Belief: If I chose a very guessable brain wallet eg:"bitcoin123" I will probably lose my coins by the end of the day because algo's are regularly testing for simple brain wallets. They do this by trying simple phrases and getting the public key from those simple phrases, and then using a blockchain explorer look fora positive balance. And then spending those coins. True?
Brain wallets are generally very easy to steal from.
A brain wallet of "bitcoin123 would probably not even be allowed by most websites/software that allows you to create brainwallets. If you were able to create a brain wallet with this password then the coins would likely be stolen before you can even check to see if the transaction was propagated throughout the network.
The best advise for brain wallets is to use something that is not found in any piece of literature (including movie scripts, songs, plays) that is in any language. At the very minimum a brain wallet should be at least 12 words that are in somewhat of a random order.
If you would like to see how quickly funds in a brainwallet can be stolen then checkout the following address: 1JwSSubhmg6iPtRjtyqhUYYH7bZg3Lfy1T