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A proposes a double B declines 1-0 B accepts, A wins 2-0 B accepts, B wins 0-2 B accepts, draw 0-2 B accepts and redoubles, A wins 4-0 B accepts and redoubles, B wins 0-4 B accepts and redoubles, draw 2-2
Apologies if something like this has been suggested: logik but with a backgammon doubling cube.
Players play to a certain number of points - a point a game. Either player (say player A) has the option of doubling before a move. If accepted points are doubled, but player B also wins the points if it's a draw. If player B accepts (and is confident!) he can immediately redouble but in this case points are shared if it's a draw