What are the odds?

[sherrardk]

Didn't know where to put this but here goes. My husband taught my 5 and 6 year olds to play clock patience/solitaire yesterday (where you have to get all the cards out before you get 4 kings). The 5 year old completed it on the second turn and the 6 year old on the first turn - they were using different packs of cards which had been thoroughly shuffled (bu being dropped on the floor and picked up again and well as the more traditional method). As there is no skill involved there must be a way to work out the odds of this happening (I don't particularly want to know how to work it out - just what the odds were of this happening). Thanks.

[Buenchico]

The probability of 'winning' a single game is 1/13:
http://orion.math.ias...litaire_solution.html

The probability of winning two out of three games is therefore 1/13 x 1/13 x 12/13 x 3. (The 3 occurs because there are three ways of doing it, i.e. Win-Win-Lose, Win-Lose-Win or Lose-Win-Win)

So that's 36/2197 or roughly "1 in 61".

Chris