Turn a shuffled deck over one card at a time. On average, how many cards until the first ace?

A shuffled 52-card deck, turned over one card at a time until the first ace. The story asks how many cards you turn on average, counting the ace. You type your answer and check it. Then you step through the answer and the breakdown.

Why quant interviews test this

Interviewers want the gaps argument and the linearity step, not a long sum. The written solution is at /brain-teasers/first-ace/solution.

The Drawing for the First Ace guide covers how scoring works, the strategy that wins, a worked example and the mistakes most players make.

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