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Three of a Kind (Posted on 2003-11-19) Difficulty: 4 of 5
You have a standard pack of 52 playing cards. You then shuffle them and begin to draw out cards until you have three of a kind. What is the most likely number of cards drawn when this happens?

You then shuffle another pack of 52 playing cards into the pile. What happens to the expected number of cards now? (i.e. does it double / halve / stay the same?)

No Solution Yet Submitted by Lewis    
Rating: 4.3333 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): | Comment 18 of 39 |
(In reply to re: by Dan)

As soon as 4 cards are drawn (and making 2 pairs possible) the
"the odds of "2 pairs" overwhelm the odds of a true poker "3-of-a-kind".
This is a facet of two pairs always being easier to make
Sometimes problems get posted that the poster doesn't know the solution to - or knows a way of doing it (using computers) but finds the problem of potential interest to others. I'd love to see the problem solved in a "Wow, that's a neat way of thinking" kinda way but if it isn't my nose retains all its epidermis. Sometimes a computer assisted answer generates interest or pointers to 'solve' the puzzle without one - and this can only be a good thing.

  Posted by Lee on 2003-11-20 13:42:26

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