Of course, the Scrabble Players Association includes a copy of the board on their official scoresheets.
So, it's very easy to play Scrabble against the computer.
The program is so good that the latest edition of Scrabble the computer game is Quackle with a fancy front end.
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Quackle is much nicer in that you don't automagically go first, you just draw a tile normally to see who goes first. It will also analyze your game afterwards (takes a long time though.)
Best of all: NO DRM. No stupid CD needed to play the game.