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We define an all-small ruleset, Bipass, within the framework of normal-playcombinatorial games. A game is played on finite strips of black and whitestones. Stones of different colors are swapped provided they do not bypass oneof their own kind. We find a surjective function from the strips to integeratomic weights (Berlekamp, Conway and Guy 1982) that measures the number ofunits in all-small games. This result provides explicit winning strategies formany games, and in cases where it does not, it gives narrow bounds for thecanonical form game values. We prove that the game value *2 does not appear asa disjunctive sum of Bipass. Moreover, we find game values for someparametrized families of games, including an infinite number of strips of value*.

Atomic weights and the combinatorial game of Bipass