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?)

(In reply to re: I think I've got it. (No computer program used). by SilverKnight)

Dear SilverKnight:

I stand by my analysis, sir.

(1) The Merriam Webster online dictionary contains the following two entries: "three of a kind" - "three cards of the same rank in one hand; see POKER"; and "full house" - a poker hand containing three of a kind and a pair — see POKER". Any casual poker player instantly recognizes the term "three of a kind" and understands it in that sense - a five card poker hand (3 matching cards, 2 unmatching), different from a full house( 3 matching cards, 2 matching cards".
(2) In your example, the following cards are drawn: Ace Ace 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 Jack Jack Queen Queen King King. After the first four cards in this sequence are drawn, it is no longer possible to draw a "3 of a kind" in the poker sense. As soon as you draw another Ace, you now have 3 Aces and two 2's, since the 3rd and 4rth cards drawn were 2's -- you have a full house, not "3 of a kind".


:-)
Edited on November 20, 2003, 12:16 pm

Posted by Dan on 2003-11-20 12:10:43