Backgammon Probability Tables

Backgammon is a game of probabilities. Every decision you make is really a judgment about how likely something is to happen: being hit, entering from the bar, winning the race or the match. Your moves can only be as good as those judgments.

Why beginners need tables

For a new player the game can feel overwhelming. Duplication, diversification, pip counts, timing, priming games, holding games: there is a lot to absorb. A few simple probability tables give you something solid to lean on. If you know how likely your opponent is to hit a blot, you may choose a different move that improves your chances or reduces his.

Many books tuck these tables away near the back, but they deserve a place near the front. Below are the three most useful ones for a beginner. Print them out and keep them close by. After some practice you will remember the key numbers and will rarely need to look.

All the numbers come from the 36 equally likely rolls of two dice. Doubles such as 3-3 can be rolled only one way, while non-doubles such as 3-1 can be rolled two ways (3-1 and 1-3).

Chances of hitting a blot

This table shows how often a single checker hits a blot that is a given number of pips away, assuming nothing blocks the path.

A blot six pips away is in the most danger. That is one reason the bar point is hard to make early in the game. Once the distance reaches seven or more, the risk falls sharply, because only combinations of both dice can hit. Keep this in mind when you or your opponent hold deep points and it is time to bring checkers home.

Two rules to remember:

1. If you must leave a direct shot (6 pips or less), leave it as close to the enemy checker as you can.
2. If you leave an indirect shot (7 pips or more), leave it as far away as you can.

Blocking points change these numbers. If your opponent's path is blocked, some combination rolls no longer hit, so count the actual rolls when the position is crowded.

Chances of entering from the bar

Every point you close in your home board makes it harder for a hit checker to come back in. The difference between two and three closed points is bigger than it looks. With one checker on the bar, the chance of entering in one roll is 1 minus (closed points / 6) squared.

Values of 100% in the later columns are rounded; the exact figures are just below 100%.

With two checkers on the bar, both must enter on the same roll to get back into play fully:

The lesson is clear: hitting checkers and closing home board points together are a deadly combination, which is the whole idea of the blitz. Home board points also pay off later, since they are already in place when you start bearing off.

1. Make home board points whenever you reasonably can.
2. When attacking, hitting a second checker is often worth more than it looks.

Winning chances in a 5-point match

Five points is one of the most common match lengths in tournaments and online play. At every score, each player has a certain chance to win the match, and these chances — collected in a match equity table — decide whether a double is a take or a pass. Modern tables are computed by backgammon programs; serious tournament players learn the key numbers by heart.

You do not need the exact figures to use the idea. The general pattern is simple: every point of lead matters more as the match gets closer to its end, the player who first gets within one point of victory is a big favorite, and in the Crawford game the cube cannot be used at all.

1. Being the first to reach 3 or 4 points is a big advantage. When you lead, play solidly and avoid needless risks.
2. When you are well behind, you need gammons and active cube play to catch up, so be willing to take on more risk.

For more on how these numbers affect doubling, read our article on the doubling cube.