Cooperative Scrabble, a very popular unofficial variant (it is also mentioned on Wikipedia), is played on a normal Scrabble board with letter tiles. The main differences are that all players' tiles can be seen by everyone else (they can be laid down, for instance), and that the objective of the game is to accumulate the highest total score possible. The randomizing element is provided by the fact that, as usual, letter tiles are drawn randomly.
The main dynamic of the game switches from individual scoring to trying to ensure board positions which, given other people's tiles, permit maximum scoring. There's no doubt that Cooperative Scrabble is more complex in that regard, as players always have to consider the entire board.
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