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?)

Except for me, no one has picked up on the use of the term "three of a kind" (rather than, say, "three matching cards") in this puzzle. "Three of a kind" is a very specific poker term. Any Internet search on "poker rules" will quickly confirm this. "Three of a kind" means: "Five cards of which three are matching cards - e.g. three jacks -- with the remaining two cards not being a pair (that would be a full house if it were)."

Therefore the puzzle can be clarified as follows: "...You then shuffle them and begin to draw out cards until you have three that match and two that do not match, as for example 3 jacks, an ace and a queen. What is the most likely number of cards drawn when this happens?"


Edited on November 20, 2003, 5:59 am

Posted by Dan on 2003-11-20 05:56:47