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I found the Master Password app which uses a password generation algorithm to generate a different password for each site based on the sites name, the users name and a master password. It seems like a good idea to keep a different password in each site without the hassle to keep a password file synced.
However, I have the feeling that, security wise, this strategy has some drawbacks compared to password manager. Particularly it seems to me that each password is the same behind the scenes. Specifically, it seems that the only secret behind each password is the master key making each password effectively the same. Furthermore, it seems that the only way of changing one password (suppose one site is compromised) is changing the master key which, in turns, changes all the other passwords (again, it seems like there is only one real password).
My question is, how secure is this strategy compared to a password manager? Specifically, is this a good strategy in practice to store my passwords compared to a password manager? Is my intuition right and there is effectively only one password?