463.Beat the Dealer's Card
★★★classical probabilityCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
You and the dealer are each dealt one card from a shuffled standard 52-card deck. You win only if your card's rank is strictly higher than the dealer's; ties and lower ranks lose. What is the probability you win?
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By symmetry you and the dealer are equally likely to hold the higher card — so first find the probability of a tie.
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