- Maths reviewed by Josh Miller
- Tested by Diana Westfield
A blot six pips away gets hit 17 times out of 36, almost half the time. Move it to seven and the shots drop to 6 in 36. That’s the most useful fact in backgammon, and the CasinoCalcs backgammon odds chart below lays out every distance. The calculator above adds two more: your chance of coming in from the bar against any home board, and whether to take a double. It’s free and exact.
Still learning the moves? How to play backgammon covers the setup, hitting, bearing off and the cube before you get into the numbers.
Backgammon odds chart: hitting a blot
Direct and indirect shots, assuming no points in the way:
| Pips away | Rolls that hit (of 36) | Chance |
|---|---|---|
| 1 | 11 | 30.6% |
| 2 | 12 | 33.3% |
| 3 | 14 | 38.9% |
| 4 | 15 | 41.7% |
| 5 | 15 | 41.7% |
| 6 | 17 | 47.2% |
| 7 | 6 | 16.7% |
| 8 | 6 | 16.7% |
| 9 | 5 | 13.9% |
| 10 | 3 | 8.3% |
| 11 | 2 | 5.6% |
| 12 | 3 | 8.3% |
| 15 | 1 | 2.8% |
| 16 | 1 | 2.8% |
| 18 | 1 | 2.8% |
| 20 | 1 | 2.8% |
| 24 | 1 | 2.8% |
Two things stand out. Shots rise from 1 to 6 pips, then fall off a cliff at 7. And 12 pips gets 3 rolls (6-6, 4-4, 3-3 with the right path open) while 11 only gets 2. Blocking points in between cut the double-dice shots, so real numbers are often lower.
Coming in from the bar
| Points closed | One checker comes in | Both of two come in |
|---|---|---|
| 0 | 100.0% | 100.0% |
| 1 | 97.2% | 69.4% |
| 2 | 88.9% | 44.4% |
| 3 | 75.0% | 25.0% |
| 4 | 55.6% | 11.1% |
| 5 | 30.6% | 2.8% |
| 6 | 0.0% | 0.0% |
The doubling cube: take or pass?
Pass and you lose one point. Take and you play for two. With no gammons, taking is right whenever you win at least 25% of the time: 25% × 2 − 75% × 2 = −1, the same as passing. Gammons change it. If 20% of your losses would be gammons and 10% of your wins, the take point rises to 30.4%. The calculator’s third mode works it out. To know who’s ahead in the race before you double, count it with the backgammon pip count calculator, and for more dice maths there’s the dice probability calculator.