Nine cards, numbered from 1 to 9 inclusive are divided between three players as follows:  Ali gets cards 1, 6 and 8; Bobbie gets cards 3, 5, 7 and Cal gets cards 2, 4, 9.

a)  Ali and Bobbie play a game: each player picks a card at random from their set of three; the winner is the player with the higher card. Show that Ali wins with probability 5/9.

Show also that when Bobbie plays the game with Cal, Bobbie is more likely to win, but that when Cal plays the game with Ali, Cal is more likely to win.

b)  Sixteen cards, one showing each of the numbers 1 to 16 inclusive, are divided between Ali, Bobbie, Cal and a fourth player, Deniz. Find a way of dividing up the cards so that:

•     when Ali plays Bobbie, Ali is more likely to win;
•     when Bobbie plays Cal, Bobbie is more likely to win;
•     when Cal plays Deniz, Cal is more likely to win;
•     when Deniz plays Ali, Deniz is more likely to win.

Are there different ways of doing this? If so, what are they?