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Greedy Galois Games

Joshua Cooper and Aaron Dutle
The American Mathematical Monthly
Vol. 120, No. 5 (May 2013), pp. 441-451
DOI: 10.4169/amer.math.monthly.120.05.441
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Page Count: 11
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Greedy Galois Games
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Abstract We show that two duelers with similar, lousy shooting skills (a.k.a. Galois duelers) will choose to take turns firing in accordance with the famous Thue–Morse sequence if they greedily demand their chances to fire as soon as the other’s a priori probability of winning exceeds their own. This contrasts with a result from the approximation theory of complex functions, which says what more patient duelers would do, if they really cared about being as fair as possible. We note a consequent interpretation of the Thue–Morse sequence in terms of certain expansions in fractional bases close to, but greater than, 1.

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