We study operators that combine combinatorial games. This field was initiatedby Sprague-Grundy (1930s), Milnor (1950s) and Berlekamp-Conway-Guy (1970-80s)via the now classical disjunctive sum operator on (abstract) games. The newclass consists in operators for rulesets, dubbed the switch-operators. Theordered pair of rulesets (R 1 , R 2) is compatible if, given any position in R1 , there is a description of how to move in R 2. Given compatible (R 1 , R 2),we build the push-the-button game R 1 R 2 , where players start by playingaccording to the rules R 1 , but at some point during play, one of the playersmust switch the rules to R 2 , by pushing the button ". Thus, the game endsaccording to the terminal condition of ruleset R 2. We study the pairwisecombinations of the classical rulesets Nim, Wythoff and Euclid. In addition, weprove that standard periodicity results for Subtraction games transfer to thissetting, and we give partial results for a variation of Domineering, where R 1is the game where the players put the domino tiles horizontally and R 2 thegame where they play vertically (thus generalizing the octal game 0.07).
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