What’s the highest possible score in a game of Scrabble?

Kevin and I had a little discussion over the Safety Words show at the Firebird last night about the wordsmith elitist board game.

Basic internet research draws forth the following results:

1) Here’s the World Record for the highest-scoring Scrabble game to occur, with 1,320 points on the board (yes, apparently, they have world records for silly junk like this).  But that’s nothing…

2) One site points out that you can feasibly, yet in the most unlikely of scenarios, score 1,962 points – not in a game, but in a single turn.  Poor Guy-Who-Played-Jinneyricksaw.  I bet he thought he had the game wrapped up.

A much more difficult question, however, is the maximum number of points possible over the course of an entire game.  Given the structure put forth by the rules of the game (limited set of letters, limited set of board space, limited permutations of letters as per the Scrabble dictionary), I propose that a maximum is possible.  Calculations become tricky when considering that adding a single letter to the end of a word constitutes an entirely new word score (such as turning Jinneyricksaw into Jinneyricksaws, in our last example).  I’d envision, therefore, that the final board would ultimately look like a giant square of uniform Scrabble letters, whereby each word played would not only result in a bingo, but create seven new words in the perpendicular direction.

The simple approach:

1. A scrabble board has 100 pieces, with an average piece score of 1.87
2. The center row (turn 1) has a double and triple word score. Working along the right edge, each row besides the two above and two below (turns 2,3,4,5) has a double word score.  The top and bottom rows (turns 14 and 15*) each have two triple word scores. I’d die if I tried to include letter multipliers too.
3. Players will take turns playing bingos horizontally, while collecting parallel words.  The game lasts 15 turns (14 plays of 7 tiles plus one play of 2 tiles).
4. Final score: 1949.81.  Which isn’t even as good as the single-word score earlier.  Although it doesn’t consider that turn 15 (which should be on the 9x multiplier) is only two letters long, or that there are letter multipliers, or that words with higher letter scores should be saved for those 9x’s.

The difficult approach: Players start by playing two-tile words, building an even square, and rather than collecting the greatest number of bingos possible, collecting the greatest number of parallels possible.  The center letter alone (hopefully a Q or Z!) becomes part of 29 distinct words vertically and horizontally, and will ultimately count for 480 points alone (counting for the initial double-word score and the two 9x board-length words created along both axis.  Knowing this to be the most valuable letter, and assuming this to be the most valuable piece of Scrabble real estate, we can come up with a theoretical maximum of possible points at 48,000 points (480*100).

But we know that not every letter sits across the double-triple word scores, and not every letter counts for 10 points.  So a more realistic estimate might be that each letter will become a part of 29 distinct words (which is inaccurate, but might roughly cancel out the effect of not considering word- and letter- bonuses), and that given the board with sixty-eight 1-point tiles, seven 2-point tiles, eight 3-point tiles, ten 4-point tiles, one 5-point tile, two 8-point tiles, and two 10-point tiles, the maximum possible score in any game of Scrabble is approximately 5,423.

Thoughts? Evidence to prove me wrong? Amazed at how silly this is? Let me know.