The analysis of a mathematical model of Scrabble can be found in

M. Lampis, V. Mitsou, K. Sołtys: Scrabble is PSPACE-complete, 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.