BetAndHedgeBackgammon Assistant
Backgammon Assistant
Set up any position, enter your roll, and see the best move, the cube decision and what the score means for your match.
How do you want to play?
Pick a game and a play style. You can change both at any time.
Game
Play style
Confirm your age to start.
The board
Turn and dice
On roll
Die 1
Die 2
No dice: shows the cube decision.
Doubling cube
Owner
The cube is centred: either player may double.
167your pip count
167their pip count
0race lead
Contactcheckers still to pass
Best moves
Rolling out
Cube decision
Match equity
Opening moves
How to read the numbers
- Entering plays
- With “Play moves” selected, follow the game as it happens: enter the roll, tap the checker that moves, then tap where it goes. A checker can use one die or both in a row, and the Off tray bears it off. Only legal plays are accepted. When the roll is used up the turn passes to the other side, ready for their roll. To set up a position from another game, switch to “Add yours”, “Add theirs” or “Remove”.
- Pip count
- The total number of points your checkers must travel to bear off: each checker counts the number of the point it's on, and a checker on the bar counts 25. The starting position is 167 each. Lower is better in a race.
- Race lead
- Their pip count minus yours. As a percentage it's the lead divided by the count of the player on roll, the form most race rules use. A 10% lead for the player on roll is usually a strong double.
- Contact or race
- While any of your checkers still has to get past one of theirs, it's a contact game: hitting and blocking matter. Once the armies have passed each other it's a pure race and only speed and efficient bearing off count.
- Equity
- What the position is worth on average, in points per game at the current cube: +1 means winning a single game for sure, −1 losing one, and gammons count double and backgammons triple, so equity ranges from −3 to +3. Move rankings use cubeless equity, as if the cube were dead; the cube section adds the value of owning and using the cube.
- Win, gammon and backgammon chances
- Win is the chance of winning the game. Gammon is the chance of winning a gammon or better (the loser hasn't borne off a checker); backgammon is the chance of a backgammon (the loser also still has a checker on the bar or in the winner's home board). "Their gammons" is the same from the opponent's side.
- Difference and the ± figure
- Each move shows how much equity it gives up compared with the best one. The ± is the 95% margin from the rollout: when two moves are closer than that, treat them as equally good.
- Rollouts
- The assistant first scores every legal play, then takes the strongest few and plays each forward many times: the opponent's reply and your next roll, with the best play chosen on both sides, before scoring the position reached. Every one of the 36 possible replies is covered evenly, so the luck of the dice evens out. Normal rolls out the top 4 plays over 216 games each; Ultimate rolls out the top 6 over 648 games each. Pure bear-offs are scored exactly from a built-in table of every home-board position.
- About this model
- Contact positions are judged by a compact neural network (212 inputs, 128 hidden units) built for this page and trained on 380,000 positions evaluated by GNU Backgammon. Its inputs are the checkers on each point plus positional features such as shots, home-board points, primes and pip counts. Races use the racing formula and an exact table of every bear-off position. On a test of 169 positions it never trained on, scored by GNU Backgammon at its 2-ply setting, the Normal style chose the same play 72% of the time and gave up 0.0085 points per move on average, with no big errors on the opening rolls. That is strong play, but it is a learned imitation, not GNU Backgammon or eXtreme Gammon itself, and it still makes the occasional real mistake. Treat close decisions as close.
- Cube decisions
- Before rolling, the player on roll can double. Double and take, double and pass, no double, and too good to double compare three equities: not doubling, doubling and being taken, and doubling and being passed (+1). "Too good" means your gammon chances are worth more than the single point your opponent would concede, so play on. Cube decisions use Janowski's model, which counts the value of the cube to whoever owns it, with a cube efficiency of 0.68 in contact positions and 0.6 in races. In contact, the winning and gammon chances come from the network averaged over all 36 possible rolls; in a money race the verdict follows the Keith count. On 170 cube-relevant test positions scored by GNU Backgammon, the double, no double or too good call matched its verdict in 89% of contact and 95% of race positions, and the take/pass call in 96% and 94%.
- Take point
- The least winning chance the opponent needs to accept a double. With no gammons and a dead cube it is 25%; because the taker then owns the cube and can redouble, the practical figure is about 21–22%. Gammons push it up: if you are losing more gammons than you win, you need more wins to take.
- Race rules: Keith, Kleinman and Trice
- Tom Keith's count adds wastage to each pip count: 2 for every checker beyond one on the 1-point, 1 for every checker beyond one on the 2-point, 1 for every checker beyond three on the 3-point and 1 for each empty 4, 5 or 6-point. Raise the roller's count by a seventh. Double if it exceeds the opponent's by no more than 4, redouble if by no more than 3, and the opponent takes if it exceeds theirs by at least 2. The Kleinman count turns the lead D and total S into a winning chance, (D + 4)² ÷ (S − 4); above about 1.2 the double is a pass. Walter Trice's 8-9-12 rule for long races says double with an 8% lead, redouble with 9%, and pass at 12%.
- Jacoby rule
- A money-game rule: gammons and backgammons count only as single games until the cube has been turned. It makes doubling earlier more attractive when you have gammon chances.
- Match equity
- In a match, points are worth different amounts at different scores. A match equity table gives your chance of winning the match from each score, and the assistant converts every outcome into that chance, so moves and cube actions are judged by match winning chances (MWC). The equivalent equity shown with them puts that back on the familiar −1 to +1 scale.
- Crawford and post-Crawford
- When one player first reaches one point from victory, the next game is the Crawford game and the cube can't be used. After it, the trailer should double at once, and the leader can sometimes drop for free when the trailer needs an even number of points.
- Gammon value
- How much a gammon adds compared with a single win, at this score, as a share of the value of a single game. In money play it's 1. Leaders near the finish often find gammons worth more to them; at some scores they're worth almost nothing.
- Play styles
- Ultimate ranks moves by equity alone and makes every cube decision at the exact break-even, with the largest rollouts. Normal uses the same numbers but breaks near-ties (within 0.01) toward the safer play. Aggressive adds a bonus of a few hundredths of a point for hitting, putting checkers on the bar, making home-board and prime points, and doubles up to 0.04 earlier. Conservative charges extra for blots and shots, doubles 0.04 later and passes takes that are within 0.04 of the line. The table always shows the plain equity, so you can see what each lean costs.