Does Luck Exist?

Wordle may hold the answer. This is a very simple game played by millions worldwide. It is basically a six try word guessing game. Getting the answer on the first guess is equivalent to having two people pick the same word out of a dictionary — very lucky. On the second guess, you are either very lucky again or learned a lot from the first guess, so still lucky, but a little less so, and so on. The honest player probably averages around four guesses over many games. So, New York Times, let’s run an experiment. It would be trivial to write a program to play the game fairly. Optimize this and see what it’s average score is. This is such a simple game, software will play like a human, and software will occasionally fall into a beach, leach, reach, teach consonant hole where luck is the only winning strategy just like a human will. Software will just reach the answer in a nanosecond instead of over a morning cup of tea.

The experiment? Teach a computer to play. That is your baseline. Look at large random groups of users who have played the game many times and filter out obvious cheaters. Looking at you Donald. Find all the normal biases. Some people have better vocabularies than others, etc. Then look for honest players who consistently best the computer and group averages. That is, lucky players. Look for those who are consistently worse. Unlucky players.

If everyone averages to four, I’ll be very depressed.

Addendum: After 500 plays with a random first word, no knowledge of the wordle word list, and no extra information (yes, if you have friends who use a standard first word and they send over their green and yellow boxes, you have extra information), I average out to 3.98 ignoring a few roll-offs and 4.04 if you assume the roll-offs are 7s. Heavy sigh.