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