That's like saying you can enumrate the real numbers by starting with the first decimal digit and building a tree with 10 children per node off into infinity. I'm quite sure I can find a unique game of scrabble for every real number. And the decision tree is trivial. Both players exchange 7 every turn. One decision. It's what's on the rack that makes it different.
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
