Kyle and Stan are playing Odds or Evens, where Kyle is designated as the "odd"player and Stan is designated as the "even"player. They decide to play the game 10 times. At the mixed-strategy equilibrium in this zero-sum game,

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In a zero-sum game like Odds or Evens, the mixed-strategy equilibrium ensures that the expected payoff for each player is zero. This is because the gains of one player are exactly offset by the losses of the other, and when players randomize their strategies perfectly at equilibrium, neither player has an advantage, leading to an expected payoff of zero for both.

Kyle and Stan Are Playing Odds or Evens, Where Kyle