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 by Lee)

OK, wiseguy...it isn't just pears your house is full of... But seriously, I know that my answer, 5, goes against intuition, but if "3-of-a-kind" is interpreted as a poker hand, as it should be, then when more than 5 cards are drawn, the odds of "2 pairs" overwhelm the odds of a true poker "3-of-a-kind". Btw...since you don't like puzzles that tempt the less ambitious among us to run crying to their programs and spreadsheets, here are 2 excellent puzzles you can try that don't require computers: "If a square has perimeter of length 32 inches, what is the length of one of its sides?" and "What are the fewest steps required to put a bag of M&Ms in alphabetic sequence?" Don't laugh; after that "An Egg-Celent Question" entry, I am half expecting to see puzzles like these on this website... :-)

Edited on November 20, 2003, 12:45 pm

Posted by Dan on 2003-11-20 12:42:53