The rule was that if both cards of any deal were red, Arthur would be the winner and would add his own and Bill’s card to his winner’s 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 “dead” pile, and would not be used again.

Doug continued dealing until he had no cards left. He then collected up Arthur’s and Bill’s winner’s piles, shuffled them thoroughly, and repeated the whole process, until again he had no cards left.

What is the probability that Arthur’s pile, at the end of the second round, had more cards than Bill’s? Express as a decimal (for example, 0.33 for 1 chance in 3).

A ÂŁ10 book token will be awarded to the sender of the first correct answer opened on Thursday 11 July. The Editor’s decision is final. Please send entries to Enigma 878, New ĐÓ°ÉÔ­´´, King’s 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.

If you add together consecutive pairs of the digits of an ENIGMA (E+N,
N+I, I+G, and so on), the results will be WRONG (if they are
right!).

In the words and letters in capitals above, different letters as usual
represent different digits. The same letter always represents the same
digit.

Send in NOW.

A ÂŁ10 book token will be awarded to the sender of the first correct
answer opened on Thursday, 8 December. The Editor’s decision is final. Please
send entries to Enigma 796, New ĐÓ°ÉÔ­´´, King’s Reach Tower, Stamford
Street, London SE99 0BB. The winner of Enigma 791 was Iain Bozier of Luton,
Beds.

Answer to Enigma 791

Magic hexagon