Doubling cube
Doubling cube
To speed up match play and to provide an added dimension for strategy, a doubling cube is usually used. The doubling cube is not a die to be rolled but rather a marker, in the form of a cube with the numbers 2, 4, 8, 16, 32, and 64 inscribed on its sides, denoting the current stake. At the start of each game, the doubling cube is placed on the bar with the number 64 showing; the cube is then said to be "centered, on 1". When the cube is centered, the player about to roll may propose that the game be played for twice the current stakes. His opponent must either accept ("take") the doubled stakes or resign ("drop") the game immediately. If the opponent takes, the cube, now showing the doubled stake, is moved to the opponent's side of the board. This is done to indicate that the right to re-double belongs exclusively to the player who last accepted a double. Whenever a player accepts doubled stakes, the cube is placed on his side of the board with the corresponding power of two facing upward.[2][3] If the opponent drops the doubled stakes, he loses the game at the current value of the doubling cube. For instance, if the cube showed the number 2 and a player wanted to redouble the stakes to put it at 4, the opponent choosing to drop the redouble would lose two, or twice the original stake.
The game is rarely redoubled beyond four times the original stake, but there is no limit on the number of redoubles. Although 64 is the highest number depicted on the doubling cube, the stakes may rise to 128, 256, and so on. In money games, a player is often permitted to "beaver" when offered the cube, doubling the value of the game again, while retaining possession of the cube.[4]
A variant of the doubling cube "beaver" is the "raccoon." Players who doubled their opponent, seeing the opponent beaver the cube, may in turn then double the stakes once again ("raccoon") as part of that cube phase before any dice are rolled. The opponent retains the doubling cube. E.g. White doubles Black to 2 points, Black accepts then beavers the cube to 4 points; White, confident of a win, raccoons the cube to 8 points, whilst Black retains the cube. Such a move adds greatly to the risk of having to face the doubling cube coming back at 8 times its original value when first doubling the opponent (offered at 2 points, counter offered at 16 points) should the luck of the dice change.
Some players may opt to invoke The Murphy rule or the "automatic double rule." If both opponents roll the same opening number, the doubling cube is incremented on each occasion yet remains in the middle of the board, available to either player. The Murphy rule may be invoked with a maximum number of automatic doubles allowed and that limit is agreed to prior to a game or match commencing. When a player decides to double the opponent, the value is then a double of whatever face value is shown (e.g. if two automatic doubles have occurred putting the cube up to 4, the first in-game double will be for 8 points). The Murphy rule is not an official rule in backgammon and is rarely, if ever, seen in use at officially sanctioned tournaments.
The Jacoby rule, named after Oswald Jacoby, allows gammons and backgammons to count for their respective double and triple values only if the cube has already been offered and accepted. This encourages a player with a large lead to double, possibly ending the game, rather than to play it to conclusion hoping for a gammon or backgammon. The Jacoby rule is widely used in money play but is not used in match play.[5]
The Crawford rule, named after John R. Crawford, is designed to make match play more equitable for the player in the lead. If a player is one point away from winning a match, that player's opponent will always want to double as early as possible in order to catch up. Whether the game is worth one point or two, the trailing player must win to continue the match. To balance the situation, the Crawford rule requires that when a player first reaches a score one point short of winning, neither player may use the doubling cube for the following game, called the Crawford game. After the Crawford game, normal use of the doubling cube resumes. The Crawford rule is routinely used in tournament match play.[5] It is possible for a Crawford game never to occur in a match.
If the Crawford rule is in effect, then another option is the Holland rule, which stipulates that after the Crawford game, a player cannot double until after at least two rolls have been played by each side. It was common in tournament play in the 1980s but is now rarely used.[6]
Some world class and professional players have defined and in some cases discovered certain laws of use of the doubling cube:
Simborg's Law (Phil Simborg) : Put yourself in your opponent's shoes and ask yourself which decision causes the most pain. Would he love to see the cube or hate to see it? Then do what he would least like you to do.
Woolseys Law (Kit Woolsey) : If offering a double and the answer to the is it a take by your opponent question is "I'm not 100% sure", then it is always correct to double.
Hills Law (Simon Hill) : The formula for the value of a gammon is: Your extra percentage match winning chances gained by winning a gammon instead of just winning the game DIVIDED BY Your percentage chances in the match if you win this game minus your percentage chances if you lose this game.
O Hagans Law (John O Hagan) : If you are going to lose your market a net 25% or more of the time then you should offer a double.
Ballard's rule (Nack Ballard) : If you are not going to get gammoned take a cube anyway. The extra point is not so important.
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