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Tricky probability puzzle

Posted By: Timothy Chow
Date: Saturday, 28 October 2023, at 4:17 a.m.

Though strictly speaking they're off-topic, some math/logic puzzles proved to be quite popular here on BGO in the old days. Here's an entertaining one that I saw on the YouTube channel, Mind Your Decisions.

There's a machine that is supposed to deal you a single random card from a standard deck of 52 cards. It begins by thoroughly shuffling the whole deck. Let's assume that this part of the procedure is executed perfectly, so that every possible ordering of the 52 cards is equally likely. But then, instead of doing the obvious thing (dealing you the first card from the deck), the machine scans through the deck one card at a time from the top, stopping when it finds the first ace. Then it deals you the card immediately after the first ace.

Does this strange procedure introduce a subtle bias? Or is every card equally likely to be dealt to you?

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