance, 29 Play strategies analytical framework analogous relation, 56 auxiliary functions, 57 conditional probabilities, 55, 57 Kronecker delta functions, 57 linear equations, 56 non-depleting, 55 count-dependent playing strategy, 37 computer simulation approach, 133 counting vector, counting vector optimal, insurance, with variable betting, of play parameters, counter basic strategy, counting vector, decks, small number of analytical framework, reordering theorem, expected return and optimal basic strategy, surrender, insurance, 71

6 150 Index Play strategies (cont.) expected number of cards, expected player return, frequency of tied hands, insurance bet, multiple hands computation of variance, 64 covariance expression, 64 intuition, 62 pair splitting, simultaneous and sequential play, 62 play parameters dependent on identities, of initial cards composition-dependent play strategy, 72, 74 pair splitting, 73 reshuffle round, 73 total-dependent (TD), 74 un-dealt cards, 37 value-dependent class, 37 variable bettor, Polynomial fits, 83 Synthesis and observations competitive player, recreational player, T Table-hopping, 34 35, 46 Total-dependent (TD), 74 True count, 45 U Unbalanced counting vectors advantages, 19 disadvantages, 19 IRC, mental arithmetic, 19 Un-dealt cards, 37 V Value-dependent class, 37 R Ramp modification, 110 Recreational player, Reshuffle return, 82 Reshuffle round, 73 Return on investment, 31 S Single-deck strategy, 39 Splitting pairs, 12 W Wong bet function, 111 Wong s Benchmark bet staircase, 110 Y Yield, players effective yield, 24, 25 expected losses, 23 ratio of, 23 risk factor, 25