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Quarter Placement Game

Medium · Market Microstructure · Quant Trader interview question · game-theory, strategy, symmetry, market-microstructure

Two players take turns placing identical quarters on a circular table. The quarters must lie completely on the table and cannot overlap. The last player who successfully places a quarter wins. What is the optimal strategy for Player 1, and what is the guaranteed outcome if both players play optimally, assuming the table is large enough to hold at least one quarter?