As exact powers of 2 in the denominator have zero probability we can ignore equality in these inequalities:
log_{2}
r > 1/2 ; 1/r < 2 even
1/2 < r < 1/4 ; 2 < 1/r < 4 odd span 1/4
1/4 < r < 1/8 ; 4 < 1/r < 8 even
1/8 < r < 1/16; 8 < 1/r < 16 odd span 1/16
1/16 < r < 1/32; 16 < 1/r < 32 even
1/32 < r < 1/64; 32 < 1/r < 64 odd span 1/64
...
p = 1/4 + 1/16 + 1/64 + ...
4p = 1 + p
3p = 1
**p = 1/3**, the desired probability |