We modify Wythoff's game by allowing an additional move, which we call a split, and show how the P -positions are coded by the Tribonacci word. We analyze the table of letter positions of arbitrary k-bonacci words and find a mex-rule that generates the Quadribonacci table.In an impartial game, the set of all positions is divided into those that are winning and those that are losing for the player that moves next. To play a game optimally, one needs to know the subset P of all losing positions. The hardness of solving an impartial game therefore depends on the complexity of P, and so one runs into set theory. Substitution sets are easy to describe and have a well-developed theory [25]. Eric Duchêne, Michel Rigo, and others, are building a framework that connects impartial games to substitutions, [11,12,13,14]. A basic example is the Fibonacci substitution 0 → 01, 1 → 0 which leads to the infinite sequence 010010100100101 • • • . If we take this to be the indicator function of a subset of N, then we find the losing positions P of Wythoff Nim. Duchêne and Rigo found other impartial games that can be described by other substitutions [12,13]. They asked in [12] if it is possible to devise an impartial game that can be described by the k-bonacci substitution. This was the motivating question for our paper.We were able to find a simple extension of Wythoff Nim that can be described by the 3-bonacci substitution. We were also able to find a mexrelation to generate the table of the 4-bonacci substitution, but we were not able to derive an impartial game from this. Our game, which we call Splythoff Nim, is closely related to the Greedy Queen on a Spiral Game, which was recently solved by Dekking, Shallit and Sloane [9]. Splythoff Nim and Greedy Queen have the same P -positions but different Sprague-Grundy values.Our paper is organized as follows. We first recall Wythoff Nim and the games and number tables that arose out of it. Then we introduce Splythoff Nim, which we solve by an analysis of number tables that come out of the k-bonacci substitution. Finally, we present some numerical evidence that indicates that a-Splythoff, which is the corresponding modification of a-Wythoff, can be coded by a substitution if a = 2 or 3.