“Drat…..I just can’t make anything good with these tiles….”
If you haven’t muttered this under your breath a few times, you likely haven’t played Scrabble very much.But are you muttering this because of a mental block or truly bad tiles? Within the vast universe of possible Scrabble racks, what does “good” look like?
The serious Scrabble player would state that the effective value of a hand depends on where you are in the game. The early game favors scrabble racks that “play well with others”, giving you relatively large words with common letters that can easily be patched onto an open board. The end game favors prefixes, suffixes, and small words you can sneak into an open space. Bonus squares and the opportunity to build on large (5 – 7 letter) existing words also boost your score. All of this is true.
But here is a simpler way to approach the question: what if we look at the highest scoring word you can create using just the letters in your rack?
Mathematically, this question became: for a standard Scrabble rack, how many points of words (aka. the expected value) should the average Scrabble rack contain?
Continue reading “What Good Looks Like: The Expected Value of a Scrabble Rack”