Final answer:
The sentence 'I want to play the game, but I don't know the rules' is a compound-complex sentence that contains two main clauses and one subordinate clause.
Step-by-step explanation:
The sentence 'I want to play the game, but I don't know the rules' is a compound-complex sentence.
It is a compound-complex sentence because it contains two main clauses ('I want to play the game' and 'I don't know the rules') which can stand alone as sentences, and one subordinate clause ('but I don't know the rules') which begins with the subordinating word 'but'.
This sentence is an example of the compound-complex sentence structure, which is used when expressing multiple ideas within a single sentence.