Film, Media & TV32 mins ago
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Hi everyone, I don't check in every day so this is a bit late.
Hammond Egg, I'm sure your'e right. I can't type a sentence right first time, let alone enter a long calculation.
Johnalex, i) 1/73 x 1/72 x... = 66!/73!
ii) 14 seconds + shuffling time, when it happens.
When does it happen? You can't say. The best you could do is to work how many draws gave a 50% chance of drawing the same 7 cards in two successive hands. To do this you have to calculate the chance of not getting two consecutive matches. For n draws the chance of not getting this is (72/73)^(n-1) [If n = 1 you've only drawn once and have nothing to match with]
The larger n gets the smaller the chance becomes until you eventually get below 0.5, giving a better-than-50% chance of two draws the same. I'll leave someone else to work it out.
If you want your last draw to match only your first draw the odds remain the same.
If you want your last draw to match any previous draw the chances of it not happening are (72/73 x 2x72/73 x 3x72/73�(n-1)72/73) = ((n-1)! )(72/73)^(n-1)