  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 that 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.
