f(a) = -a log2a
f(1/2) = 0.5
f(1/3) = 0.526
f(2/3) = 0.390
f(1/4) = 0.5
f(2/4) = 0.5
f(3/4) = 0.311
f(1/5) = 0.464
f(2/5) = 0.529
f(3/5) = 0.442
f(4/5) = 0.258
f(1/6) = 0.431
f(2/6) = 0.528
f(3/6) = 0.5
f(4/6) = 0.39
f(5/6) = 0.219