You can know your chances of winning a backgammon position and still have another question to answer when the cube arrives: what happens to the match if you pass?
The answer depends on the score and on the games you would have left to play. Sometimes taking gives you the better chance of winning the match even though you are likely to lose the current game. Sometimes passing preserves a more promising route through later games.
We will use a position with one checker left on each side, where we can count exactly which rolls win. We will then compare taking and passing while varying your assumed chances of winning the games that follow.
What the cube does
The doubling cube records the stakes of a game. It starts in the middle at a value of 1, usually with 64 showing. Before rolling, either player can offer to raise the value to 2. The opponent can take, continuing at the new value, or pass, conceding the old value: 1 point in this case.
The player who takes also receives the cube and the right to offer the next redouble, from 2 to 4, before one of their own rolls. Winning before your opponent has borne off any checker is a gammon, worth twice the cube’s value; a backgammon pays three times. The USBGF beginner’s guide explains the full rules.
In a match, the aim is to reach an agreed score. That makes the cube more than a question of how many points a position is worth: those points can also determine whether there is another game.
An offer at 5–5
You are playing Ivory in a seven-point match, level at 5–5. Both players need 2 points. You each have one checker left: yours is on your 1-point, Red’s is seven pips from the exit. Red is about to roll and offers the cube at 2.
If Red finishes, you lose. If Red cannot finish, you bear off on any roll and win. You have already both borne off 14 checkers, so neither side can lose a gammon.
Counting the 36 equally likely dice pairs gives you 13 chances in 36, or about 36.1%. That count allows Red to play doubles four times: even 2–2 is enough to cover seven pips.
Taking and passing lead to different matches
If you take, the game is worth 2 points. The winner reaches 7, and the match is over. Your chance of winning the match is therefore exactly your chance of winning this position: 13/36.
If you pass, you concede 1 point and trail 5–6. Because a player has just reached one point from the target for the first time, the next game is the Crawford game: no doubling is allowed. Win a single game and you reach 6–6, where one more win takes the match. A gammon during Crawford would give you the two points you need immediately.
To start, suppose you have a 50% chance of winning each later game, and leave gammon wins out of that calculation. Passing then requires two wins: half of a half, or 25%. Taking with 36.1% is better.
Compare the two routes to winning the match
You play Ivory, toward point 1. Red moves toward 24; Red’s own 7-point is marked 18 here.
Read the position
Ivory, point: number of checkers. 1: 1. Red: 18: 1. On the bar: Ivory 0, Red 0. Borne off: Ivory 14, Red 14.
Where do the 13 winning rolls come from?
The checkmarks show rolls on which Red cannot finish. Ivory then bears off on any roll. Doubles count four times: 2–2 and 3–3 finish, but 1–1 does not.
Take the 2-cube
36.1%Chance of winning the match
Pass and concede 1 point
25.0%Chance of winning the match
Under these assumptions, taking gives you the better chance of winning the match.
Follow the scores after each choice
Take the 2-cube
A win makes it 7–5; a loss makes it 5–7. Either ends the match.
Pass and concede 1 point
At 5–6, the next game is Crawford: no cube. A single win takes you to 6–6, where one more win decides the match.
- Win Crawford for 1 point 50.0%
- Then win at 6–6 50.0%
A gammon or backgammon in Crawford wins the match immediately.
How the paths add up
50% × 50% = 25.0%
The first percentage is for Crawford; the second is the chance of winning at 6–6 if you get there. With gammons, add the immediate wins and remove them from the single wins before multiplying. Displayed values are rounded.
Your edge cannot change the next roll
Now suppose you are favoured in the later games, with a 65% chance of winning each one. We are choosing that number to explore the idea; it is not a measurement of professionals or a conversion from a rating.
There is almost no checker-play judgement left in the position on the board. Your assumed advantage cannot turn 13 winning rolls into 14. Taking still gives you 36.1% to win the match.
Passing, however, leaves two fresh games in which that advantage could matter. Without gammon wins, 65% multiplied by 65% gives 42.25%. Under those assumptions, passing is now better. Adding the possibility of winning a gammon in Crawford makes that route more valuable still; the control above lets you include it.
The choice has reversed without changing the board: with a 50% chance in each later game, taking is better; with 65%, passing is better.
Why a stronger player may prefer a smaller cube
This is an established part of match strategy. In his 1980 discussion of the doubling cube, Danny Kleinman explained how differences in playing strength affect cube decisions: higher stakes can leave fewer games for an advantage to show. We credit him for that principle.
In our example, passing at 5–5 leaves the stronger player a way to win through fresh games, where their checker-play advantage can matter. Taking settles the match in a position with almost no checker-play choices left.
That does not mean a stronger player should always avoid the cube, or that a weaker player should double every position. The offer, the score, gammons and the right to redouble all matter.
More skill does not promise a winning evening
In our article about playing well and still losing, a small advantage can take many results to show up clearly. The cube does not remove that uncertainty. It adds decisions about how a particular game affects the rest of the match.
That article gives every whole match a fixed win chance. Here, we follow the possible outcomes of one cube decision inside a match, using exact dice odds now and stated assumptions about later games.
For your next cube decision, try asking what each choice leaves you: the score after a pass, the score after a win or loss with a take, and who could redouble. Then compare the routes to winning the match. This is also the kind of decision you can revisit with CUBE Backgammon’s coach, alongside your checker moves.
The match score can also change which checker move to choose. Compare a hit and a running play on the same board at 0–0 and 6–6.
The principle connecting playing strength, cube stakes and match length is established; we credit Danny Kleinman’s The Care and Feeding of the Doubling Cube, Part 2 (1980). We constructed the bear-off example, score paths and interactive comparison for this article.
Rules and calculation
Rules follow the USBGF tournament rules, including Crawford and dead cubes. In the current race, Red finishes with a non-double totalling at least 7, or any double except 1–1: 23 of the 36 ordered rolls. Ivory wins the other 13, then bears off on any roll.
For the future games, let W be your assumed chance of winning Crawford, G the part of that chance won by gammon or backgammon, and D your chance of winning at 6–6 if you reach it. Passing wins the match with probability G + (W − G) × D. All losses in Crawford end the match. The controls use the same assumed chance for W and D; these can differ in real play. The gammon option sets G to 10% of all Crawford games, not 10% of wins. The base case sets G to zero. These are hypothetical inputs, not an empirical match-equity table or a general cube advisor.
Taking ends this match, so there is no further useful redouble. At 6–6 the cube cannot help either player either. The example is specifically about match play; in unlimited points play, a point has a different role and there is no seven-point finish line.