Eugene Deon wrote: > The number of valid games of Scrabble is uncountably infinite. For any > real number, I can find a unique, valid scrabble game by mapping 7 digit > chunks of it's decimal representation to the alternating racks of both > players as they both change 7 an infinite number of times. I won't > waste people's time with the details. Someone asked for the complexity > of scrabble. It's at least infinite (not just "approaching infinity"), > and I would argue that it's uncountably infinite, since an infinite > number of change 7s (while unplayable in practice) is not invalidated by > any rulebook statement that I have read.
Even allowing a game with an unbounded number of consecutive exchanges, it's still countably infinite, because you can enumerate not just all the games, but all the infinite moves in these possibly-infinitely-long games by a breadth-first scan of the decision tree starting with turn one. Now, if you want to figure in the length of time taken for each move, you're getting somewhere, maybe, until you run into the quantization of time (the nature of which has not yet been plausibly postulated to date). --gvc
