Backgammon Probability & Odds: The Math Behind the Game (2026)

Understanding probability is what separates good backgammon players from great ones. Every decision in backgammon involves risk, and knowing the actual odds helps you make better choices at every point in the game.

Dice Probability Fundamentals

With two six-sided dice, there are 36 possible combinations (6 × 6). However, since the order of dice matters in probability but not in play, some totals are more likely than others.

Probability of Each Total

Total	Combinations	Probability	Ways to Roll
2	1	2.78%	1-1
3	2	5.56%	1-2, 2-1
4	3	8.33%	1-3, 3-1, 2-2
5	4	11.11%	1-4, 4-1, 2-3, 3-2
6	5	13.89%	1-5, 5-1, 2-4, 4-2, 3-3
7	6	16.67%	1-6, 6-1, 2-5, 5-2, 3-4, 4-3
8	5	13.89%	2-6, 6-2, 3-5, 5-3, 4-4
9	4	11.11%	3-6, 6-3, 4-5, 5-4
10	3	8.33%	4-6, 6-4, 5-5
11	2	5.56%	5-6, 6-5
12	1	2.78%	6-6

Key insight: 7 is the most likely total, and extreme values (2, 12) are rare.

Probability of Doubles

The chance of rolling any specific double: 1/36 = 2.78%

The chance of rolling any double at all: 6/36 = 16.67%

Doubles happen about once every 6 rolls.

Hitting Probabilities

One of the most important probability tables in backgammon is the chance of being hit based on distance. This assumes a single opposing checker can reach your blot:

Direct Hitting Chances (One Checker)

Distance	Out of 36	Probability
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%

Key insights:

6 or fewer points away = direct hit range (30-47% chance)
7+ points away = indirect hit only (needs combination or doubles)
Distance of 7 is a major safety threshold — hitting chance drops from ~47% to ~17%

The Rule of Eights

A quick mental shortcut: Count the number of “shots” (dice combinations that hit) and multiply by 3 to get a rough percentage. For more precision, divide by 36.

Entering from the Bar

When you have a checker on the bar, your ability to enter depends on how many points in your opponent’s home board are open:

Open Points	Chance to Enter	Chance to Stay on Bar
6 (all open)	100%	0%
5	97.2%	2.78%
4	88.9%	11.1%
3	75.0%	25.0%
2	55.6%	44.4%
1	30.6%	69.4%
0 (closed board)	0%	100%

Key insight: With only 2 open points, you’ll fail to enter nearly half the time. A closed board is absolute — no entry is possible.

Bearing Off Probabilities

Bearing Off in One Roll

From various positions in the home board, the probability of bearing off all remaining checkers in exactly one roll:

2 checkers remaining:

Both on the 1-point: 100%
1-point and 2-point: 100%
Both on 6-point: 17/36 = 47.2%

The last two checkers: The probability of bearing off your last 2 checkers in one roll varies dramatically based on their positions. High point numbers require specific high rolls.

Pip Count and Race Probability

In a pure race, the relationship between pip count and winning probability is approximately:

Equal pip count: ~50% each
Leading by 5 pips (at 80 total): ~58%
Leading by 10 pips (at 80 total): ~66%
Leading by 15 pips (at 80 total): ~73%
Leading by 20 pips (at 80 total): ~80%

The value of each pip depends on the total distance remaining. A 5-pip lead at 80 total pips is more significant than a 5-pip lead at 150 total pips.

Practical Applications

Should You Leave a Blot?

When deciding whether to leave a blot:

Count the number of rolls that hit you
Divide by 36 to get the probability
Consider what happens if you’re hit vs. not hit
Compare with the expected value of safer alternatives

Slotting Decisions

Slotting (placing a single checker to build a point) is worthwhile when:

The probability of being hit is low
The value of making the point is high
You have good timing to cover the blot next turn

Double/Take Decisions

Probability directly drives cube decisions:

Know your approximate winning percentage
Compare against the 75%/25% thresholds (money play)
Factor in gammon probability