Table of Contents
1 Introduction 1
1.1 Reference Players 4
1.2 Naughty List 4
2 My History 5
3 European Bridge Team Championship 2014 11
4 August/September 2015 13
5 42nd Bermuda Bowl, Chennai, India, 2015 19
6 Post Bermuda Bowl 21
7 Law of Large Numbers (LLN) 23
8 Bridge is a Game of Mistakes 27
9 Bridge Cheating Concepts 29
10 Science 35
11 Data Collection 37
12 Data Sources 39
12.1 ACBL Data 39
12.2 European Bridge League (EBL) Data 40
12.3 World Bridge Federation (WBF) Data 40
12.4 BBO and The Vugraph Project (TVP) Data 41
12.5 Errors with the Data 42
13 Magic Formula (MF)/Mistakes Function (MF) 45
14 Advanced Cheating Detection Functions (ACDFs) 51
15 Opening Lead Functions (OLFs) 53
16 Traditional Anatomy of an Investigation 55
17 New Anatomy of an Investigation 57
18 Buratti/Lanzarotti 59
18.1 Statistical Evidence 60
19 Elinescu/Wladow 63
19.1 Statistical Evidence 69
20 Fantoni/Nunes 71
20.1 Statistical Evidence 75
21 Fisher/Schwartz 77
21.1 Statistical Evidence 77
22 Piekarek/Smirnov 79
22.1 The Third Pair 79
22.2 Statistical Evidence 80
23 Balicki/Zmudzinski 81
23.1 Statistical Evidence 86
24 American Contract Bridge League (ACBL) Data 87
24.1 Sectionals and Regionals 87
25 European Bridge League (EBL) Data 95
25.1 Open 96
25.2 Seniors 97
25.3 Women 98
26 World Bridge Federation (WBF) Data 99
26.1 Open 100
26.2 Seniors 101
26.3 Women 102
27 Computer Bridge 103
28 Top Players 105
28.1 Other Pairs 108
29 Opening Leads 109
30 Various Opening Lead Partnership Statistics 119
30.1 Opening Lead Function 1 (OLF1) 120
30.2 Opening Lead Function 1a (OLF1a) 121
30.3 Opening Lead Non-Competitive Function 1 (OLNCF1) 122
30.4 Opening Lead Non-Competitive Function 1a (OLNCF1a) 123
30.5 Opening Lead Function 2 (OLF2) 123
30.6 Opening Lead Function 2a (OLF2a) 124
30.7 Opening Lead Non-Competitive Function 2 (OLNCF2) 125
30.8 Opening Lead Non-Competitive Function 2a (OLNCF2a) 125
30.9 Opening Lead Function 3 (OLF3) 126
30.10 Opening Lead Function 4 (OLF4) 127
31 Other Opening Lead Statistics 131
32 Par 133
33 False Positives 139
34 Women 141
35 Seniors 143
36 Tournaments after September 2015 145
36.1 United States Bridge Championships (USBCs) 146
37 Best Defensive/Declarer Pairs – Played Cards 147
38 It Takes One to Know One 153
39 Access to Hand Records 157
40 Contracts 163
41 Best Card to Lead? 173
42 Bridge Data Formats 181
43 What Would You Lead? 185
44 It’s All About the Data 187
44.1 Under the Table – The Case Against the Blue Team 187
44.2 Spain v. USA, Wroclaw 2016 – Bathurst/Lall 188
44.3 Belladonna/Garozzo 1NT Answers 192
45 Impact of Cheating Players on Top Level Bridge 193
45.1 Costs of Going After Cheats 194
46 1955-1991 Bermuda Bowl Data 195
46.1 Summary 200
47 MD5 Protected Statements 201
48 Summary 203

Table of Figures
Figure 1. Bridge abbreviations xiii
Figure 2. Bridge pairs’ abbreviations xiii
Figure 3. Naughty Bridge pairs’ abbreviations xiii
Figure 4. Top seven pairs from top 66 using ACDF3 1
Figure 5. List of naughty players 4
Figure 6. Skills needed for detecting cheating in Bridge 9
Figure 7. EBTC 2014 final result and qualifiers for Bermuda Bowl 11
Figure 8. Fisher/Schwartz placement of board to indicate suit 15
Figure 9. EBL qualifiers to 2015 Bermuda Bowl 19
Figure 10. Expected number of heads from 10 fair coin tosses 24
Figure 11. Expected number of heads from 50 fair coin tosses 24
Figure 12. Expected number of heads from 100 fair coin tosses 25
Figure 13. Tournament MF values based on categories 47
Figure 14. MF values for top 13 tournaments from 1997-2014 48
Figure 15. WBF/EBL Events 1997-2018 MF values, 2,900 board minimum 49
Figure 16. Buratti/Lanzarotti board from Tenerife, 2005 59
Figure 17. Top 100 pairs percentage of opening leads to an ace or king 61
Figure 18. Top 100 pairs percentage of opening leads to an ace, king or queen 61
Figure 19. Elinescu/Wladow lead data from Bridgewinners 67
Figure 20. Elinescu/Wladow 1 in X values for finding lead 68
Figure 21. Binomial probability chart for orientation/high honor 72
Figure 22. Fantoni/Nunes leads from Monaco v. Iceland 72
Figure 23. Balls in urn without replacement Excel spreadsheet 74
Figure 24. EBL data on Balicki/Zmudzinski calls mentioned in Woolsey article 82
Figure 25. Balicki/Zmudzinski narrow bids, strong hands from EBTC 2014 83
Figure 26. Balicki/Zmudzinski wide bids, weak hands from EBTC 2014 84
Figure 27. MF values for ACBL MP ranges 2014-2018 87
Figure 28. MF values for MP ranges at NABCs 2013-2018 89
Figure 29. MF values for MP ranges at NABC+ events 2013-2018 89
Figure 30. Top 200 defensive MF values for NABC+ events 90
Figure 31. Top 300 pairs at ACBL Sectionals/Regionals defensive MF value 91
Figure 32. ACBL Sectionals and Regionals Pairs, 500+ boards. One player declares more than 65+% of boards 92
Figure 33. ACBL pairs, less than 1 in X chance playing ethically 93
Figure 34. ACBL partnerships with undisclosed partnership agreements 94
Figure 35. MF values for different types of EBL tournaments 95
Figure 36. Percentage of contracts made at EBL tournaments 96
Figure 37. Defensive MF value for top 100 pairs from EBL tournaments 96
Figure 38. ACDF2 applied to EBL tournament data 97
Figure 39. Top 50 EBL Seniors’ pairs defensive MF values 98
Figure 40. Top 43 EBL Women's pairs defensive MF values 98
Figure 41. MF values for different types of WBF tournaments 99
Figure 42. Percentage of contracts made for different types of WBF tournaments 99
Figure 43. Top 175 pairs from WBF tournaments 100
Figure 44. ACDF2 applied to WBF tournaments 100
Figure 45. Top 49 pairs defensive MF value - WBF Senior events 101
Figure 46. ACDF2 applied to WBF Senior tournaments 102
Figure 47. Top 50 WBF Women’s pairs defensive MF value 102
Figure 48 Top 87 pairs defense against top 120 pairs 106
Figure 49 Top 80 pairs on declarer play 107
Figure 50. Top 100 pairs safe opening leading percentage 111
Figure 51. Top 100 pairs safe opening leading percentages 112
Figure 52. Top 100 pairs opening lead - partner has an honor (AKQ) percentage 115
Figure 53. Fisher/Schwartz leads from EBTC 2014 that gave up a trick 115
Figure 54. Safe lead percentage for top 210 players - all contracts 116
Figure 55. Safe lead percentage for top 210 players - non-makeable contracts 117
Figure 56. Opening lead to AK (OLF1) top 100 pairs percentage 120
Figure 57. Opening lead to AK (OLF1) top 200 pairs percentage 121
Figure 58. Opening lead to AK (OLF1a) top 100 pairs percentage 122
Figure 59. Opening lead to AK (OLNCF1) top 100 pairs percentage 122
Figure 60. Opening lead to AK (OLNCF1a) top 100 pairs percentage 123
Figure 61. Opening lead to AKQ (OLF2) top 100 pairs percentage 123
Figure 62. Opening lead to AKQ (OLF2) top 200 pairs percentage 124
Figure 63. Opening lead to AKQ (OLF2a) top 100 pairs percentage 124
Figure 64. Opening lead to AKQ (OLNCF2) top 100 pairs percentage 125
Figure 65. Opening lead to AKQ (OLNCF2a) top 100 pairs percentage 125
Figure 66. Opening lead, non-competitive auction, P has A or K percentage 126
Figure 67. Opening lead, non-competitive auction, P has A, K or Q percentage 128
Figure 68. xx non-trump opening lead percentage in trump contract 131
Figure 69. Top 100 pairs trump lead percentage 132
Figure 70. Top 100 pairs average IMPs to par 133
Figure 71. Top 10 out of 50 Seniors pairs average IMPs to par 134
Figure 72. Top 10 out of 50 Women’s pairs average IMPs to par 134
Figure 73. Top 100 Open pairs declaring average IMPs to par 135
Figure 74. Top 10 out of 50 Seniors declaring average IMPs to par 135
Figure 75. Top 10 out of 20 Women’s pairs declaring average IMPs to par 136
Figure 76. Top 100 pairs defending IMPs to par 137
Figure 77. Top 10 out of 50 Seniors pairs defending average IMPs to par 137
Figure 78. Top 10 out of 20 Women’s pairs defending average IMPs to par 138
Figure 79. Pre and post summer 2015 tournament data 145
Figure 80. Top 26/181 defenders safe played card percentage excluding opening lead 147
Figure 81. Top 20/181 defenders safe played card percentage including opening lead 148
Figure 82. Top 15/50 defenders safe played card percentage excluding opening lead 148
Figure 83. Top 10/50 defenders safe played card percentage including opening lead 149
Figure 84. Top 10/50 pairs declarer safe played card percentage 149
Figure 85. Top 20/100 defenders ranked by percentage of safe played cards ignoring opening lead 150
Figure 86. Top 23/100 defenders ranked by percentage of safe played cards including opening lead 151
Figure 87. Top 10/100 declarers ranked by percentage of safe played cards from top tournaments 152
Figure 88. 48 bit keys and compute time for Charlotte Regional, October 2016 159
Figure 89. Mnemonics for card ranks 161
Figure 90. Likelihood of game, slam, grand slam 163
Figure 91. Likelihood of different hand shapes 163
Figure 92. Different hand generator results for ACBL 164
Figure 93. Contracts by suits in ACBL events 165
Figure 94. Contracts by suits in major IMP events 165
Figure 95. Contract frequency from different databases 167
Figure 96. Club contracts made percentage in ACBL tournaments 167
Figure 97. Diamond contracts made percentage in ACBL tournaments 168
Figure 98. Hearts contracts made percentage in ACBL tournaments 168
Figure 99. Spades contracts made percentage in ACBL tournaments 168
Figure 100. No trumps contracts made percentage in ACBL tournaments 169
Figure 101. All contracts made percentage in ACBL tournaments 169
Figure 102. Club contracts made in selected Vugraph tournaments 169
Figure 103. Diamond contracts made in selected Vugraph tournaments 170
Figure 104. Heart contracts made in selected Vugraph tournaments 170
Figure 105. Spade contracts made in selected Vugraph tournaments 170
Figure 106. No trump contracts made in selected Vugraph tournaments 171
Figure 107. All contracts made in selected Vugraph tournaments 171
Figure 108. Most popular, most successful and safest leads against IMP contracts 174
Figure 109. Most successful leads against makeable and non-makeable IMP contracts 176
Figure 110. Statistics on led card for suit contracts 179
Figure 111. Statistics on led card for no trumps contracts 180
Figure 112. Opening lead quiz 185
Figure 113. Answers to opening lead quiz 186
Figure 114. Belladonna/Garozzo 1NT range hands, 1973-1975 188
Figure 115. Third seat non-vulnerable calls by Kevin Bathurst/Justin Lall 190
Figure 116. Number of TVP/BBO boards in Bermuda Bowl 1955-2017 196
Figure 117. Number of boards for top 10 players 1955-1991 197
Figure 118. MF values for 1955-1983 Bermuda Bowls with different groups 198
Figure 119. Statements hashed by MD5 202