6

This is one for simulation and some guesses on the strategy to used e.g. is it best to always get the bonus every turn or do the most combinations even if it doesn't use up all the letters every turn.

You don't need to definitively prove your answer is the highest (which is way too hard) just come up with a reasonable answer using a particular strategy

Defining a strategy (such the following) would reduce the computing power needed: Long word: Find all the 8 and 14 letter words that are respectively 1 and 7 letters longer than 7 letter words. Determine what subsets have a long continuous net of those words together. Remove those that use more of the individual letters than the Scrabble set allows. Finally lay the net on the board as a standard one player game and determine the score.

  • This is a very interesting question to me, but I doubt that anyone can currently PROVE what the highest theoretically possible score is. I imagine that there is no definitive answer to this question possible with our current computing power. – James Sep 10 at 11:34
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    It's not technically dependent on the strategy: given sufficient computing power (and time), this can be solved explicitly. – L. Scott Johnson Sep 10 at 11:34
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    All that needs to be done is agree on the dictionary. 😂 – LeppyR64 Sep 10 at 12:04
  • @LeppyR64 That's why all competitive Scrabble is played with a standard word list, which human players do their best to memorize. – user45266 Sep 12 at 18:49
1

This is an open problem that hasn't been resolved yet.

That said, the highest known possible score is in the vicinity of 4000 points. See page 69 of Total Scrabble.

  • That is a great source! There are several high scores based on different word lists, all at about 4000 points. It also gives an upper bound of 5811 points ("Highest Combined Score - With Phonies" - i.e. allowing any combination of letters as a word). – tttppp Sep 16 at 11:54

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