About

Shot counting is a foundational backgammon skill: out of 36 possible dice rolls, how many let you (or your opponent) hit a blot in a given position? This is useful for evaluating checker plays (e.g., choosing the play that minimizes opponent's shots, or evaluating a tradeoff between shots and some other benefit) and cube decisions (e.g., evaluating market losers or game-winning chances). Counting shots quickly and accurately is worth practicing since it is useful in almost every backgammon match.

This page focuses on learning to count single shots (i.e., from one attacking point) at a single blots 1 through 12 pips away. This is a fundamental building block that should be mastered before learning to count double or triple shots.

Counting single shots

Shots can be divided into three types:

1. Direct shots: rolls where the blot can be hit using the number on one die. There are 11 direct shots at any blot 1-6 pips away, and zero at blots more than 6 pips away.
2. Indirect shots using 2 moves: rolls where the blot can be hit using the sum of the two dice. For example, 41 and 32 both hit a blot 5 pips away. The number of indirect shots peaks at 7 pips away, where there are 6 indirect shots (61 52 43, x2 ways of rolling each). If you like formulas, the number of indirect shots at a blot X pips away is X − 1 (for X in 1-7) or 13 − X (for X in 7-12).
3. Doublet shots using 3 or 4 moves: since doublets are played 4 times, some additional shots can be hit using 3 or 4 moves (e.g., a blot 12 pips away can be hit with 3+3+3+3 or 4+4+4). These can add up to 2 extra shots, depending on the distance.

Working through the three buckets is a good way to develop intuition, but for actual play it is best to memorize the totals so you can easily recall this sequence instantly over the board: 11, 12, 14, 15, 15, 17, 6, 6, 5, 3, 2, 3 shots for blots 1 through 12 pips away.