First-movers in a specific team-picking game have no advantage and cannot force a win regardless of their strategy.
Game theory reveals that the picker-chooser method of dividing players completely neutralizes the power of going first. In most competitive scenarios, the person who moves first can dictate the outcome or claim the best resources. This mathematical model shows that alternating roles between two players creates a perfectly fair division of talent. Even if one person is a master strategist, they cannot overcome the structural balance of the game. It provides a blueprint for fair division in everything from sports to corporate asset allocation.
How to pick your football team
arXiv · 2605.04034
Team captains Alice and Bob divide up $2m$ footballers, each reduced to a real-valued score, into two teams of $m$ 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 roles alternate. The game ends as soon as either captain has a full team of $m$ footballers, at which point the other team receives all rem