[pizza]

Not exactly the same game but you might be interested in Mathematical Structure of Syntactic Merge, Marcolli, Chomsky, Berwick (2023).

When we speak we give a string. When we think we don't have to use a string. But we do have to have a functionality to map something that has no single ordering to something that has an ordering (externalization) - a sentence. And vice versa we have a functionality to turn strings into things without a specific ordering (internalization) - thoughts.