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Backgammon Books
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Backgammon Funfair
Facts, Figures and Numerical Musings
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AUTHOR:
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Raymond Kershaw
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YEAR:
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2012
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PUBLISHER:
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Rake Publishing
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CITY:
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London England
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ISBN:
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978-0-9572488-1-6
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BINDING:
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Softcover
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PAGES:
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viii+198
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SIZE:
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30 cm high, 21 cm wide
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WEBSITE:
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https://www.facebook.com/rakepublishing/
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NOTE:
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This book is now in its second edition. There are four new pages addressing omissions noted by Timothy Chow. You can view these changes here.
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DESCRIPTION:
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A book of puzzles, curiosities, and mathematical diversions related to backgammon.
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READERS
COMMENTS:
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"The book was a nice surprise. It's not a standard backgammon book. It's a book of puzzles and mathematical oddities about backgammon. Many of the curiosities have been written about before, but a lot of them were new to me. Although the book is a little on the expensive side ($35), it is nicely bound, with good paper, and every page is in full color. It's a worthwhile read for anyone that enjoys looking at backgammon from a mathematical and logical perspective, and a unique offering in backgammon literature."—Tom Keith, July 2012.
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"I bought Ray's book and enjoyed it thoroughly. It's a really splendid collection of backgammon paradoxes and oddities, very attractively printed and organized. There's nothing else like it. If you have enjoyed some of the offbeat backgammon puzzles that appear on BGO from time to time, such as finding the fewest number of rolls to return to the starting position, finding the position with the lowest nonzero winning chances, cataloging Jacoby paradox positions, and so forth, then this book is for you."—Timothy Chow, August 2012.
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"Barclay Cooke wrote a book called Paradoxes and Probabilities, but Cooke's title fits this book to the seventh decimal place. Think of it as the Guinness Book of Backgammon Records, with all the Best, Worst, Least, and Most collected between its covers. Most of the positions in the book are of little or no direct practical value, but there are some useful positions, especially in the sections devoted to bearing off. An example is the Jacoby Paradox, which appeared in a number of sources years ago and might easily be missed over the board by an advancing player not familiar with "out of date" texts."—Jake Jacobs, Flint Area BackgammoNews, Summer 2012.
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CONTENTS:
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Introduction
Style
XG Rollouts
From the Start ...
1. Fewest moves to return to the starting position
2. Fewest moves to return to the starting position again
3. Create a prime in three moves
4. Create a 5-prime in two moves
5. Fewest rolls to pick a four-leaf clover
6. Greatest lead in pips after one roll each
7. Greatest lead in pips after two rolls each
8. Lowest total pips rolled to get each player's checkers on own side of board
9. Lowest total pips rolled to get all Red checkers on own side of board
10. Shortest game without the doubling cube
11. Fewest rolls for Red to close out White
12. Fewest rolls to put all White's checkers on the bar
13. Red's greatest equity after one roll each
14. Worst plays of the opening roll
15. Choosing your die for the opening roll
The Least
16. Fewest rolls which hit when there is one direct shot
17. Fewest rolls which hit when there are two direct shots: (a) two hitters and one blot
18. Fewest rolls which hit when there are two direct shots: (b) one hitter and two plots
19. Fewest rolls which hit when there are three direct shots
20. Fewest rolls which hit when there are four direct shots
21. Fewest rolls which hit when there are five direct shots
22. Fewest rolls which hit direct shots because of the higher number rule.
23. Positions with exactly zero equity
24. Lowest non-zero chance to win
The Most
25. Greatest number of plays with a non-double
26. Greatest number of plays with a double
27. Greatest gain in pip difference by rolling a non-double
28. Greatest gain in pip difference by rolling a double
29. Greatest gain in pip difference resulting from two rolls by Red and one by White
30. Greatest gain in pip difference resulting from three rolls by Red and two by White
31. Greatest gain in pip difference resulting from four rolls by Red and three by White
32. Greatest equity difference between correct checker plays with and without Jacoby rule
33. Greatest joker
34. Greatest anti-joker
35. Greatest checker move error
36. Red's greatest gammon or backgammon percentage less than 100%
37. Red's greatest gammon or backgammon percentage when he can still lose
38. Most checkers on the bar
39. Greatest pip count for race leader
Bearing Off
40. Who won?
41. Number of bear off races
42. Percentage of bear off races which are gin
43. Two checkers better than one in bear off race
44. Three checkers better than two in bear off race
45. Most pips you wish you had not rolled in bear off race
46. Count down
47. Gammon saving fun
48. Effective pip count
49. Better off with 35 more pips
50. Double 5 better than double 6 in bear off race
51. Double 4 better than double 6 in bear off race
52. Double 3 better than double 6 in bear off race
53. Better not to move in bear off race
54. Greatest and smallest gains from doubling and redoubling
55. Doubling with mirror bear off positions
56. Optional to take or pass
57. Greatest cubeless probability of winning with which you will be correctly beavered
Doubling Paradoxes
58. Jacoby paradox
59. Cube provocation plays with Jacoby paradox and Wisecarver paradox
60. Kauder paradox
61. Latto paradox
62. Kulseth paradox
Number of Positions in Backgammon
63. Counting positions
64. Impossible positions
Appendices
1. Cubeless probabilities of winning and correct cube actions in bear off races where each player has one or two checkers
2. Calculation of zero equity position: {644} (on roll, owning cube) versus {1111}
3. Jacoby Paradox
4. Kauder Paradox
5. Latto Paradox
6. Kulseth Paradox
7. Distributions of checkers on points
8. Number of rolls to bear off 15 checkers on 1pt
The A to Z of Backgammon
Sources
Abbreviations and Glossary
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COVER:
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Backgammon Funfair provides a unique insight into the statistics of backgammon, examining the myriad of possibilities of this centuries-old board game.
Affordable computer programs like eXtreme Gammon have generated an explosion in our understanding of the game. But if you've ever wondered, "How many ...? then Backgammon Funfair will provide the answer.
- How many checkers can legally end up on the bar?
- Why is it not always best to throw double six in a bear off race?
- Just how many billion possible positions are there?
Whether you are a casual player, a dedicated devotee or just a number-loving student of dice games, Backgammon Funfair will keep you entertained. Can you find better solutions to the numerous puzzles it contains?
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ABOUT THE
AUTHOR:
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Raymond Kershaw lives in London, England where for several decades he has been accumulating much of the material for this book. If he had concentrated more on serious backgammon, and spent less time pondering fun positions, he might have more trophies in his cabinet.
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