ARTHUR, Bill and Doug were playing with an ordinary standard pack of 52 cards, with no Joker. Doug shuffled the pack thoroughly and dealt Arthur and Bill one card each.
The rule was that if both cards of any deal were red, Arthur would be the winner and would add his own and Bill鈥檚 card to his winner鈥檚 pile; and if both cards were black, Bill would add both cards to his pile. If the cards were of different colours, regardless of who was dealt them, they would be discarded to a 鈥渄ead鈥� pile, and would not be used again.
Doug continued dealing until he had no cards left. He then collected up Arthur鈥檚 and Bill鈥檚 winner鈥檚 piles, shuffled them thoroughly, and repeated the whole process, until again he had no cards left.
Advertisement
What is the probability that Arthur鈥檚 pile, at the end of the second round, had more cards than Bill鈥檚? Express as a decimal (for example, 0.33 for 1 chance in 3).
A 拢10 book token will be awarded to the sender of the first correct answer opened on Thursday 11 July. The Editor鈥檚 decision is final. Please send entries to Enigma 878, New 杏吧原创, King鈥檚 Reach Tower, Stamford Street, London SE99 0BB. The winner of Enigma 872 was Mike Rudin of Milton, Cambridge.
Answer to Enigma 872
All move around
1, No; 2, No; 3, Yes; 4, No.