MathDB

The game of backgammon has a "doubling" cube, which is like a standard 6-faced die except that its faces are inscribed with the numbers 2, 4, 8, 16, 32, and 64, respectively. After rolling the doubling cube four times at random, we let

a

be the value of the first roll,

b

be the value of the second roll,

c

be the value of the third roll, and

d

be the value of the fourth roll. What is the probability that

\frac{a + b}{c + d}

is the average of

\frac{a}{c}

and

\frac{b}{d}

Problem Statement