Risk and reward: the science of casino blackjack
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 131 S. graph. Darst. |
| ISBN: | 9781441902528 9781441902535 |
Internformat
MARC
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| 245 | 1 | 0 | |a Risk and reward |b the science of casino blackjack |c N. Richard Werthamer |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XVIII, 131 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Mathematisches Modell | |
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Datensatz im Suchindex
| _version_ | 1804140666162249728 |
|---|---|
| adam_text | Contents
Preface
..............................................................................
v
Introduction
.......................................................................
vii
Part I Strategy
1
The Game
...................................................................... 3
1.1
History of Casino Blackjack and Its Analysis
.......................... 3
1.2
Rules, Procedures, and Terminology
................................... 5
2
Playing the Hand
............................................................. 9
2.1
Basic Strategy
............................................................ 9
2.1.1
Expected Return with Variant Rules and Procedures
.......... 13
2.1.2
Expected Return vs. Return on Investment
.................... 13
2.2
Composition-Dependent Play
........................................... 14
3
Tracking the Cards
........................................................... 15
3.1
Linear Counts
............................................................ 16
3.2
Choosing a Counting Vector
............................................ 17
3.3
Unbalanced Counting Vectors
.......................................... 19
3.4
Relating the True Count to the Expected Return
....................... 20
4
Betting
......................................................................... 21
4.1
Yield, Risk, and Optimal Bet Strategies
................................ 21
4.1.1
Camouflage
...................................................... 26
4.2
Betting Proportional to Current Capital
................................ 27
4.2.1
Multiple Hands with Rescaling
................................. 28
4.3
Back-Counting and Table-Hopping
..................................... 29
5
Playing the Hand When the Count and Bet Vary
......................... 31
5.
Ì
Play Strategies that Vary with the Count
............................... 31
5.1.1
Reconsidering the Counting Vector
............................ 31
5.1.2
Count Dependence of the Play Parameters
.................... 33
xii Contents
5.1.3 The Insurance
Bet
............................................... 34
5.2
Counter Basic Strategy for the Variable Bettor
......................... 35
6
Synthesis and Observations
................................................. 37
6.1
A Practical, Nearly Optimal Strategy
................................... 37
6.2
Blackjack as a Recreation vs. a Profession
............................. 43
Part II Analysis
7
Play Strategies
................................................................ 47
7.1
Basic Strategy, Large Number of Decks
................................ 47
7.1.1
Analytical Framework
.......................................... 47
7.1.2
Expected Player Return
......................................... 49
7.1.3
Frequency of Tied Hands
....................................... 52
7.1.4
Multiple Simultaneous Hands: Return, Variance,
and Covariance
.................................................. 53
7.1.5
Expected Number of Cards Used per Round
.................. 56
7.2
Basic Strategy, Small Number of Decks
................................ 58
7.2.1
Analytical Framework
.......................................... 58
7.2.2
Expected Return, and Optimal Basic Strategy, vs.
Number of Decks
................................................ 61
7.2.3
Surrender; Insurance
............................................ 62
7.3
Play Parameters Dependent on Identities of Initial Cards
............. 63
7.3.1
Comparison with Previous Authorities
......................... 65
8
Card Counting
................................................................ 67
8.1
Analytical Framework
................................................... 67
8.1.1
Asymptotic Distribution
........................................ 67
8.1.2
Expected Return;
Invariance
Theorem
......................... 70
8.1.3
Hermite Series
................................................... 72
8.2
Expected Return at Nonzero Depth
..................................... 73
8.3
Optimizing the Counting Vectors
....................................... 75
8.4
Optimizing the Counting Vectors: Many-Cards Limit
................. 76
8.5
Computation of the Derivatives of the Expected Return
............... 78
8.6
Unbalanced Counts
...................................................... 78
Appendix
1
Asymptotic Distribution of Card Likelihoods
................ 79
Appendix
2
Eigenmodes
.................................................... 80
9
Bet Strategies
.................................................................. 81
9.1
Risk and Capitalization
.................................................. 81
9.1.1
Risk in a Game with Fixed Return
............................. 81
9.1.2
Optimal Betting When Return Fluctuates: Expected
Capital and Risk
................................................. 85
9.1.3
Connections with Finance
...................................... 89
9.1.4
Properties of the Risk and Expected Capital Expressions
..... 90
Contents xiii
9.1.5 Optimal
Betting When
Return
Fluctuates: Bet Strategy
....... 93
9.1.6
Yield When the Bet Size Is Discrete; Wong
Benchmark Betting
.............................................. 98
9.2
Betting Proportional to Current Capital
................................ 100
9.2.1
One Hand per Round
............................................ 100
9.2.2
Multiple Simultaneous Hands
.................................. 103
9.3
Back-Counting and Table-Hopping
..................................... 105
9.3.1
Entry
............................................................. 105
9.3.2
Entry and Exit
................................................... 107
9.3.3
Entry and Departure
............................................. 110
9.3.4
Entry, Exit, and Departure
...................................... 112
Appendix
1
The Risk of Ruin Formula
..................................... 113
Appendix
2
Chain Rule Convolution
....................................... 114
10
Play Strategies with Card Counting
........................................ 115
10.1
Count-Dependent Playing Strategy
..................................... 115
10.1.1
Counting Vector Optimal for Play Variation Alone
........... 117
10.1.2
Single Counting Vector Optimal for Bet and Play Together
..119
10.1.3
Two Distinct Counting Vectors
................................. 121
10.1.4
Insurance with Variable Betting
................................ 122
10.2
Counter Basic Strategy
.................................................. 124
References
.......................................................................... 127
Index
................................................................................ 129
|
| any_adam_object | 1 |
| author | Werthamer, N. Richard 1935- |
| author_GND | (DE-588)171633881 |
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| dewey-ones | 795 - Games of chance |
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| dewey-search | 795.423 |
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| dewey-tens | 790 - Recreational and performing arts |
| discipline | Sport Mathematik Wirtschaftswissenschaften |
| format | Book |
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| spelling | Werthamer, N. Richard 1935- Verfasser (DE-588)171633881 aut Risk and reward the science of casino blackjack N. Richard Werthamer New York, NY Springer 2009 XVIII, 131 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell Blackjack (Game) Handbooks, manuals, etc Blackjack (Game) Mathematical models Siebzehn und Vier (DE-588)4116494-5 gnd rswk-swf Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Spielstrategie (DE-588)4182285-7 gnd rswk-swf Technische Mathematik (DE-588)4827059-3 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Angewandte Mathematik (DE-588)4142443-8 s Technische Mathematik (DE-588)4827059-3 s Statistik (DE-588)4056995-0 s 1\p DE-604 Siebzehn und Vier (DE-588)4116494-5 s Spielstrategie (DE-588)4182285-7 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 2\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018609228&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Werthamer, N. Richard 1935- Risk and reward the science of casino blackjack Mathematisches Modell Blackjack (Game) Handbooks, manuals, etc Blackjack (Game) Mathematical models Siebzehn und Vier (DE-588)4116494-5 gnd Angewandte Mathematik (DE-588)4142443-8 gnd Statistik (DE-588)4056995-0 gnd Spielstrategie (DE-588)4182285-7 gnd Technische Mathematik (DE-588)4827059-3 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
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| title | Risk and reward the science of casino blackjack |
| title_auth | Risk and reward the science of casino blackjack |
| title_exact_search | Risk and reward the science of casino blackjack |
| title_full | Risk and reward the science of casino blackjack N. Richard Werthamer |
| title_fullStr | Risk and reward the science of casino blackjack N. Richard Werthamer |
| title_full_unstemmed | Risk and reward the science of casino blackjack N. Richard Werthamer |
| title_short | Risk and reward |
| title_sort | risk and reward the science of casino blackjack |
| title_sub | the science of casino blackjack |
| topic | Mathematisches Modell Blackjack (Game) Handbooks, manuals, etc Blackjack (Game) Mathematical models Siebzehn und Vier (DE-588)4116494-5 gnd Angewandte Mathematik (DE-588)4142443-8 gnd Statistik (DE-588)4056995-0 gnd Spielstrategie (DE-588)4182285-7 gnd Technische Mathematik (DE-588)4827059-3 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Mathematisches Modell Blackjack (Game) Handbooks, manuals, etc Blackjack (Game) Mathematical models Siebzehn und Vier Angewandte Mathematik Statistik Spielstrategie Technische Mathematik Wahrscheinlichkeitsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018609228&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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