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The El Farol Bar problem is treated as an iterated N-person battle of the sexes or leader game for any initial attendance ratio and any value of the bar capacity. It is shown that the bar attendance always fluctuates around the value of the bar capacity. The fluctuations' amplitude is inversely proportional to the total number of the participating agents. Complex Systems, 21doi:10.25088/complexsystems.21.2.153 fatcat:voi2jfcsyjcineyecs6i2ecb7q