In that case, the options are really limited and the main simple ideas for that (eg: guess before you know other player’s guesses) have been mentioned already.
One other simple method for one-shot number games I can think of is:
Automatic Interval Equalization:
When all players guesses are known, you take the two players whose guesses are closest and calculate half the difference between them. That amount is the allowable error, and each player’s interval is his or her guess, plus or minus that allowable error.
You win if and only if the answer is in your interval.
Example:
Player 1 guesses 44
Player 2 guesses 50
Player 3 guesses 60
The allowable error for this would be ((50-44)/2) = 3
So the winning intervals would be:
Player 1: 41-47
Player 2: 47-53
Player 3: 57-63
This would result in at most one winner (unless the answer is half way between the 2 closest guesses). Everyone’s winning interval would be the same size and none would overlap. And nobody would have an incentive to guess near someone else’s (stated or expected) guess, unless they thought the answer was actually close to that.
However, it has the disadvantage that a lot of such contests would end up with no winner.
In that case, the options are really limited and the main simple ideas for that (eg: guess before you know other player’s guesses) have been mentioned already.
One other simple method for one-shot number games I can think of is:
Automatic Interval Equalization:
When all players guesses are known, you take the two players whose guesses are closest and calculate half the difference between them. That amount is the allowable error, and each player’s interval is his or her guess, plus or minus that allowable error.
You win if and only if the answer is in your interval.
Example:
This would result in at most one winner (unless the answer is half way between the 2 closest guesses). Everyone’s winning interval would be the same size and none would overlap. And nobody would have an incentive to guess near someone else’s (stated or expected) guess, unless they thought the answer was actually close to that.
However, it has the disadvantage that a lot of such contests would end up with no winner.