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Mathematical analysis demonstrates the first picker cannot force a win in alternating-role team drafts, settling Eccles's open problem.
Team captains Alice and Bob divide up footballers, each reduced to a real‐valued score, into two teams of footballers each. On each turn, one captain plays picker , and the other chooser : the picker names a footballer yet to be selected, and the chooser decides which captain's team receives that footballer. Alice starts as picker, Bob as chooser, and the roles alternate. As soon as either captain has a full team of footballers, the other captain receives all remaining footballers, and the team with the larger sum of scores wins. Settling a problem raised by Eccles in 2015, we show that Alice cannot win.
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Bhargav Narayanan (2026) studied this question.
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