Fog of war type elements were possible back then, they just required a third party to act as umpire and determine what each party can see/know, and probably duplicate (or triplicate) copies of the game.
And if all fails, the only thing you can do is sit idly by and watch how all your moves turns to dust as your former allies turn against you.
It's much more limited than what computers make possible of course, but it worked well enough.