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In the game of Pitch what are the odds of the jack of trump being dealt in the 24 cards?

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This question almost answers itself. If trumps were chosen randomly, then the answer would be approximately 46%, as it says in the title ($24/52 \simeq 0.46$). However, in reality the trump suit is determined by the first player, and therefore the probability is a function of this player's strategy.

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