Probability, Scrabble, and Star Trek

When I study words for Scrabble, one focus of study is bingoes; 7 and 8 letter words that can gain a 50 point bonus for using all seven of your letters in one turn. There are over 25,000 valid 7-letter words and 31,000 valid 8-letter words. So where to start? There are several clever methods, but they are all based on probability. Since there are 12 E’s in the bag but only one K, words that have E’s in them are more likely. In fact, when Alfred M. Butts designed Scrabble in the early 20th century, he made his tile distribution (there are 100 tiles) based on a sample of letter frequency from the front of newspapers. This Monte Carlo method made a decent approximation of letter distribution. He also then assigned point frequencies based on the rarity of the letter showing up. So while there are many E’s, they are only worth one point. But the singular Z is worth 10, thus giving some balance.

If I were to randomly pick 7 tiles out of the bag, I would be much more likely to draw AEDINOR than CCNOOTU. The first set of letters makes the lesser known word ANEROID, while the second set makes the common word COCONUT. But it makes mathematical sense to study the high probability words as they are much more likely to appear in my rack. The unusual words that I know are chosen because of the letter distribution, and not in any way connected to the English language.

I have been recently studying the eight letter words with a probability range between 7000-8000. (ANEROID is #1, COCONUT is #22060). Some words are common, others are not. The letters ACEHIPRT give rise to three words; PATCHIER (known), CHAPITER (which is that top fancy part of a column, apparently, but I can remember as a funny way of spelling CHAPTER) , and PHREATIC, which pertains to underwater flows. I had a hard time remembering that last word until in Star Trek Discovery they were trying to blow up the Klingon homeworld Kronos (not a valid Scrabble word, though it anagrams to the valid kroons) from the vast network of caves below, and they were talking about using the phreatic flow! I never would have given that word a second thought in that episode.

Later, I had to anagram AADILNRP which is the word PRANDIAL, meaning “pertaining to a meal” and is of course best know from Star Trek IV: The Voyage Home (yes, the one with the whales, a sterling example of 80s culture as well) when McCoy tries to sneak in the hospital and says the patient has “Immediate postprandial upper abdominal distension” which he tells Kirk is “cramps.” All these years of saying that line, having no idea what “postprandial” meant, and here it is just “after eating.” Here is the clip:

Two Star Trek connections in just a few days. What are the odds?

Michael Waski