A Look at Bill Robertie’s New Series on Backgammon Openings

It was not my intention to spend a lot of time on backgammon, as backgammon is not my game of choice — nor is it really much of a gambling game anymore. But just as we were preparing to air two GWAE shows with Bob Wachtel on his Backgammon Chronicles, Richard and I received a review copy of Bill Robertie’s first book in his series How to Play the Openings in Backgammon.

Robertie is a two-time world champion in backgammon and author of numerous books on the game. In addition, he’s published several books on chess and co-authored a popular series of poker books with Dan Harrington. He’s the publisher for Gammon Press and moderates the backgammon forum on the Two Plus Two website. Simply put, he’s at the pinnacle of gaming/gambling writers. 

If he puts out a new book, I want to review it — regardless of who else we’ve reviewed recently. When you are playing any game with a high intellectual component, there’s at least some overlap with other such games. So, I want to learn from the best in several such games, even if some of them only apply tangentially to video poker.

His new series on backgammon openings is divided into three parts, only the first of which has been released so far:

Part 1 A New Way of Thinking

Part 2 Points and Hits

Part 3 Slotting, Splitting, Running and Doubling 

In Chapter 1, he explores the 15 possible opening rolls. (If you and your opponent roll the same number, you re-roll until the numbers are different.) Some of these are essentially forced, for which there isn’t a lot of discussion. But many have split-or-slot choices, or contact-or-run choices, or where-to-split choices. (I know that’s a lot of jargon for non-players. In the book itself, there are hundreds of diagrams demonstrating these terms and others.) He tells you which ones are absolutely best, which ones are close plays, and among those close plays, what circumstances would lead you to play one way or the other.

He uses the currently preferred AI Bot, eXtreme gammon (XG), as the authority, but there’s a lot of discussion that can only come from being a world-class player playing top competition. I, as an intermediate player and a competent writer, could certainly write a book listing all of XG’s preferred plays, but there’s a whole lot of nuance and overall theory that comes from being at the very top that I simply do not have.

In Chapter 2, he gives the preferred 21 responses to each of the 15 opening rolls. (The six doubles are included in the first number and not in the second.) That multiplies out to 315 possible permutations — but there are actually quite a few more than that because there are choices in how the first 15 numbers are played and even more choices as to how the 21 responses are played. The actual number of permutations considered (I didn’t count them) comes out to around 500 — all listed in charts.

It’s the discussion that goes along with these 500 combinations that’s important. For example, I suspect most intermediate players play 6-2, 6-3, and 6-4 essentially the same as a response to the opening roll. But there are differences between them that are discussed — and how those differences are exacerbated by whatever the opening roll was. This isn’t easy going — but it’s very useful if you want to start your game off in the best way possible.

At the start of a game, your 5-point and your opponent’s 5-point (also called your 20-point) are the two most important unmade points. Chapter 3 begins by discussing the cases where you can make either point, but not both. Which do you choose? Robertie lists the factors that determine this, including whether you’re ahead or behind, whether one of the plays is safer than the other, whether one of the plays leaves a better distribution of checkers, and other factors as well.

The chapter then goes on to discuss positions where you could make your five-point and numerous other points. The idiom learned by beginners of When in doubt make your five-point,” is correct often enough to make it a useful idiom, but incorrect often enough to make the exceptions worth studying. 

Several of the positions described are virtual toss-ups, where it doesn’t much matter which play you make.  But, if you memorize these positions, a slight improvement on either side will make it no longer a toss-up.

Chapter 4 is similar to Chapter 3 except it’s based on making the 20-point versus other good plays. Likewise Chapter 5, except it’s based on making your 4-point versus other good plays.

And the appendix lists the results of the XG rollouts of each of the 250 or so positions in the book. One example from Chapter 3, which Robertie called a toss-up in the text, shows the position is worth +0.272 if you make your 5-point versus +0.269 if you make your 4-point. That sounds like a toss-up to me, and future generations of AI bots may well switch the order of preference.

I suspect this book will be considered required reading for serious students of the game. I’m not such a student (for this game anyway), but I’m glad I read it nonetheless.