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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)

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Comments on poker hand solutions | Comment 33 of 39 |
(In reply to by )

The only justification for rejecting the maximum count of 27 is that it results in a full house; and a full house beats three of a kind(3oK). The two pair can be ignored because 3oK beats two pair. I agree that a count of five is the lowest count that can produce 3oK but disagree on 14 being the maximum. Consider drawing the cards 2 thru king and three aces, thats 15 by my count. Also consider that a straight beats 3oK thus run lengths can be a maximum of 4. As an example 2-5, 7-10, QK, and three aces for a count of 13. Flushes can be ignored - well yes the first 5 cards can be the same suit - when considering ranges since we cannot guarantee a flush with fewer than 14 cards.

Overall I'm not a big fan of the poker hand requirement and am studying the wording in the hope of finding inspiration.
  Posted by Lorne Hrynkiw on 2003-11-21 05:40:13

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