A standard deck of 52 cards contains,
inter alia, four Queens.
After a perfect shuffle, one turns cards from the top one after another, until the first Queen appears.
Please provide your justified estimate at what step will the 1st Queen appear.
(In reply to
Excel (spoiler) by Steve Herman)
I like this idea.
I'll start by thinking naively about a single queen. I expect that at the midway point in the deck. But we can also add a "ghost queen" to the "53rd" slot of our 52 card deck. Then we have a queen at the half-way point and the endpoint.
So expanding on that idea with Q queens and an N card deck. (Still adding the ghost queen at the N+1 th position.)
I expect the queens to evenly partition the deck, so I will have a queen at the (N+1)/(Q+1) point, one at 2*(N+1)/(Q+1), one at 3/(Q+1), ... etc, until we get to the ghost queen at the N+1 th position of the N card deck.
Now back to the given problem of four queens in a 52 card deck, then the four (real) queens, using this idea, I expect to occur at 53/5=10.6, 106/5=21.2, 159/5=31.8, and 212/5=42.4. Rounding to whole cards I get my expected positions of the queens to be at the 11th, 21st, 32nd, and 42nd positions.
re: Excel (spoiler)
