Scrabble Board Density Index

Putting down a few letters in little gaps to make several words at a time may or may not optimise your score for a given turn, but it is a tactic which makes the next person's turn more difficult; the board of a competitively played scrabble game can start to look as if a tightly twisted rope of words is being stretched out along one of the diagonals, with lots of inaccessible empty space to either side.

The relevant amount of empty space in this case is not the difference between the number of square on the board and the number of pieces played; that will always be about the same by the time the game is over. Rather, it is the amount of *contiguous* empty space in which no letters have been played and to which no letters are even adjacent which bespeaks the tight game.

Where the game is computerised, that number can be updated in real time, maybe divided by the number of turns played and then compared with historical data for other games. Elsewhere, a reasonable proxy might be the diagonal length of the largest square of board where no letter has been placed, or maybe the area of the largest rectangle, or perhaps the largest right- angle triangle of which this is true.

Statistics like these would be a great help to anyone calling the plays over the radio to a rapt audience of the kind of people who would listen to a game of scrabble being played on the radio.