My wife and I like to play a Scrabble variant, “Word Chums,” against each other on our phones. While we’re waiting for each other to take turns, we’ll usually also play computer opponents.
The computer AIs are ranked in four levels of smartness, and basically the major difference is just how much of the dictionary they have access to and whether the app handicaps them. At the highest level they have access to pretty much the whole dictionary and can make any move they want, so unless you’re very lucky in letter selection, you’re boned. The computer routinely plays ridiculous words for gigantic points and before you can blink you’re 200 points behind. The computer always knows all the words; furthermore, it always knows what the highest possible score given a rack of letters is. (I know this because it’s a feature of the game; if you make the highest possible score on your turn, it tells you so.)
I expressed my frustration to my wife the other day about this saying “If the AI knows every word and always know the best play, you can’t possible beat it.” Which insofar as I am concerned is true, I’m good at Scrabble but not great.
But then it got me to thinking;
Is Scrabble a solved game if you know every word and can, in a reasonable time frame, always determine the point-maximizing play?
If not, how far is it from being solved at that point?
As to question 1, I am quite certain the answer is “no.” The point-maximizing play is not always the optimal play because of course sometimes a 26-point play will give your opponent a golden opportunity to grab some bonus tiles off an easy play, where the 20-point play does not.
As to question 2, though, I am pretty sure a computer that simply knows every word and never errs in making the point-maximizing play, while not mathematically playing the perfect game, is so close that no human can defeat it. But maybe I’m wrong and my Google-fu is not working today.
Sorry I think I misunderstood you’re first question.
Scrabble would be solved if from an opening set of tiles the AI could say:
I win, you win or it is a draw.
As you point out, playing the highest value word isn’t always the best move if it allows the opponent to get more points. This gets more complex when you consider what’s called an N-level trap. This is where the best move now leads to a game losing or really bad move after N moves. It is a trap if it is beyond the horizon of what the AI can see. I.e. the AI looks 5 moves ahead but the 6th move is bad. So just knowing the best move now, or the next best set of moves, does not make the game solved.
But as you point a game need not be solved to be nigh unbeatable by even the best of humans.
Scrabble is not in the set of games for which being “solved” is meaningful, because it has an unpredictable random element. The best it’s even theoretically possible to do is to be able to calculate which move has the highest probability of leading to a win. In principle, it would be possible to program a computer to do this, but in practice, it’d probably be a lot harder than solving chess: Whereas a typical chess position has in the neighborhood of 30 moves possible, a typical Scrabble position has literally thousands of moves possible, and that’s even assuming you know which tiles in play (which has a combinatorically-large number of possibilities).
Chronos is right: using the stricter definition of ‘solved’, you can’t do that for Scrabble because there’s random chance, so there’s no possible way to say “This move is guaranteed to win”. Even if you went with a bit looser definition, where you’re OK with accepting “This move is not guaranteed to win, but it is mathematically proven to give the best chance of winning”, it’s still nigh-impossible, because there are too many possibilities every turn. In fact, without actually checking or doing any calculations, I’m fairly confident that the large number of possibilities make it impossible to completely solve using any physical device.
That said, while it’s true that there might be situations where the highest-scoring play isn’t the best one, there’s no inherent reason that you can’t program a computer to look ahead a move or two, so it doesn’t give up a juicy triple word score just to gain five more points. Again, it wouldn’t be perfect, but there’s no reason you couldn’t make it good enough to nearly always beat humans. Computers haven’t mathematically solved chess either, but they can do well enough to beat unassisted humans.
When the computer is analyzing the possible moves it could make, it could also try to predict how many points the opponent can score on his turn. All the starting tiles are known, and you can see which tiles have been played. The computer could analyze what tiles are possibly in the opponent’s rack and modify it’s own play accordingly. Still not “solved”, but a computer could look beyond playing for the maximum score on every turn.
Can any game with a random element be considered solved? You’ll never know what tiles the opponent has in his rack, or what tiles you’ll draw next, but you could calculate the probabilities and make plays that maximize the score differential over your opponent. If the game is not truly solved, is it still possible to play perfectly and give yourself the best possible chance to win (subject to the random factors)?
My Bridge partner is a world class Scrabble player - he has played in the world championships and placed well - and I asked him tonight. He said that a computer would beat him.
When ESPN aired the Scrabble National Championship, it used some sort of software that used a Monte Carlo approach to determine the best move - it would play thousands of games starting with the current board setup, and determine which move resulted in the most game wins. How it determined what each subsequent play was - random, highest-scoring word, or something else - I don’t know.
Quackle gives a valuation of a potential play you might make, which isn’t always the highest scoring word. I assume it marks down words that have “leads” to bonus squares, and it also evaluates what you will have left in your rack. So wasting a blank in the current move when your rack has a great chance of a seven letterer next time gets marked down very badly.