Backgammon bear-off calculator
Exact rolls to finish, race win chances, and the best play for every roll — for any backgammon bear-off position.
Enter your home-board position and the calculator computes the exact probability of finishing in 1, 2, 3 rolls or more — plus the best play for every possible dice roll. All math runs in your browser with deterministic (not simulated) results.
Your position
Opponent position
Opponent uses the same position as yours (15 checkers · 45 pips) and updates automatically as you edit above.
Analysis
Calculating — this takes under a second for most positions.
Current roll
Enter a dice roll to see the best play for that specific roll.
Enter a dice roll above to see the best play for that roll.
How to read the results
"Expected rolls" is the average number of turns to bear off every checker assuming perfect play — the lower the better. "Win race" compares both players' expected finishing times; you win if you bear off on the same roll as the opponent when you're on roll (and strictly before them otherwise). "Gammon chance" is the probability that you finish before the opponent has borne off a single checker — a double-stake win in match play.
How to use
- Click a point on your board to add a checker. Click the − button (or right-click) to remove one. Maximum 15 checkers per side.
- Toggle "Customise opponent" if you want to enter a specific opponent position. Otherwise the opponent is mirrored from your own board.
- Enter a specific dice roll to see the best play for it — the table at the bottom shows the best play for every possible roll regardless.
- Results update in real time. All calculations run locally in your browser with exact dynamic programming — nothing is sent to a server.
Frequently asked questions
How accurate is the calculator?
Every number is exact (to numerical precision), not simulated. The calculator memoises an exact expected-value DP over all reachable bear-off positions and solves the roll distribution exactly. Re-running it always gives the same answer.
Does it assume perfect play?
Yes. The "expected rolls" and "best play" figures assume both players always make the move that minimises their own expected finishing time. Real games will usually take slightly longer.
Does it handle contact positions or checkers on the bar?
No — the calculator is strictly for bear-off positions where all checkers are inside the home board and the race is pure. For earlier positions you'd need a full rollout tool.
Why is my win race percentage not 50% when both boards are identical?
Because whoever is on roll has the advantage. With identical boards, if you're on roll you win around 62%; the roller always finishes first on tie rolls.