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Two players compete to reach a certain number N of points (for example 100) to win the game by throwing a each roll two regular dice and noting the amount accumulated since their first roll. So, the first player reaching N points wins the game.

Each game starts with a stake of S dollars. A fair coin is tossed to designate the first player.

When a player to roll feels he has a sufficient advantage, he can choose , before he rolls the two dice, to offer to double the stake of the game to 2S dollars. The opposing player can:

-turn down the offer, but concedes the game by doing so and loses S dollars, OR

-accept the offer: then the stake of the game doubles (to 2S). When a player accepts a double, he takes control of the right to (re)double the stake and he is the only player who can make the next offer of a new double (to 4S), etc.

Assuming the player to roll reached s1 points (N-s1 to go to N) and his opponent has s2 (N-s2 to go to N), how to compute if and when:

-he must offer to double (redouble)

-his opponent must accept

  • 2
    Do you just have to exceed the target, or hit it exactly? If we express the answer just in terms of winning probability for each player, it doesn't matter, but if you want to calculate winning probabilities it does.2011-04-29
  • 1
    If you search for "backgammon doubling strategy", there are many pages. Probably some are right. When calculated in terms of winning probability, this is the same except for the possibilities of gammons, which are often ignored at the start of the analysis.2011-04-29
  • 0
    For backgammon a couple of rules-of-thumb can be found at http://www.bkgm.com/glossary.html2011-06-06

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