I'm going to invent a game

 it's called 1,000 knights

there's two kingdoms, each with an army of 1,000 knights and they're going to meet on the battlefield and have it out. So there's two teams and they're each trying to decide the proper number of soldiers to bring to the battle. If you send too few then you risk being overwhelmed. If you send too many then you risk stretching your troops too thin and leaving yourself vulnerable to other attacks and such. So a third, impartial player decides a number between 1 and 1,000 and the other two teams are trying to determine what that number could be. 

The only hint the teams get is a completely opaque and non-sequitur clue/sentence provided by the judge. 

So the number could be something like 521 and the judge could say something like "It was compulsory to use coconut shells to make horse trotting noises." And the game is you make up a really tenuous reason why that's a hint. So you could say "compulsory" means "have to" which can sound like "hafta" which sounds like "half" and also you would use two halves a coconut to make the noise so the guess is probably somewhere around half of a 1,000. 

And maybe there's also something where each person gets to ask an open-ended, equally opaque question to try to figure something out.

Whichever team is closer to the correct number wins the round and battle.