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Hi to all i have a very simple problem

Lets assume that i have a well shuffled deck of 52 cards.

I start drawing the top card always and when the card matches it's rank i lose. J=11 Q=12 K=13

If there were only 13 cards i could easily use the $\ \frac{!n}{n!}$ for derangements in order to solve this. The problem is that there are 52 cards so when i pass 13 i start from 1 again so i don't know what is the probability to win. Example of the game

1st card: 4 - Continue 2nd Card: A - continue 3rd Card: K - Continue 4th Card: K - Continue 5th Card: 6 - Continue 6th Card: 9 - Continue 7th Card: 10 - Continue 8th Card: A - Continue 9th Card: J - Continue 10th Card: 3 - Continue 11th Card: 2 - Continue 12th Card: 8 - Continue 13th Card: A - Continue 1st card: 5 - Continue 2nd Card 2 LOSE

So actually i have to count from 1 to 13 4 times and if i draw all 52 cards then i win. What's the Probability?

  • 0
    See also the answers at [this duplicate question](https://math.stackexchange.com/questions/495991).2018-07-31

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