Cashing in a single card draw

Question

You draw one card from a standard 52-card deck. The payout: a face card (Jack, Queen, or King) pays \10, an Ace pays \20, and any other card pays \0. What is the fair value of one draw?

Accepted Answer

Count the cards in each tier and weight the payouts. - Face cards: 12 of them (J, Q, K in four suits), each paying \10. - Aces: 4 of them, each paying \20. - Everything else: the remaining 36 cards pay \0. Expected payout: E = \frac{12	imes 10 + 4	imes 20 + 36	imes 0}{52} = \frac{120 + 80}{52} = \frac{200}{52} = \frac{50}{13} \approx 3.85. A fair price for one draw is about \3.85. Takeaway. Expected value is a probability-weighted average of payouts: multiply each outcome's value by how many cards produce it, sum, and divide by the deck size. Tiered payouts are just several such terms adde…

Cashing in a single card draw

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