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Not all achievements add to the player's gamerscore. Some achievements are worth zero points, and are usually awarded for failing in a game repeatedly or spectacularly. Developers may add them as a tongue-in-cheek way to permanently memorialize poor or unlucky play, as achievements cannot be removed from a gamertag.
For example, in Dead or Alive 4, there are several zero point achievements for losing 5, 10 and 20 consecutive online matches, as well as having your online ranking drop to grade D or E.
Not all zero point achievements are signs of failure. In Kameo: Elements of Power, a later update to the game added online co-op; achieving 'A' Rank in cooperative mode on the various levels would unlock zero point achievements, as would beating individual levels on the new 'Expert' Mode, or achieve 'A' Rank in Time Attack mode; point worthy achievements all. This update took place before Microsoft allowed developers to add an additional 250 points worth of achievements through downloadable content.
Retail games do not have a monopoly on zero point achievements, as notably seen in Marathon: Durandal with the online viral achievement 'World Domination'.
Zero point achievements make it possible for a player to have 100% achievement point completion in a given game (1000/1000), while simultaneously not having 100% of the achievements in the game.