25 Oct, 2022

Bettering Butts: Tiles tallied for fluid fun

When Alfred Mosher Butts invented his classic crossword game in 1938, originally called Lexico, he had no computer at hand to calculate the optimal score or number for each English letter. Instead, Mr. Butts chose to count the letters on the front page of the New York Times by hand in order to establish the foundation for the points system in the game that became Scrabble®. He also chose a nice round number of 100 tiles in the bag, and 187 as the total number of points for all tiles.

These fundamentals of the game have not changed since then. Although many programs have been developed to assist players in creating words, holding tournaments and calculating odds, no one has really dared to suggest an update of the original game’s tile bag. But word games are not like the Ten Commandments, and a Moses of our times would undoubtedly explore his options and come back from the mountain with an updated bag.

A modern Alfred Butts, glued to his computer, would create his wordgame with the help of a software simulator and optimizer where the goal would be to make all letters stay in the rack for approximately the same number of turns, on average. And that´s what we did, trying various distributions of the letters and points; tweaking here and there to find the best solution.

After simulating over 100,000 games in the computer we believe we have a more fluid and more fun game. In short: A modern version of an old standard. We still have 100 tiles with 187 points total and two blanks. 56 consonants, 42 wovels. The basic idea is the same. We have just updated the count of each letter and their points.

What’s changed?

The S´s are now 9 in total instead of 4, reflecting the frequency of the letter in English and doubling the chances of pluralizing a noun on the board. X and Z have been demoted, and rightly so, but the always-difficult Q is now at 12 points, deserving all of them!

There are other subtle changes. The table below shows the new distribution of points and letters. The letter counts are on the horizontal axis, and the points on the vertical axis.

x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12
0 [b]
1 I O S A E
2 H P Y M D T U L N R
3 F K B C G
4 W
5 V X
6 J Z
12 Q

After relentless calculations and explorations, we have an optimized and modernized game: fluid, not too easy but not too difficult. What has not changed is that we are still laying down words on the board to have fun, rack our brains and stretch our imagination. Just as Alfred intended over 80 years ago.

Tile bag
Green figure