Consider the four “unfolded” dice in Figure 3.9 designed by Stanford professor Bradley Effron. Clearly, none of these dice is an ordinary die with sides numbered 1 through 6. A game consists of two...

Consider the four “unfolded” dice in Figure 3.9 designed by Stanford professor Bradley Effron. Clearly, none of these dice is an ordinary die with sides numbered 1 through 6. A game consists of two players each choosing one of these four dice and rolling it. The player rolling a larger number is the winner. Show that if all four dice are fair, it is twice as likely for die A to beat die B, twice as likely for die B to beat die C, twice as likely for die C to beat D, and surprisingly, it is twice as likely for die D to beat die A.