# Backgammon is Mathematics

I have played backgammon about 45 years. For the first 20, I did not take the game very seriously…I mostly played with friends and family. I never entered a tournament or played for money.

Then one day, about 25 years ago, I walked into a restaurant in Chicago and there was a group of people gathered around a backgammon board all playing together. I found out later that it was called a “chouette” game, where several players competed for money, with one player on one side competing against all the rest on the other side.

I watched for a while, introduced myself, and was invited to play. The stakes weren’t high, and it looked like fun, so I tried it. And then, probably the worst thing that could possibly happen, happened–I won! Not only did I win, but I won a lot; I got paid; and I had a lot of fun in the process. I was hooked.

I think that was the last time I won for a long time. Turns out that I won that first time simply because I was very lucky and often on the right side with the right players. In a very short period of time I learned that every player in the game, and every player who showed up to play over the next few weeks, was far better than I.

Now, I am not a dumb person. After winning once and losing about 23 times, it occurred to me that I might not be as good a player as the others in the game. But I am also not a person to give up. Just as I had become a Life Master at Bridge many years before, I realized that in order to be really skilled at any game, I must take it seriously and I must study.

I went out and bought a couple of books on Backgammon, and through the internet, I got the names of some top teachers. I have spent the last 25 years reading and studying this game. I am happy to say that my chouette and tournament play has improved, and my win/loss record is now a little better than 23 to 1.

What I learned, the “hard way,” I will be happy to share with you now. For the first 20 years I played Backgammon I concentrated on the “look” of the game. I knew a 6 point prime looked good; I knew holding points in your opponent’s board only looked good if you had good timing so that you could play a successful back game. I would drop a cube if it looked really bad, and I would give the cube if it looked really good.

I actually got to be a fairly decent player relying on my “looks.” Plenty good in fact, to beat most of my friends and family most of the time. But when I got out into the “real world” of backgammon, and started playing others for money, and started competing in tournaments, it was obvious that my game was pretty lousy in comparison to the truly good players.

By reading books and articles and talking to top players and taking lessons from some of the best players in the world, the most important thing I learned was that in order to become a really good player, it is not about looks at all—it’s math.

This is the big secret to success in backgammon. IT’S ALL MATH! You can be a decent player relying on looks and feel, but you cannot become a really great, or even really good player, without doing the math.

For every single checker play there is usually one best play (one in a while there are two or three that tie, but not often), and that play is better because your odds of winning the game or match are higher with that play than with any other. Every time you have a cube decision, there is one decision that is best because of the odds. And odds is percentages…it’s all numbers…all math.

The winner of every game of backgammon is either the player who gets his last checker off first, or the player who gets his opponent to drop the cube because his odds of getting that checker off first are too high. Every checker play and cube decision along the way is done with this outcome in mind. And the only way to know who has the best odds of removing that last checker first, and what those odds are, is by doing the math.

What all the books and teachers taught me, more than anything else, is what math I needed to do and how to do it. And that is what any advanced backgammon lessons are all about.

When I first came to this realization, I have to admit, it kind of took the fun out of the game for me. I am not great mathematician. I don’t have a lot of fun calculating odds and percentages in my head–on top of all the other aggravation of playing backgammon, they don’t even allow you to use a pencil and paper to do the math, much less a calculator! I even said to myself that if you have to be a great mathematician to be a great backgammon player, why bother with backgammon? If I were that good at math I’d be better off studying quantum mechanics and coming up with the solution to the string theory.

Turns out, quantum mechanics is actually a little harder than backgammon, and backgammon, to me, is a lot more fun. Yes, making the right plays and decisions is all about math, but there is also luck, and fun, and the “human element.” Once you understand the basic math, backgammon, like poker and other player vs. player games, also includes reading your opponent, having the guts to make the tough plays and decisions, and dealing with the luck factor. (Even dealing with the luck factor is all about the odds.)

I also found out that the math is really not that terribly difficult once you do a few things to make it easier:

The experts have saved us a lot of time and trouble and have given us some basic formulas, match equity tables, race formulas, and rules of thumb to apply that are pretty easy to memorize. We don’t each have to recreate the wheel—people like Magriel, Robertie, Woolsey, Kazaross, Jacobs, Trice, and others have been very generous in giving us the basic formula. Just as I know that to find the area of a circle I have to multiply the radius time Pi, I know that I generally should be up over 10 percent in a race for me to double.

The more you do the math, the easier it becomes. It’s like any other learned skill. At first I got frustrated counting pips, and now I can do it much faster and easier…especially after learning some shortcuts that anyone can find out about from articles and books. I hated calculating match equities, and to do it right used to take me well over 10 minutes some times. Now, I can pretty much figure out most match equities in less than a minute.

Once you memorize the basic formulas and tables, you often don’t need exact mathematical answers to make the right decision—often you can estimate, and if you fall into an acceptable range, you can make the right play.

The more you play and study, the more “reference positions” you have in your head. I no longer have to do any math to realize I get hit 17 out of 36 times if I leave a direct 6 shot with no points in between, and only 11 out of 36 if I leave an ace shot. I know that if I have a closed board and perfect bearoff and my opponent has 2 checkers on the bar, I win gammons about 40% of the time. There are hundreds, maybe even thousands of positions in my head where I already know the numbers. So a lot of the time, I already pretty much know the odds from experience. I know that if my opponent is leading 4-3 Crawford in a match to 5, my odds of winning the match are 30% (assuming we are equal players). Knowing this number helps me decide just how much to gamble to try to win a gammon as opposed to playing simply for a win.

So, do you want to not waste the 20 years I wasted playing backgammon at a mediocre level? Learn the math. And the way to do that is a three-fold process.

First you need to learn what you need to learn. No matter how smart you are, it is doubtful that in a single lifetime you could learn this without getting help from the experts. Fortunately, there are many ways to get this help from books, articles, from lessons, and also from the Computer Programs which the experts have programmed to help you see what the best plays are and what math to apply.

Once you learn what you need to learn, you have to memorize the basic formulas and principles. It’s as simple as that. You cannot calculate the area of a circle if you don’t know that Pi is 3.1416. And you cannot calculate match equity if you don’t know the tables and the price of gammons.

Once you know what you need to know, and you have memorized the formulas, you then need to learn how and when and where to apply the math. That means you have to play, and practice. And not just play “for the fun of it.” You have to keep your mind engaged and thinking and keep honing your skills.

“How do I know, for sure, that this is right?” you might ask. The proof is in the results. Not only can I show better results for my own tournament play, I can sit down and get my game rated by Snowie or Jellyfish (computer programs) and they will show that my skill level is higher. And of course, I am doing better in chouettes now as well. But the best proof is to look at the major tournament results. With few exceptions, the winners of major tournaments, and the players who are the highest ranked in the world, can all tell you that they use math, or reference positions that include the math, in EVERY PLAY THEY MAKE. It is no accident that ALL the players who win the most approach the game mathematically.

Backgammon is Mathematics . If you want to improve your game, work on the math. It’s that easy.