When each player has only one hand (formula_7), the game becomes degenerate, because splits cannot occur and each player only has one move. Given a roll-over of formula_2 each position after formula_9 moves in the game can be represented by the tuple formula_10, where formula_11 is the formula_9-th Fibonacci number with formula_13 and formula_14. The number of positions is given by least positive number formula_9 such that formula_2 divides formula_17. This variant is strongly solved as a win for either side depending upon formula_2 and the divisibility properties of Fibonacci numbers. The length of the game is formula_19.