Backgammon Funfair is unlike any other backgammon book I have read. It comprises the author’s collection of curiosities and puzzles assembled over 35 years from backgammon books, magazines and the internet, combined with his own original material. Examples are “Shortest game without a doubling cube”, “Greatest joker” and “Most pips you wish you had not rolled in a bear off race”. It’s a beautifully produced volume, extending to 194 pages, all clearly set out with colourful diagrams. Within its pages are 63 expositions, some of them whimsical, some mysterious, and all delightfully entertaining. Some of the subject areas are fanciful and obscure, and could be dismissed by backgammon players as being of limited usefulness. To do so would be to miss the point of their inclusion. The joy is in their study and the unpicking of the logic, mathematics and reasoning that underlie them.


Serious students of backgammon will probably skip forward to the section describing the doubling paradoxes. Here you will find such esoteric topics as “Cube provocation plays with Jacoby paradox and Wisecarver paradox”. The Latto, Kauder and Kulseth paradoxes are also ably described with numerous examples.

This book is unashamedly not intended to help its readers play better backgammon. But there are a few gems here that will add to your armoury of tricks, techniques and shortcuts for use over the board. Its real value, however, is as an entertaining departure from traditional backgammon manuals. It is absorbing and enjoyable, and deserves its place alongside more serious backgammon literature.

Julian Minwalla. June 2012

Double 3 better than double 6 in bear off race


Red on roll: 33 is better than 66



Red has played 33: 3/off(4)
Red has played 66: 4/off, 3/off(3)
  • 33 is much better if followed by 22; it leaves one extra pip but only ten checkers instead of eleven
  • 33 is much better if followed by 62, 52, 42, 32 or 21; it leaves one extra pip but Red slots his 2pt
  • 33 is slightly better if followed by 33, 11 or 31; it leaves one extra pip but Red has potential to slot his 2pt later
  • 33 and 66 leave identical positions if followed by 66, 55, 44, 65, 64, 63, 61, 54, 53, 51, 43 or 41

33 makes better use of a 2 on Red’s next roll.

Similar positions can be created and tested with XG to exploit the ability after 33 to make better use of a 2 next. Whether or not 33 is better than 66 is sensitive to the number and location of both Red’s and White’s checkers and to the location of the doubling cube.

Copyright © 2012 by Raymond Kershaw


Backgammon Funfair

Facts, figures and numerical musings

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?

About the author
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.

Backgammon Funfair is available now at a cost of £22. For customers in the UK or Europe, copies can be purchased from Peter Bennet. Email or phone +44 (0)7976 514024 for more details including payment method and postage costs.

Carol Cole is the supplier for the USA and RoW on