Backgammon Odds: Hitting, Entering and Doubles
Backgammon is a race with two dice, and every strong player carries a few numbers in their head: how likely a lone checker is to be hit, how hard it is to come in from the bar, and how far a roll moves you on average. All of them come from the same simple fact: two dice have 36 equally likely rolls. Here are the odds, worked out exactly.
The Rolls That Matter
- Two dice give 36 possible rolls. A roll like 3 and 5 can happen two ways (3-5 or 5-3), a double like 4-4 only one way.
- Doubles are 6 of the 36 rolls, so 1 roll in 6. A double lets you move the number four times.
- The average roll moves 8 1/6 pips, counting doubles four times. A player 100 pips from home needs about 12 rolls with no waste.
Chance of Hitting a Single Checker
A checker standing alone (a blot) is hit if the opponent rolls the right distance with one die, with both dice added together, or with a double. Counting all 36 rolls, assuming no blocked points in between:
| Distance to the checker | Rolls that hit it (out of 36) |
|---|---|
| 1 | 11, about 31% |
| 2 | 12, 33% |
| 3 | 14, 39% |
| 4 | 15, 42% |
| 5 | 15, 42% |
| 6 | 17, 47% |
| 7 | 6, 17% |
| 8 | 6, 17% |
| 9 | 5, 14% |
| 10 | 3, 8% |
| 11 | 2, 6% |
| 12 | 3, 8% |
| 15, 16, 18, 20 or 24 | 1 each, about 3% |
| 13, 14, 17, 19, 21 to 23 | 0, cannot be hit |
Two things stand out. Close shots, within 6 pips, are hit far more often than far ones, because a single die can do it. And 6 pips away is the most dangerous distance of all, at 17 rolls in 36, because any 6 hits as well as 5-1, 4-2, 3-3 and 2-2. Once you are 7 or more pips away the chance drops sharply, since only combinations can reach.
Points the opponent holds in between can block some combinations, so in a real game the chance is sometimes lower than the table.
Coming In from the Bar
A hit checker must re-enter in the opponent’s home board, on the point that matches one of your dice. If some of those six points are closed (two or more of the opponent’s checkers), a die showing that number cannot be used. You fail only if both dice show closed points:
| Points closed in the home board | Chance to enter at least one checker |
|---|---|
| 1 | 35 in 36, 97% |
| 2 | 32 in 36, 89% |
| 3 | 27 in 36, 75% |
| 4 | 20 in 36, 56% |
| 5 | 11 in 36, 31% |
| 6 | 0, you cannot enter |
With all six points closed you cannot enter at all and miss your turn. This is why a closed home board is so strong: against five closed points you fail more than two times in three.
A Few Rules of Thumb
- If you must leave a blot, leave it 7 or more pips from the opponent if you can.
- A blot 6 away is more exposed than one 1 away.
- Each extra closed point in your home board makes it much harder for a hit checker to come back.
- Rolls do not remember. A player who has not rolled a double for a while is not "due" one; see the gambler’s fallacy.
Is Backgammon Luck or Skill?
Both. In a single game the dice decide a lot, and a beginner can beat a strong player. Over many games, choices like which blots to leave and when to double decide most results, which is why the same players rise to the top. The dice are fair; the skill is in playing the odds above. You can try any roll with our Dice Roller.
Where Backgammon Comes From
Race games with dice and a track are among the oldest board games known. The Roman game tabula is generally seen as a close ancestor of backgammon, and the modern rules with the doubling cube took shape much later. For simpler dice and board games, see Ludo, and for the maths behind any roll, our guide to dice probability.
FAQ
What is the chance of hitting a blot in backgammon?
It depends on the distance. With no blocks in between, a checker 1 pip away is hit by 11 of 36 rolls (31%), 6 pips away by 17 of 36 (47%), and 7 pips away by only 6 of 36 (17%).
What is the most dangerous distance to leave a blot?
6 pips, which is hit by 17 of the 36 rolls. Within 6 pips a single die can hit, so close blots are much more exposed than far ones.
How often do you roll doubles in backgammon?
6 of the 36 rolls are doubles, so 1 roll in 6 on average.
What is the average roll in backgammon?
8 1/6 pips, counting doubles four times.
What are the chances of entering from the bar?
You fail only if both dice show closed points. Against 3 closed points you enter 75% of the time, against 5 closed points only 31%, and against 6 you cannot enter.