Fake Dice

There are three dices whose faces have different numbers from one another faces. Therefore numbers from 1 to 18 are distributed on the all the faces of three dices.

Well, we prepare the following dices which have the configuration:

Dice A Dice B Dice C

1 2 5

10 3 6

11 4 7

12 15 8

13 16 9

14 17 18

The rule of the game is simple. First, your friend can choose any dice, then roll it. After that, you choose the different one, then roll it. The winner is the person who got larger number.

Dice A	Dice B	Dice C
1	2	5
10	3	6
11	4	7
12	15	8
13	16	9
14	17	18

Actually, the above dices have an intriguing feature as follows. If your friend choose the dice A, you can win by dice B with the probability 7/12. If your friend choose the dice B, you can win by dice C with the probability 7/12. If your friend choose the dice C, you can win by dice A with the probability 25/36.

Therefore, you can always earn the higher probability than your friend.