Sitting on my [AT's] to-do list for a while now has been an exploration of Scrabble from an experimental design point of view; how to better design a tournament to make the variance as small as possible while still preserving the appearance of the home game to its players. . . .
I’m proud (relieved?) to say that I’ve finally finished the first draft of this work for two-player head-to-head games, with a duplication method that ensures that if the game were repeated, each player would receive tiles from the reserve in the same sequence: think of the tiles being laid out in order (but unseen to the players), so that one player draws from the front and the other draws from the back. . . .
One goal of this was to figure out how much of the variance in score comes from the tile order and how much comes from the board, given that a tile order would be expected. It turns out to be about half-bag, half-board . . .
Some other findings from the simulations:
- The blank is worth about 30 points to a good player, each S about 10.
- The Q is a burden to whichever player receives it, effectively serving as a 5 point penalty for having to deal with it due to its effect in reducing bingo opportunities, needing either a U or a blank for a chance at a bingo and a 50-point bonus.
- The J is essentially neutral pointwise.
- The X and the Z are each worth about 3-5 extra points to the player who receives them. Their difficulty in playing in bingoes is mitigated by their usefulness in other short words.
I [AT] have yet to make any other conclusions about how I think the game should be modified . . .