Along the way to developing a Scrabble variant meant to reduce the influence of luck from random tile draws, Andrew Thomas, Visiting Assistant Professor in the Carnegie Mellon University Department of Statistics, has managed to figure out the real value of each of those letter tiles (in Scrabble and the derivative online game, Words with Friends), as well as some other very interesting facts.

Prof. Thomas ran computer simulations of both Scrabble and Words with Friends—more than 4 million times each. According to his analysis, the bag (that is, the randomness of tile draws) accounts for 44 percent of a player’s score variance in Scrabble and 34 percent in Words with Friends. The data also shows that going first in Scrabble is worth 14 points to a player’s final score. In Words with Friends the double-word bonus is eliminated, but the first player still enjoys a 10 point advantage.

One factor in the first player advantage is the letter Q. Even though the point value of Q is relatively high (10), the letter is also more difficult to use and interferes with the possibility of getting a bingo (the seven-letter play worth a 50 point bonus in Scrabble or 35 in Words with Friends). In effect, drawing a Q is worth on average -5 points net to a player’s final score. And the first player to draw has a lesser chance of drawing that Q.

Also with an assigned point value of 10 but at the other end of the net value spectrum, is the letter Z, which is worth about 8 points to a player’s final score (in either game). The letter S is worth a lot more in Scrabble, 10 points versus 7 in Words with Friends, largely because of the difference in bingo bonuses. The opposite is true for the letter J—its net value is 6 points in Words with Friends but almost nothing in Scrabble. Blanks are worth about 32 points in Scrabble and 24 in Words with Friends.

[via IEEE Spectrum]