Is Scrabble Greedy?

I was killing some time playing Scrabulous, and I started thinking about strategies. I don’t really regard Scrabble as being a particularly strategy based game, but there is a certain element of it to the game – and that strategy can help you win. So this lead me to think:

Is the best strategy to adopt in Scrabble a purely greedy one?

i.e., if at each turn, you play the word which will gain you the most points, do you have more chance of winning than if you were to adopt a different strategy. For example: if I have a Q in my tile set, and the highest score I can make this turn is by playing that with an I (a legal two letter word) – is it better for me to play this and grab some points now rather than hold back the Q and hope that I get some nice letters in the next few moves to make an even higher score?

Intuitively, I would hope there is a nicer solution than a purely greedy approach – but of course one would be difficult to find. As well as this, such a strategy might involve “counting tiles” in order to calculate probabilities.

Were the Greedy solution to be adopted, I think one would have to create a compound value for each playable word – which takes into account certain things. For example, does the word leave the Triple Word Score open to your opponent? Can your opponent append something to your word and gain more points from it (by, for example, extending the word to pass over a Double or Triple score)?

I think this is quite an interesting problem – and one which I shall be thinking about each time I can’t think of a good word to put down in Scrabulous. But I thought I might open it up to the internet in the hope that someone else, more intelligent than I, would find it interesting and propose a solution. Enjoy!

Comments ( 3 )
  • Dan says:

    Griff – did you ever work this out? How does Scrabulous do it?

  • Dan says:

    Also, might you be able to obtain information on the tiles in your opponents hand by the words they DIDN’T play on previous moves, assuming their strategy might mirror your own? Indeed, it’s clear from this that there is no such thing as a predefined perfect strategy (at least not always an “optimal move”) in Scrabble, right?

  • Griff says:

    I haven’t worked it out – it’s not the subject of my third year project. I’m currently thinking about a way of modeling the game using a Max Flow method, whereby the nodes of the graph are legal states of the playing board, and the weights are the number of points you gain by playing that move, or by the number of points you lose by your opponent playing that move. I’ll keep you informed!

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