Backgammon hit probability: the complete shot table
How often a blot actually gets hit, at every distance from one pip to twenty-four. Every number below is enumerated over all 36 ordered outcomes of two dice when this page is built, so it cannot drift and you can check it yourself.
Direct and indirect
A blot six pips away or closer can be reached by one die on its own. That is a direct shot. From seven pips out the roll has to combine both dice, which is an indirect shot, and the difference is much larger than it looks: 47.2% against 16.7%.
The full shot table
Assumes the intermediate points are open, which is the standard convention for a shot count. If a combination shot has nowhere to land halfway, the real chance is lower.
| Distance | Rolls that hit | Chance | Type |
|---|---|---|---|
| 1 | 11 of 36 | 30.6% | Direct, a single die reaches it |
| 2 | 12 of 36 | 33.3% | Direct, a single die reaches it |
| 3 | 14 of 36 | 38.9% | Direct, a single die reaches it |
| 4 | 15 of 36 | 41.7% | Direct, a single die reaches it |
| 5 | 15 of 36 | 41.7% | Direct, a single die reaches it |
| 6 | 17 of 36 | 47.2% | Direct, a single die reaches it |
| 7 | 6 of 36 | 16.7% | Indirect, needs two dice combined |
| 8 | 6 of 36 | 16.7% | Indirect, needs two dice combined |
| 9 | 5 of 36 | 13.9% | Indirect, needs two dice combined |
| 10 | 3 of 36 | 8.3% | Indirect, needs two dice combined |
| 11 | 2 of 36 | 5.6% | Indirect, needs two dice combined |
| 12 | 3 of 36 | 8.3% | Indirect, needs two dice combined |
| 13 | 0 of 36 | 0% | Cannot be covered by one checker |
| 14 | 0 of 36 | 0% | Cannot be covered by one checker |
| 15 | 1 of 36 | 2.8% | Indirect, needs two dice combined |
| 16 | 1 of 36 | 2.8% | Indirect, needs two dice combined |
| 17 | 0 of 36 | 0% | Cannot be covered by one checker |
| 18 | 1 of 36 | 2.8% | Indirect, needs two dice combined |
| 19 | 0 of 36 | 0% | Cannot be covered by one checker |
| 20 | 1 of 36 | 2.8% | Indirect, needs two dice combined |
| 21 | 0 of 36 | 0% | Cannot be covered by one checker |
| 22 | 0 of 36 | 0% | Cannot be covered by one checker |
| 23 | 0 of 36 | 0% | Cannot be covered by one checker |
| 24 | 1 of 36 | 2.8% | Indirect, needs two dice combined |
The seven distances that cannot be hit
13, 14, 17, 19, 21, 22, 23 pips. A single checker can play one die, the other die, both added together, or up to four of the same number on a double. No combination of those reaches those distances. It is worth knowing, because a blot left exactly 13 or 14 pips from a lone enemy checker is completely safe from it, while a blot one pip closer is not.
Entering from the bar
The same enumeration answers the other question that decides games: with a checker on the bar, how often do you come in? Each die is a separate chance to enter, which is why the odds stay high until the board is nearly closed and then collapse.
| Opponent's home board | Rolls that enter | Chance |
|---|---|---|
| 1 point made | 35 of 36 | 97.2% |
| 2 points made | 32 of 36 | 88.9% |
| 3 points made | 27 of 36 | 75.0% |
| 4 points made | 20 of 36 | 55.6% |
| 5 points made | 11 of 36 | 30.6% |
| 6 points made | 0 of 36 | 0.0% |
The step from five points to six is the whole argument for closing your board. At five made points you still come in 30.6% of the time. At six you do not come in at all, and you sit there until the board opens.
These odds only matter if you apply them under pressure. Play a rated game and every decision is reviewed afterwards against the best play available, with dice committed before you roll and checkable after, so what the review measures is your judgement rather than your luck.
Play a rated game freeFrequently asked questions
What are the chances of hitting a blot in backgammon?
It depends entirely on the distance. The most likely single distance is 6 pips at 17 rolls out of 36, which is 47.2%. Anything from 1 to 6 pips away is a direct shot and is hit between 30.6% and 47.2% of the time. From 7 pips out the chances fall away quickly, because the roll has to combine two dice.
What is the difference between a direct shot and an indirect shot?
A direct shot is six pips or fewer, so a single die can reach it. An indirect shot is seven or more and needs both dice combined, which is far less likely. The gap is large: a blot six away is hit 47.2% of the time, and a blot seven away only 16.7%.
Which distances cannot be hit at all?
Seven of them: 13, 14, 17, 19, 21, 22, 23 pips. A single checker can move a die, the other die, both dice added, or up to four of the same number on a double. No combination of those produces those distances, so a blot sitting exactly that far from a lone checker cannot be reached by it at all.
What are the odds of entering from the bar?
Against one made point you enter 97.2% of the time, against two 88.9%, three 75%, four 55.6%, and five 30.6%. Against a closed board of six points you cannot enter at all, which is why closing your board is worth so much.
Do these numbers assume the intermediate points are open?
Yes. Combination shots need somewhere to land halfway, so if the intervening point is blocked the real chance is lower than the table shows. Direct shots of six or fewer are unaffected, since they need no landing square.
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