I saw a variation of this game in an episode of Taskmaster. Take an odd number of people – 3, 5, 101, whatever – and instruct each to choose a number between one and whatever. Or, in a more specific iteration, determine how many Skittles are in a jar that contains between one and several hundred (or several thousand or whatever). You are not trying to guess the right amount or right number. Rather, all players are told to aim to guess the median – which is to say, the winning player will have an equal number of players who guessed a number below his, and an equal number of players who guessed above his.
For example, everyone is told to pick a number between 1 and 100, and aim for the median. Say Players One and Two guess 8 and 16, respectively; Player Three guesses 29; and Players Four and Five guess 62 and 71, respectively. Player Three wins.
Intuitively, it seems prudent to guess right in the middle: 50. But every other player is thinking the same thing. So is there a mathematical way to work an advantage in this?
And if every other player is thinking the same thing, then everyone will pick that number, and so that number will in fact be the median, and so everyone will win. What do the rules say happens in the event of a tie?
I don’t know if there’s a mathematical way to game this game, because it’s not really a math game, it’s a ‘how well do you know the other players’ game. I’ve never heard of such a game, but it could be fun. Or quite maddening. Possibly both!
Since the information is symmetrical and everyone plays simultaneously, there is a mathematically optimal play for any / everyone.
IOW, if everyone else played optimally, your optimal move it to play optimally too.
As @ricepad says, what’s optimal against unskilled players might be different from game to game. But if everyone is smart & learns (two bad bets in one ), then pretty quickly the game theoretic optimal will be discovered and play will converge there.
As Chronos said, picking between 1-100 leads to ties. Guessing skittles is better.
I assume the only worthwhile
strategy is to try to guess about half hte number of skittles…
It’s a good thing the object is not to guess the number of Skittles, because if you gave me a jar of Skittles, I’d be eating some. Possibly more than just some.
Hm, then there’s the possibility that an odd number of guesses will be voided, and hence there will be an even number of remaining players, and hence (depending on how you look at it) no median, two medians, or a median that isn’t any of the guesses.
If there’s no voiding for duplicates, and it’s only “pick a number from 1 to X” then the optimal pick is always right in the middle. You need some other factor to make it asymmetrical (or base it on an actual number like the skittles jar).
For example, pick a number from 1 to 100. If you are the exact median, you get $10. If you are under the median, you get $1. And if you’re over the median, you get nothing.
), then pretty quickly the game theoretic optimal will be discovered and play will converge there.