The doubling cube is typically ignored by beginner players. It’s that extra cube that comes in a backgammon set with numbers in powers of two (2, 4, 8… 64) on its faces:
There are So. Many. Articles. about the doubling cube. Cube play is almost its own game within a game. Entire books are written on how to best take advantage of it in different stages of match play, and it constitutes some of the most exciting theory in backgammon.
But… it’s admittedly super daunting to newcomers. I remember personally not having any idea what to do with it when I started using it after learning how it works. It took a few rules of thumb for me to get comfortable enough to start enjoying it. Don’t worry, by the end of our course, we’ll get you there too.
For now, here’s a crash course on how it works: every game begins with the cube centered, with the number 64 facing up. At this point, it is not yet in play — the “64” appears so rarely that it represents “we haven’t really started yet.” At some point in the game, if someone thinks they are the favorite to win, then before they roll the dice, they will pick up the cube, turn it to “2” and place it in front of their opponent. A challenge. They are offering to continue the game at doubled stakes, meaning that whoever wins a single will gain 2 points, a gammon 4 points, and a backgammon 6 points. The opponent must make a choice: they may choose to accept (or take) the cube, at which point it goes to live on their side, with a “2” facing up. (As a perk for accepting the cube, only they have the capability to offer the cube and raise the stakes further). Otherwise, if it is refused (or dropped or passed), they give up the game entirely and the player who offered the cube wins immediately at the current stake. If this is the first time the cube gets turned, they lose 1 point; if the cube was previously turned to 2, they lose 2 points, etc.
And those are the two options — you can’t just say “no thanks” and play on at the current stakes.
It’s obvious that the leader would want to double the stakes immediately. Why not build on your advantage? The question you must be asking yourself is — why would anyone bother accepting a cube if they are expected to lose? Sure, they might turn it around (this is backgammon after all) but why bet on a losing proposition?
The answer is that by accepting the cube, the trailer is expecting to lose less than they would by dropping the cube. By dropping, they never win any points that they potentially might win if they accept! This is a very subtle point that is best explained by way of example.
Suppose you play 100 games against your opponent, Gary. Gary opens with a 31 roll, making their 5 pt. This is the best opening in backgammon, immediately giving him a 55% chance to win. He then offers you the cube at his first opportunity. If you drop every time, you will have lost 100 games, and Gary will lead 100 – 0. If, on the other hand, you accept every time, Gary should win 55 games, and you 45. At 2 points a pop, this will result in a score of 110 – 90 — instead of trailing the score by 100 pts, you are only trailing by 20! You aren’t really thrilled to be trailing in either outcome, but accepting the cube has turned into a great deal for you!
This example highlights the potential benefits of accepting the cube as the trailer, but this benefit doesn’t last forever! Surely, the leader would have preferred to double with a larger lead to further secure their win and leave fewer potential points to the trailer. Let’s see what happens if Gary doubled with a 95% lead instead of 55%: if you accepted every time, the resulting score would be 190 – 10, a lead of 180 points. You would have done better to reject the cube each time! A good backgammon player will know this, and this is why they typically don’t offer the cube with such a commanding lead; hopefully they offered it earlier for the chance to win 2 points instead of just 1.
This illustrates the whole play of the cube: it’s the search for this sweet spot, the doubling window, where it’s safest for you to double while still being worth it for your opponent to accept. It turns out that the break-even point is to double with a 75% lead.1 (Said otherwise, the trailer’s take point, the minimum win chances they are willing to accept, is 25%.) Here, after 100 games, the leader expects 150 points, and the trailer expects 50 points, that is, they trail by 100 points. Recall that this is the same result when dropping the cube every time, as well! The trailer would, of course, prefer the cube to appear at values below 75% to increase their own expected outcome, but it’s on the leader to choose the right moment to double.
We are going to learn a ton about the cube, but for the immediate next short series of articles we are going to set it aside. There is more work to be done first!
Further reading:
- An article by Steg on the origins of the doubling cube.
- A short article by Hank Youngerman on Doubling Cube strategy
- A video by GM Marc Olsen explaining how to play with the doubling cube on the Backgammon Galaxy youtube channel
- A lecture by Chris Bray that covers many topics on how to use the doubling cube
- This actually varies dramatically by match score, and isn’t even exact for unlimited/money games because of the possibility of a redouble. We will get into all those details in future articles. ↩︎
Next lesson: Match Play vs. Unlimited Games
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