First move variance

[jdonland]

Sometimes the initial dictionary will contain no three-letter word for the first player. The difference seems considerable to me, since playing all three of their pieces allows them more control of the words available to the second player on their first turn.

I determined via simulation that this occurs 25% of the time. A more skilled combinatorialist could confirm this mathematically.

One rather inelegant option to address this would be to modify the setup procedure such that if the initial dictionary contains no monochrome three-letter word consisting of exactly one piece of each size, reshuffle it until it does. (This also addresses the much rarer situation of having only one-letter words available, forcing the first player to pass the first turn.)