We present a class of two-player Wythoff game variations we dub Wyt(f) that depends on a given function f(k). In this class a move consists of removing either a positive number of tokens from precisely one of two given piles, or k tokens from one pile and ! from the other, subject to the constraint 0 < k ≤ ! < f(k). We analyze three classes of integer-valued functions f(k): constant, superadditive and polynomial of degree > 1 with nonnegative integer coefficients. The nature of the winning positions in the games is essentially unique for each class.
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