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Dice probability & shots
Every roll of two dice is one of 36 equally likely outcomes. Knowing how many of them hit a blot at a given distance is the single most useful piece of arithmetic in backgammon — it tells you when leaving a checker exposed is a small risk and when it is reckless. Pick a distance below to see the odds.
Distance to the blot (pips)
Full shots table
Number of the 36 rolls that hit a blot at each distance, assuming a clear path.
| Distance | Rolls that hit | Ways (of 36) | Chance |
|---|---|---|---|
| 1 | 1-1, 1-2, 1-3, 1-4, 1-5, 1-6 | 11 | 30.6% |
| 2 | 1-1, 1-2, 2-2, 2-3, 2-4, 2-5, 2-6 | 12 | 33.3% |
| 3 | 1-1, 1-2, 1-3, 2-3, 3-3, 3-4, 3-5, 3-6 | 14 | 38.9% |
| 4 | 1-1, 1-3, 1-4, 2-2, 2-4, 3-4, 4-4, 4-5, 4-6 | 15 | 41.7% |
| 5 | 1-4, 1-5, 2-3, 2-5, 3-5, 4-5, 5-5, 5-6 | 15 | 41.7% |
| 6 | 1-5, 1-6, 2-2, 2-4, 2-6, 3-3, 3-6, 4-6, 5-6, 6-6 | 17 | 47.2% |
| 7 | 1-6, 2-5, 3-4 | 6 | 16.7% |
| 8 | 2-2, 2-6, 3-5, 4-4 | 6 | 16.7% |
| 9 | 3-3, 3-6, 4-5 | 5 | 13.9% |
| 10 | 4-6, 5-5 | 3 | 8.3% |
| 11 | 5-6 | 2 | 5.6% |
| 12 | 3-3, 4-4, 6-6 | 3 | 8.3% |
| 15 | 5-5 | 1 | 2.8% |
| 16 | 4-4 | 1 | 2.8% |
| 18 | 6-6 | 1 | 2.8% |
| 20 | 5-5 | 1 | 2.8% |
| 24 | 6-6 | 1 | 2.8% |
How to read this
The closest distances are the dangerous ones. A blot one to six pips away can be hit directly with a single die, so it is exposed to a large share of the 36 rolls. Distance six is the worst spot of all, hit by 17 rolls. Further out, only combinations and doubles reach, the numbers thin quickly, and several distances beyond twelve cannot be hit at all.
Two cautions. First, indirect shots — those needing both dice — require the intermediate point to be open; if it is blocked, the real risk is lower than the table shows. Second, danger is only half the decision: a hit that costs your opponent their whole plan may be worth offering. For when to accept that trade, see hitting and the bar and the wider judgement in the strategy guides.
Common questions
How many ways can you roll a given number in backgammon?
There are 36 equally likely rolls of two dice. A single number from 1 to 6 can be made in 11 of them as a direct shot. Sums and doubles add more ways for larger numbers, which is why a 6 is hit more often than a 1 and why some indirect numbers are surprisingly hard to reach.
What is the most likely number to be hit?
Six. A blot six pips away is hit by 17 of the 36 rolls — the most of any distance — because it can be made directly with either die, as 5-1, 4-2 and 3-3, and by other combinations. Distances of 1 through 6 are all far more dangerous than anything further away.
What is the difference between a direct and an indirect shot?
A direct shot is a hit made with a single die, so it applies to blots one to six pips away. An indirect, or combination, shot uses both dice added together — for example hitting at distance eight with 6-2 or 5-3. Indirect shots are fewer, and they can be blocked if the intermediate point is occupied.
Does this calculator account for blocked points?
No — it assumes the path is clear. Indirect and doubles shots need their intermediate landing points to be open, so if your opponent holds one of them the real number of hitting rolls is lower. Treat the figures as the maximum danger on an open board.