Bridge, Probability & Information
MacKinnon (Robert F.)
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BOOK ABSTRACT:

Cover Blurb

    Bridge, unlike chess, is a game of incomplete information. We bid with thirteen cards in view, and play each deal seeing only twenty-six: the positions of the rest we must deduce from the auction and from the cards played. Bridge players deal in likelihoods, and only rarely in certainties, therefore some knowledge of the laws of probability is a critical weapon in a successful player's arsenal. In this book, using a semi-fictional narrative approach, the author develops the ideas (but not the equations!) that underlie basic probability and its modern descendant, information theory, and shows how both fields relate to bridge. In fact, they have enormous practical application to the game. Among the topics discussed:
  1. The idea of visualizing ‘sides', the complete combined holdings of both defenders, and not just the splits in individual suits
  2. How a known split in one suit can affect the odds in another
  3. Empirical rules to help make decisions based on incomplete information or in a situation too complex to analyze accurately
  4. How a priori probabilities (the ones with which we are all familiar) change with each card played
  5. How an imbalance of vacant places in the defenders' hands affects the odds — and when to change your line of play as a result
  6. The ‘Monty Hall Problem' and its bridge cousin, Restricted Choice
  7. HCP distribution — what partner's bidding tells you about where his high cards are • Information versus frequency: the trade-off in choosing conventions
  8. Losing Trick Count — does it work, and if so, why?
  9. Probability, statistics and the Law of Total Tricks — how far can you rely on the LAW? • Cost versus gain: information theory as applied to bidding systems
  10. Using statistics to help you choose a bidding system that works for you
Table Of Contents
    Introduction – 1
  1. WHEN THE DUMMY COMES DOWN – 3
    … Counting Cards - Alice in Bridgeland – 4
    … The Inferential Count – 7
    … Percentage Play – 9
    … When Virtue Goes Unrewarded – 10
    … How Probabilities Accumulate – 13
    … The Enlightenment of Scrooge – 16
    … In Conclusion – 17
  2. EMOTION, LOGIC, AND HOW WE DECIDE – 19
    … Where Do Blunders Come From? – 20
    … Luck, Chance and Design – 23
    … The Gods Love the Odds – 24
    … Is Bridge a Science? – 25
  3. THE CONCEPT OF PROBABILITY – 27
    … Mathematics and Bridge – 28
    … Probability Is Synonymous with Information – 31
    … A Glimpse into the History of Probability – 32
    … Pascal's Triangle – 34
    … Information and Probability in the 20th Century – 35
    … Interlude of Movie Madness – 37
    … Is Bridge Beautiful? – 38
  4. COMBINATIONS AND PERMUTATIONS – 39
    … Vacation at the Hotel du Paradis – 41
    … Back to Pascal's Triangle – 45
    … Card Combinations – 48
    … Comparisons of Even and Odd Splits – 50
  5. A PRIORI ODDS AND VACANT PLACES – 51
    … Old Hat Problem – 53
    … Vacant Places and Variable Odds – 55
    … The Dog that Didn't Bark – 61
    … Reese's Reading of the Much Maligned 3-3 Split – 63
    … Playdown in a Suit – 65
    … What Exactly Are Vacant Places? – 67
    … Vacant Places and Playing for the Drop – 70
    … Kelsey's Rule – 71
  6. INFORMATION THEORY AND DECLARER PLAY – 75
    … The A Priori Odds and Suit Splits – 75
    … The Division of Sides – 80
    … The Holistic Approach to the Division of Sides – 80
    … The Distribution of Sides – 83
    … The 8765 Distribution of Sides – 85
    … Going with the Odds – 86
    … The 7766 Division – 90
    … Emeritus Jones's 7766 Disaster in the Dining Hall – 91
  7. INFORMATION AND SURPRISE ON THE OPENING LEAD – 95
    … Edith Kemp Was Surprised at First – 102
    … Silence Is Golden – 103
    … The Heart Lead Against 3NT – 105
    … Prelude to Bayes' Theorem — The Journey so Far – 107
  8. APPLYING BAYES' THEOREM – 109
    … Monty, Marilyn and the Theorem of Bayes – 110
    … Bayes' Theorem Applied to Card Play – 113
    … The Bayes Equation – 115
    … Monty's Messages – 116
    … Bayes' Theorem and Random Discards – 117
    … The Effect of a Partial Playdown – 122
  9. NINE-NEVER, EIGHT-EVER, AND BEYOND – 127
    … When A Priori Doesn't Work – 131
    … The Eight-Ever Rule – 134
    … Missing the Jack-Sixth – 141
    … The Majority Rule Revisited – 144
  10. DEMONSTRATOR DEALS – 147
    … ET Plays a Hand – 147
    … The Changing Seascape – 150
    … Professor Emeritus Jones Takes a View – 152
    … Aim for the Harbor, but Look for the Shoals – 154
    … Odds and Evens – 156
    … Hey. Mister, What's Your Rush? – 158
    … T L. Abbot's Giant Leap of Faith – 162
    … Subjectivity and Probability – 164
    … Descartes Was Understandably in a Bad Mood – 166
  11. HOW EXPERTS PLAY THE HAND – 167
    … If You Want to Play like Zia – 167
    … A Shanghai Probability – 169
    … When Several Honors Are Missing – 172
    … Fear of the Unknown – 174
    … Jason Hackett's Direct Approach – 177
    … Common-sense Probability – 180
    … A Dubious Signal – 182
  12. HIGH CARD POINTS AND ALL THAT JAZZ – 185
    … Expectations of HCP Distributions – 186
    … Information and Flannery 2D Bids – 188
    … The Obligation to Inform – 190
    … Conflicting Methods at the USBC 2007 – 191
    … Long Suits versus Short Suits – 194
    … LTC - The Losing Trick Count – 197
  13. PROBABILITY, STATISTICS AND THE LAW – 205
    … Statistics and the LAW – 207
    … Refining the LAW – 209
    … The Losing Trick Count and Total Tricks – 212
    … An Appropriate Statistical Approach – 213
    … Probability in Competition – 216
    … In Defiance of The LAW? – 218
    … A Consultative Double – 219
    … Ms. Lee Regrets... – 220
  14. BIDDING SYSTEMS: INFORMATION AND COSTS – 223
    … Chen Scores Are Relative – 225
    … Kludge Rhymes with Fudge – 226
    … Do Bidding Systems Make a Difference? – 227
    … Determine Your Pass Rate Comfort Zone – 228
    … Bidding Space: The Basic Cost of Information – 231
    … Strong Jumps Must Be Informative – 231
    … Information and Cost in Modern Systems – 233
    … What Did They Gain by Passing? – 235
    … The Cost of Passing – 236
    … The Majors-First Movement – 237
    … Finale: Kit's Cri de Coeur – 239
    … Final Thought – 241



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  2. Mauve: Text by correspondent(s) or other author(s); © the author(s)



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