Question

How many cards do you expect to pull from a poker deck until you get an ACE?

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Nash

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To determine the expected number of cards you need to pull from a poker deck until you get an Ace, we can use the concept of geometric distribution.
In a standard poker deck, there are 4 Aces. Each card draw can be considered a Bernoulli trial with a probability of success (drawing an Ace) of 4/52 (since there are 4 Aces in a deck of 52 cards).
The expected value of a geometric distribution with probability p is given by 1/p. Therefore, the expected number of cards you need to pull until you get an Ace is:
Expected number = 1 / (4/52) = 13.
So, on average, you can expect to pull 13 cards from a poker deck until you get an Ace.

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