Crossword strategy which aims to minimize lost potential, rather than cl...

...imb the hill in the steepest direction.

Optimistic in some cases, pessimistic in others (w.r.t. BasicStrategy).

[I do wonder if there's much more you can do with a strategy for this game, given you have (or should have) zero information of your opponents]. Some parametrised hill-climbing seems like the best you could do. I guess you could infer your opponents strategics and possible words from their picks.

 Perhaps a big corpus of games and reinforcement learning would yield something interesting.