The doubling cube is the youngest rule of backgammon, and the one that sets it apart from Narde most sharply. Checkers move by the dice; the cube decides how much the game is worth, and a decision about the cube usually costs more than any single move.
What follows is how the cube works, how points are counted in match play and in money play, and why two rules with surnames are attached to it.
What is the doubling cube
It is a six-sided die, but not one you roll: its faces carry the numbers 2, 4, 8, 16, 32 and 64. It shows the current stake of the game.
At the start of the game the cube sits in the middle — on the bar or at the side of the board — with 64 face up: nobody has raised the stake yet. The cube is held to be essential when the game is played for high stakes, and it is what raises the stakes as the game goes on.
How to double
A player who believes he has a sufficient advantage may double — on his own turn and before rolling the dice. He offers to continue the game at twice the stake.
The opponent has two answers: take or drop. Whoever drops loses the game at once at the current stake — the one that stood before the offer was made.
The player who accepts becomes the owner of the cube: from that moment only he may offer the next double in this game. Hence a simple rule that is easy to forget: whoever has once dropped a double can never double again — that game is already over.
What a win is worth
The game starts with a one-point stake. The win is worth:
- one point — regular win;
- two points — a gammon: the winner has borne off all his checkers and the loser none;
- three points — a backgammon: the same, but the loser also still has a checker on the bar or in the winner’s home board. In Russian this outcome is called mars — a loss at double the score.
All of it is multiplied by the value of the cube. With the cube at 2, a gammon is worth twice as much as a plain win at the same stake; a backgammon, three times as much. These are exactly the three things that raise the stakes: gammons, backgammons and the cube.
The limit of the arithmetic is theoretical: a backgammon with the cube at 64 would be worth 192 points. In practice such games do not happen.
Match play: to points, not to games
In match play the game is played to a specified number of points, and the match goes to whoever reaches them first. The number of points is usually odd — 7 or 25, for instance — so the match cannot end in a tie; tournament formats most often run from 9 to 17 points. That changes what each game is worth: the same double at 0:0 and at a score where the opponent is one point from victory are two entirely different decisions.
The Crawford game is not begun in silence: before it, the players must confirm to each other that this game is the Crawford game.
Hence the Crawford rule. When one of the players reaches a score one point short of the match-winning score, the doubling cube is removed from play for one game. Without it the trailing player would have nothing to lose: he would double in every game simply because losing costs him nothing more. After the Crawford game the cube is back in play.
All games after it are called post-Crawford. In them the cube works again and the logic reverses: now it is the trailing player who has nothing to lose and doubles almost always — while the leader, conversely, almost always takes.
Money play and the Jacoby rule
Money play uses the cube too, and the stake grows as the game goes on. But here each game is settled on its own, and that brings a rule of its own.
The Jacoby rule: a gammon and a backgammon give no extra points if the cube was never turned in that game — that is, if no double was offered and accepted. The point is to stop anyone from dragging out a hopelessly won game in hope of a gammon instead of doubling. In match play the Jacoby rule is never used — there the value of a gammon is set by the match score anyway.
Two optional rules of money play live next to it:
- automatic doubling — if on the first roll both players throw the same number, the stake is doubled. Usually it is agreed not to allow more than one doubling per game, otherwise the stake grows to the point of losing touch with the game;
- the beaver — a player who has just been doubled may raise the cube one more level immediately, keeping ownership of it.
Chouette: when there are more than two players
A chouette is the format for a group. One player, the box, plays on a single board against all the others, who form a team led by a captain. In a multiple-cube chouette each member of the team has his own doubling cube — that is, his own decisions about the stake and his own result.
When to double: one reference number
The exact borderline is computed by programs, but the reference figure is simple: in a game without the cube a player breaks even if he wins one game in four (25 %). That is the starting point for take-or-drop: from roughly this share on, a win stops being a gift.
The gammon price
Sometimes it is right to trade part of your wins for gammons, and the trade has its own measure: the gammon price tells you how many wins you may accept turning into losses in exchange for gammons won. When to double, and on what chances, is on the strategy page.
Match equity and the take point
The reference 25 % holds in money play, where each game stands on its own. In a match the value of a game depends on the score, and then one reckons in match equity — the probability of winning the whole match from the current score with perfect play by both sides. It is also called MWC (Match Winning Chances), and the value of a position in a match is measured not by the chance of winning the game but by exactly this number.
A particular but important score is double match point (DMP): both players are one point from winning the match, and the game is the last one. Match equity is especially simple here — it equals the chances of the game itself.
Hence the take point: the lowest chances of winning the game at which accepting a double is already better than refusing. In money play it sits around that same 25 %, but under a match score it shifts, and the correction is read from an equity table — a table of match chances by how many points each player still needs. Programs do the exact reckoning; the player need only know that the “take or pass” borderline has its own number under a match, not a universal 25 %.
→ The full rules of backgammon · The backgammon glossary
And in Narde?
There is no doubling cube there. Narde is a race without hitting and without a stake that grows during the game, and the price of a win is counted differently.
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