what does "a game of fool"mean?
The fire had died down. Singer was playing a game of fools with himself at the table. Jake had been asleep. He awoke with a nervous quiver. He raised his head and turned to Singer.

Question

Answer

He was playing cards. 'Fool' is the name of a card game.

Here's the Wikipedia entry about it:
https://en.wikipedia.org/wiki/Durak

and here's a youtube video about how to play it: https://www.youtube.com/watch?v=TX5aB1FVNow

Nowadays, it's more commonly known by its Russian name 'Durak'.

Answer

Hey, loulou703!

A fool's game means any game that you're more likely to lose than win, no matter how much it looks you are up to win.
Sometimes it's used in different circumstances to mean that is a waste of time, or there will be no chance for you, for example:

Love is a fool's game.

I hope this helps!