Not sure about the lotteries you play, but I think the chances are even worse.
I wasnt trying to hint at collision, but rather at "be carefull you take proper randomness" since so many "brain wallets" get "hacked". Probably could have been more clear there.
On the other hand 16 random(!) words might be easier to remember for you than a 20 char random(!) password.
Probably is - was simply using it to emphasise the improbability of an actual collision.
I think I misinterpreted, I thought you were referring to randomly reproducing a private key that would enables coins to be spent from the same address as one already in use. Brain wallets are most certainly not advisable - they are a good theoretical idea but humans are incapable of randomness. Any text from any book/movie is pretty much bruteforced and the coins stolen (there was a guy who chose a few lines from an obscure poem who lost some coins IIRC).
I would think a password of equivalent length to a brain wallet would be more secure as unlike brain wallets where they can generate the combinations offline without havin gto have your wallet - the password you use is individual to your wallet and hence they would need your wallet and then bruteforce it making it far less viable than simply going through a dictionary list.