100 Backgammon Puzzles by Paul Lamford
a review by Dan Pelton
 

There are many backgammon books on the market, with topics dealing from help in learning the game to analysis of matches between experts. Paul Lamford’s book presents 100 backgammon problems, 50 checker play decisions and 50 cube decisions. Both checker plays and cube decisions are presented for a variety of situations, either money play with the Jacoby rule in effect or match play.

Recent rollouts of the problems in the book have shown that the checker plays are generally correct, while the doubling decisions are less so. The problems in the book were rolled out using Snowie 1, which was the best bot available at the time, but in retrospect had more difficulty evaluating cube decisions than checker plays.

The format of the book gives only 3-4 sentences of analysis. Each problem contains a hint as to the correct play. While this keeps the book concise, further analysis would be helpful in many cases. The concise format makes using the book for review very easy. The book is organized with problems of increasing difficulty, and each problem presents a different point to consider when making the proper decision.

Prior to the problems, Lamford presents a brief introduction to backgammon and different winning strategies. He also introduces the concept of PRAT for doubling decisions. PRAT is an acronym for Position, Race and Threats. These are good factors to consider when making cube decisions.

Examples of decisions that were changed by rollouts with today’s stronger bots (Gnu 2-ply) are as follows.
 

Position 30


Money Game
 

Lamford’s play 7/3 4/2(2) (3rd best). Best play is 7/3 7/5(2). 77/3(2) was 2nd best.

After Lamford’s play, 3-4, 3-5, 3-6 and 3-1 do not cause black’s board to crunch. (8 rolls).
After best play any 6 and 5-1 do not cause black to crunch (13 rolls)
The worst rolls for black after either play are 33 and 44, which cause black’s board to crunch.
The best play maximizes builders, while killing 6’s. White’s plan to win is to have black crunch while keeping the board intact. White has a backgame, and can still win by hitting a late shot while black is trying to bring his men in and bear off. 7/3 7/5(2) wins about 3.5% more games according to the rollout.

The way to win this game is hit a 2nd checker, and then close the board. Black has 9 off already. By not closing our board with 23/17 5/1, we keep the chance to hit a 2nd checker, at the risk of only 3 rolls, 1-1 and 1-2. By closing our board, we cannot hit the 2nd checker until we are bearing off. Rollouts show that sending a 2nd checker back increases our winning chances by 4%, while closing the board decreases our chance of being gammoned by 2.6%.

White has 11 checkers off to Black’s 4. On 11/36 rolls white will hit, and black has no spares to return hit without leaving a shot. Black needs to take a take a man off while covering the blot to have the best chances to win. Even with that, black will trail by 3 rolls and we will have at least 2 open points to re-enter. All non-doubles for Black only allow 1 checker to be removed, leaving black 4 rolls behind in the race. 6-6 takes off 4 checkers but still leaves the blot on the ace point, other doubles can take off only 2 men without leaving a blot.
The rollout shows that white is correct to double in this position by .138. The correct cube action for this position is to double and take, even though black will have an automatic recube to 4 if they accept the double. For money, the double is correct by .074. If the score is revised to white leading 2-away, 4-away, the correct action is no double/take, since white is only a 73% favorite to win the game.

In summary, 100 Backgammon Problems is a good book for intermediate players. I would not recommend it to beginning players, since the book does not do a great job of presenting basic backgammon strategy, and there are several other books more suited to beginning players. Caution should be used for the cube decision portion of the book, since analysis by today’s stronger evaluation programs have shown many of the answers to be incorrect. For intermediate players, the book is priced to give good value, and is available thru Carol Joy Cole's Backgammon a la carte as well as Amazon and other major booksellers.

I would like to thank Mary Hickey for her work in helping me prepare this article.

Dan Pelton (aka Pegger on DailyGammon, FIBS and others.)
Phoenix, Arizona USA

Many thanx to Dan Pelton for this review - published 7th March 2009