You don't just want good words, you want to position yourself so your next move is also a good word. So you don't just have to iterate over the current board, you have to iterate over all possible upcoming boards.
But it's even worse than that! You want to set up your opponent for a bad move, and vice versa, so you're trying to infer each others' tiles from past moves and bluffing starts to matter. So you also have to reason about counterfactual games where your opponent would have done the same thing, meaning you have to care about the entire game tree instead of just the sub-tree you're in...
In the general case, solving games involving partial information requires super-exponential time. It's no picnic. (Of course in practice we use approximations, and those can work quite well.)
Good point regarding setting up for double/triple word scores, however I doubt there is much soul reading or bluffing in scrabble - I think the cost of making a sub-optimal move is too great, you'd need to be very sure that it hurt your opponent even more than yourself.
Also although the remaining letters are known, your selection is random. I don't know how you could possibly choose between words to maximize your next move when you don't know what letters you will get?
> I don't know how you could possibly choose between words to maximize your next move when you don't know what letters you will get?
Your selection is random amongst a determined pool of tiles. You can easily maximize your move even if the move is not 100% deterministic. The fact that there is a random factor does not mean strategy is useless.
This is trivially true in a lot of cases, but sticking with games: The dealer's concealed (hole) card in Blackjack is not known precisely but by counting cards, you can determine the best play even if the effect is small.
But it's even worse than that! You want to set up your opponent for a bad move, and vice versa, so you're trying to infer each others' tiles from past moves and bluffing starts to matter. So you also have to reason about counterfactual games where your opponent would have done the same thing, meaning you have to care about the entire game tree instead of just the sub-tree you're in...
In the general case, solving games involving partial information requires super-exponential time. It's no picnic. (Of course in practice we use approximations, and those can work quite well.)