The economics of Scrabble

In a profile of macroeconomist Jacques Polak, the IMF magazine Finance and Development has a comment on Polak's work on, of all things, the economics of Scrabble,

During a lengthy recuperation from surgery in 1955, Jacques Polak whiled away the hours playing the popular board game Scrabble. It wasn't long before he subjected the word-building game to economic analysis—invoking such common concepts as the Keynesian multiplier and Marshallian profit maximization to divine a formula to maximize a player's total score.

The fundamental mistake inexperienced players make is trying to maximize their score in each turn, a strategy that, in the argot of economics, involves a cost: the "sacrifice of the score that might have been obtained with the same letter in another word," Polak opined in a 1955 article in the American Economic Review.

Polak developed a profit-maximizing formula of how best to make words using the 100 letter tiles in each game that have values running from 1 for common letters such as E to 10 for hard-to-use letters Q and Z. He propounds three rules:
• Letters with face values of 1 and 2 should, and those with a face value of 3 may, be used any time.
• Letters with face values of 4 and 5 should be used only if they score at least double, but a player should not hold onto them for a triple score.
• Letters with face values of 8 and 10 should almost always be kept for triple scores.

The derivation of the rules may be complicated, but they "can easily be followed in practice, even by beginners," he concluded. And apply them he did, Polak noted long after the article was published. Sadly, he was regularly bested by his wife, who cares nothing about the economics of Scrabble.