Mathematics in games, sports, and gambling: the games people play
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2010
|
| Schriftenreihe: | A Chapman and Hall book
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 354 S. Ill., graph. Darst. |
| ISBN: | 9781439801635 1439801630 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804141107160809472 |
|---|---|
| adam_text | Titel: Mathematics in games, sports, and gambling
Autor: Gould, Ronald
Jahr: 2010
Contents
List of Figures xi
List of Tables xv
Preface xvii
Author Biography xix
1 Basic Probability 1
1.1 Introduction ........................ 1
1.2 Of Dice and Men ..................... 2
1.3 Probability......................... 9
1.4 The Laws Which Govern Us ............... 12
1.4.1 Dependent Events................. 15
1.5 Poker Hands Versus Batting Orders ........... 23
1.6 Let s Play for Money! ................... 28
1.7 Is That Fair?........................ 32
1.8 The Odds Are against Us................. 39
1.9 Things Vary ........................ 41
1.10 Conditional Expectation ................. 45
2 The Game s Afoot 49
2.1 Applications to Games .................. 49
2.2 Counting and Probability in Poker Hands........ 49
2.3 Roulette .......................... 54
2.4 Craps............................ 58
2.4.1 Street Craps .................... 60
2.4.2 Casino Craps.................... 61
2.4.3 Other Bets..................... 62
2.5 Let s Make A Deal ? The Monty Hall Problem .... 66
2.6 Carnival Games ...................... 69
2.7 Other Casino Games ................... 72
2.7.1 Caribbean Stud Poker............... 72
2.7.2 Keno......................... 74
2.7.3 Blackjack...................... 76
2.8 Backgammon........................ 79
2.8.1 Hitting Blots.................... 81
2.8.2 Off the Bar..................... 81
2.8.3 Bearing Off..................... 83
2.8.4 Doubling...................... 86
Repeated Play 93
3.1 Introduction ........................ 93
3.2 Binomial Coefficients ................... 94
3.3 The Binomial Distribution ................ 103
3.4 The Poisson Distribution ................. 113
3.5 Streaks ? Are They Real? ................ 120
3.6 Betting Strategies ..................... 124
3.7 The Gambler s Ruin.................... 129
Card Tricks and More 135
4.1 Introduction ........................ 135
4.2 The Five-Card Trick.................... 135
4.2.1 Adding a Joker to the Deck............ 139
4.2.2 More Variations of the Trick ........... 140
4.3 The Two-Deck Matching Game ............. 147
4.4 More Tricks ........................ 151
4.4.1 Friends Find Each Other ............. 152
4.4.2 The Small Arithmetic Trick............ 153
4.4.3 The Nine-Card Trick................ 154
4.5 The Paintball Wars .................... 155
Dealing with Data 159
5.1 Introduction ........................ 159
5.2 Batting Averages and Simpson s Paradox........ 160
5.3 NFL Passer Ratings.................... 166
5.4 Viewing Data ? Simple Graphs ............. 169
5.4.1 Time Plots and Regression Lines......... 175
5.4.2 When To Find the Regression Line........ 181
5.5 Confidence in Our Estimates............... 186
5.6 Measuring Differences in Performance.......... 190
5.6.1 Coefficient of Variation .............. 194
5.6.2 Relative Performance ............... 196
Testing and Relationships 201
6.1 Introduction ........................201
6.2 Suzuki Versus Pujols ................... 201
6.3 I ll Decide If I Believe That................ 204
6.3.1 Errors........................ 207
6.3.2 Summary of Hypothesis Testing ......... 208
6.3.3 One-Sided Tests.................. 208
6.3.4 Small Sample Sizes................. 209
6.4 Are the Old Adages True? ................ 212
6.4.1 Home Field Advantage............... 212
6.4.2 Lefty Versus Righty................ 215
6.5 How Good Are Certain Measurements? ......... 219
6.5.1 Batting Average and Runs Scored........ 222
6.6 Arguing over Outstanding Performances ........ 224
6.7 A Last Look at Comparisons............... 227
6.7.1 Small Sample Comparisons............ 227
Games and Puzzles 233
7.1 Introduction ........................ 233
7.2 Number Arrays ...................... 233
7.2.1 Magic Squares................... 233
7.2.2 Variations on Magic Squares ........... 239
7.2.3 Sudoku....................... 242
7.3 The Tower of Hanoi .................... 245
7.3.1 Finding Solutions.................. 248
7.3.2 Bicolored Tower of Hanoi............. 251
7.3.3 The Derangement Tower of Hanoi ........ 253
7.4 Instant Insanity ...................... 255
7.5 Lights Out ......................... 262
7.6 Peg Games......................... 266
7.6.1 English Board ................... 267
7.6.2 Triangular Peg Solitaire.............. 272
Combinatorial Games 277
8.1 Introduction to Combinatorial Games.......... 277
8.2 Subtraction Games .................... 278
8.3 Nim............................. 280
8.3.1 Poker Nim ..................... 286
8.3.2 Moore s Nim.................... 287
8.3.3 Other Games.................... 289
8.4 Games as Digraphs .................... 291
8.4.1 Sums of Games................... 292
8.4.2 The Sprague-Grundy Function.......... 293
8.4.3 More about Impartial Games........... 296
8.5 Blue-Red Hackenbush................... 298
8.6 Green Hackenbush..................... 306
8.6.1 Pruning Green Hackenbush Trees......... 306
8.7 Games as Numbers .................... 310
8.8 More about Nimbers ................... 315
9 Appendix 319
9.1 Review of Elementary Set Theory ............319
9.2 Standard Normal Distribution Table...........326
9.3 Student s ^-Distribution..................327
9.4 Solutions to Problems...................328
9.5 Selected Even Exercises..................331
References 347
Index 351
|
| any_adam_object | 1 |
| author | Gould, Ronald J. 1950- |
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| dewey-ones | 510 - Mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV036062165 |
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| isbn | 9781439801635 1439801630 |
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| spelling | Gould, Ronald J. 1950- Verfasser (DE-588)140578307 aut Mathematics in games, sports, and gambling the games people play Ronald J. Gould Boca Raton [u.a.] CRC Press 2010 XIX, 354 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Chapman and Hall book Mathematik Mathematisches Modell Gambling Mathematics Games Mathematics Mathematical analysis Problem solving Mathematical models Sports Mathematics Kombinatorisches Spiel (DE-588)4164753-1 gnd rswk-swf Glücksspiel (DE-588)4021329-8 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Sport (DE-588)4056366-2 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Glücksspiel (DE-588)4021329-8 s Sport (DE-588)4056366-2 s DE-604 Kombinatorisches Spiel (DE-588)4164753-1 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018953618&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 |
| spellingShingle | Gould, Ronald J. 1950- Mathematics in games, sports, and gambling the games people play Mathematik Mathematisches Modell Gambling Mathematics Games Mathematics Mathematical analysis Problem solving Mathematical models Sports Mathematics Kombinatorisches Spiel (DE-588)4164753-1 gnd Glücksspiel (DE-588)4021329-8 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Sport (DE-588)4056366-2 gnd |
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| title | Mathematics in games, sports, and gambling the games people play |
| title_auth | Mathematics in games, sports, and gambling the games people play |
| title_exact_search | Mathematics in games, sports, and gambling the games people play |
| title_full | Mathematics in games, sports, and gambling the games people play Ronald J. Gould |
| title_fullStr | Mathematics in games, sports, and gambling the games people play Ronald J. Gould |
| title_full_unstemmed | Mathematics in games, sports, and gambling the games people play Ronald J. Gould |
| title_short | Mathematics in games, sports, and gambling |
| title_sort | mathematics in games sports and gambling the games people play |
| title_sub | the games people play |
| topic | Mathematik Mathematisches Modell Gambling Mathematics Games Mathematics Mathematical analysis Problem solving Mathematical models Sports Mathematics Kombinatorisches Spiel (DE-588)4164753-1 gnd Glücksspiel (DE-588)4021329-8 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Sport (DE-588)4056366-2 gnd |
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