A. J. Cole and A. J. T. Davie introduced Euclid game in a 1969 paper. They explicitly designed it to illustrate an algorithm for a winning strategy, making a familiar arithmetic procedure into a problem of combinatorial game theory.[ref]
A Game Based on the Euclidean Algorithm and a Winning Strategy for It by A. J. Cole and A. J. T. Davie. Original byline and introductory extract
The Euclidean algorithm repeatedly subtracts multiples of the smaller integer from the larger. Allowing a player to choose the multiple creates branching choices: termination alone is no longer the main question, because the player also cares who makes the last legal move. The terminal convention must therefore accompany any strategy statement.
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