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Analysis in Scrabble - an O.R. perspective

Some years ago, I wrote a paper on dynamic programming and board games, which looked at a number of references in the O.R. literature to the topic.  One game that I didn't mention, though it had been in my mind while I wrote the paper, is Scrabble.  Each week, a columnist in The Times writes about aspects of the game, and last Saturday (7th September 2019) the problem he studied has aspects of dynamic programming.

In any position of Scrabble, the player has to decide what letters to play from the rack and where, bearing in mind what the other player might do, what letters will be left on the rack, and what letters are in the bag to be chosen.  In terms of dynamic programming, the state space is too large to consider, which is why I steered clear of it in my survey paper.  But the problem in the column is interesting, nonetheless.

Imagine that it is early in the game, so the bag of tiles is almost full.  And your rack has low value letters.  Then your choice is "between scorin…

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