The analysis of a mathematical model of [Scrabble][1] can be found in

M. Lampis, V. Mitsou, K. Sołtys: [Scrabble is PSPACE-complete][2],  in E. Kranakis, D. Krizanc, F. Luccio (eds) Fun with Algorithms. FUN 2012. *Lecture Notes in Computer Science* **7288**, Springer (2012).

It turns out that Scrabble-Solitaire is NP-complete and (as the title suggests) Scrabble is PSPACE-complete.


  [1]: https://en.wikipedia.org/wiki/Scrabble
  [2]: https://link.springer.com/chapter/10.1007/978-3-642-30347-0_26