I got 58% after 100 attempts.

My method uses the fact that the letters a-k + u make up around 49.9% of letters in a normal text. So I just go through a text letter by letter in my mind, giving 0 if the letter is a-k or u, and a 1 if it's l-t or v-z.

For example, the Gettysburg Address:

f - 0

o - 1

u - 0

r - 1

s - 1

c - 0

o - 1

r - 1

e - 0