1

Suppose you're playing (classical, not duplicate) Scrabble and it's your turn. My question is:

What would be a good general defintion of a best move for you?

The definition could be of a theoretical interest only, but I'd prefer a definition which could be translated (at least partially) in program code in order to generate automatically the list of your best moves.

Some constraints of objectivity

It might be argued that the concept of best move is a subjective one. In effect, when choosing your move, you might take these factors into consideration:

  • Your opponent last moves, in order to evaluate the probability that he has certain letters in his current rack. Note that in general, you can't know for sure what his letters are, except if there's no letters remaining in the bag.
  • Your opponent strength. Note that in general, you can't know for sure if your opponent will know particular words or if he will see particular variations.
  • Your opponent style (open or close).
  • Your opponent psyche. This is what you exploit when you bluff.

The three last factors apply only if you play against a human. Indeed, a program would theoretically be of the greatest strength and it would only care about playing a good objective move.

I think that it is reasonable, therefore, to distinguish between two types of best moves: subjective ones and objective ones. My question asks for a definition of the objective one, since it is the one which can be used . In other words, we must not

closed as too broad by Drunk Cynic, Michael Snook, Philip Kendall, tsuma534, JonTheMon Oct 28 '16 at 12:53

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • "In other words, we must not".... editing failure :-) – Philip Kendall Oct 26 '16 at 22:14
  • 1
    Is @Amateur the same person as OP? 'cause that's quite an edit they're suggesting... – Benjamin Cosman Oct 26 '16 at 22:22
  • 1
    @Amateur you should use the "contact us" link at the bottom to request that your user profiles be merged. – murgatroid99 Oct 26 '16 at 23:16
  • 1
    Also, after reading your proposed edit in full, I'm not actually sure what your question is. You say that you are asking for a good general definition of a best move, but you later say "Intuitively, a best move should give you the biggest probability of winning the game". This looks like a perfectly valid and good answer to the question, and if that's not what you're looking for, than what is? – murgatroid99 Oct 26 '16 at 23:37
  • 1
    If you're really serious about this, you'd want to consider using machine learning to derive that notion of the quality of a move, rather than creating heuristics manually. Look for "value network" and "policy network", or look for things about AlphaGo. (You can use those ideas even without being on the same scale as AlphaGo.) – Cascabel Oct 27 '16 at 22:25
5

Any move in Scrabble has a few effects on the game:

  • It earns you points.
  • Unplayed tiles remain on your rack.
  • You draw new tiles (usually).
  • The board changes, which can make scoring easier or harder.

This suggests that the best move is one that can maximize as many of these (sometimes conflicting) aspects:

  • It scores a bunch of points.
  • It leaves you with complementary tiles for future points, especially having a good vowel-consonant balance. It often pays to forego a few points this turn for a good opportunity at a bingo the next turn.
  • It lets you draw many tiles. This means more opportunities for getting "lucky" with high point tiles (JXQZ) or super useful blanks.
  • It shapes the board in a way favorable to your current gameplan. The best advice I've heard is to open the board up when behind (for more opportunities to catch up) and to close the board down if you're ahead (for just the opposite reason).

You won't always have an obvious best choice, but the more bullet points you can achieve the better. Bingos are especially important because they score a bunch of points and give you more chances of drawing important tiles.

2

I hope I understand the question enough.

You could say, the best move is the one that gives you the most points. But that only looks at the current move, not the entire game. If your best moves gives you X points, but it enables another player to get X + Z points the overall effect of the move is negative.

Unfortunately, you don't know the hand of the other players. So you need to use some judgement. If you can choose between two moves, and one of these has a high likelyhood that another player plays an even better move, you probably better use the next one.

So you should play a move that:

  • give you a decent amount of points.
  • minimizes the obvious connections for other players.
  • exploits obvious connections (so other players can't use that).
  • preferably one that includes a lot of hard tiles.

Not the answer you're looking for? Browse other questions tagged or ask your own question.