Chopsticks

Chopsticks (sometimes called Calculator, or just Sticks) is a hand game for two or more players, in which players extend a number of fingers from each hand and transfer those scores by taking turns to tap one hand against another. Chopsticks is an example of a combinatorial game, and is solved in the sense that with perfect play, an optimal strategy from any point is known. If you have the same number of fingers on each hand you can strike them together and divide them leaving you with one finger on each hand. When the player only has one finger left it can not be swapped between hands and must attack the opponent. Abbreviation A chopsticks position can be easily abbreviated to a four-digit code [ABCD]. A and B are the hands (in ascending order of fingers) of the player who is about to take their turn. C and D are the hands (in ascending order of fingers) of the player who is not about to take their turn. It is important to notate each player's hands in ascending order, so that a single distinct position isn't accidentally represented by two codes. For example, the code [1032] is not allowed, and should be notated [0123]. Therefore, the starting position is [1111]. The next position must be [1211]. The next position must be either [1212] or [1312]. Treating each position as a 4-digit number, the smallest position is 0000, and the largest position is 4444.