If we are thinking of the same time in the book, the game they are playing is poker.
I am thinking of the first time that Montag comes back to the fire station after he has taken some time off from work. He took the time off because of how shaken up he was from the old lady killing herself. Beatty had to come and give him a pep talk before he was able to come back to work.
So he comes back to work, with the "bullet" from Faber in his ear. The other firemen are playing poker when he comes in.
They are playing with the mechanical houd. they give him rats that he chases and injects with poision. The firemen think this is funny and amusing.