[T-hawk]

English has roughly 100,000 words, so that password scheme has 10^15 combinations. Suppose the latter scheme incorporates the 96 printable Ascii characters. log96(10^15) is 7.5, so yes the latter scheme gets ahead on entropy at 8 characters or longer.

But it's not a question of maximizing entropy. It's a question of maximizing entropy relative to the human brain's ability to remember it. The brain handles words as single units, so it's a lot easier to remember three of them than eight or more arbitrary characters.

[aiiane]

I go by the xkcd standard of 4 words, though that doesn't change the math, just the numbers.