# A median lottery **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [December 3, 2006, 10:18am UTC](https://boards.straightdope.com/t/a-median-lottery/382676 "2006-12-03T10:18:35Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [December 3, 2006, 10:18am UTC](https://boards.straightdope.com/t/a-median-lottery/382676/1 "2006-12-03T10:18:35Z")
A hypothetical situation. I’m not running an actual contest. The rules are simple. You pay a dollar to play. Everybody secretly picks a number - you can pick any number you want (no hypercomplex or transfinite numbers - don’t show off). Everybody reveals their number at the same time. Whoever has the median number (which is the one that has an equal amount of other guesses that are higher and lower than it) wins the money. If there’s an even number of guesses and two medians, then the one that comes closer to the mean is the winner. Now assuming such a game was being played, would you play and what would your strategy be? Would your startegy vary depending on the number of people playing? ---
**Author:** ![Cunctator](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Cunctator](https://boards.straightdope.com/u/Cunctator)\ **Post date:** [December 3, 2006, 9:24pm UTC](https://boards.straightdope.com/t/a-median-lottery/382676/2 "2006-12-03T21:24:48Z")
Is there a range for the numbers from which players can choose? ---
**Author:** ![Fern\_Forest](https://avatars.discourse-cdn.com/v4/letter/f/71c47a/32.png) [@Fern\_Forest](https://boards.straightdope.com/u/Fern_Forest)\ **Post date:** [December 3, 2006, 10:22pm UTC](https://boards.straightdope.com/t/a-median-lottery/382676/3 "2006-12-03T22:22:54Z")
If it’s a set range I’d always pick the one that’s in the middle. But if you had no limits, merely that it’s … oh let’s say a positive integer then I would guess 50. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [December 3, 2006, 10:29pm UTC](https://boards.straightdope.com/t/a-median-lottery/382676/4 "2006-12-03T22:29:52Z")
I seem to recall _Games Magazine_ ran a contest a while back where the winners were the persons whose numbers were closest to the median and mean averages. I think the mean was around 621 or so, suggesting (to me) that most people kept their guesses around 500, with a few high-guessers skewing the average up slightly. ---
**Author:** ![garygnu](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/garygnu/32/2924_2.png) [@garygnu](https://boards.straightdope.com/u/garygnu)\ **Post date:** [December 4, 2006, 7:42am UTC](https://boards.straightdope.com/t/a-median-lottery/382676/5 "2006-12-04T07:42:07Z")
Don’t forget about mode. Everybody forgets about the mode. ---
**Author:** ![Scuba\_Ben](https://avatars.discourse-cdn.com/v4/letter/s/278dde/32.png) [@Scuba\_Ben](https://boards.straightdope.com/u/Scuba_Ben)\ **Post date:** [December 4, 2006, 3:02pm UTC](https://boards.straightdope.com/t/a-median-lottery/382676/6 "2006-12-04T15:02:24Z")
[QUOTE=Bryan Ekers] I seem to recall _Games Magazine_ ran a contest a while back where the winners were the persons whose numbers were closest to the median and mean averages. I think the mean was around 621 or so, suggesting (to me) that most people kept their guesses around 500, with a few high-guessers skewing the average up slightly. [/QUOTE] I remember the same thing. I _think_ the object was to guess the lowest number that nobody else guessed. Or they may have run the contest twice, once each way. As I recall, the number range in the contest was the integers from 1 to 1,000,000 inclusive. For the hypothetical contest in the OP, I’d simplify the situation by restricting entries to the set of positive integers. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [December 5, 2006, 7:12am UTC](https://boards.straightdope.com/t/a-median-lottery/382676/7 "2006-12-05T07:12:49Z")
In theory, you want to figure out what numbers everybody else would pick. But that’s difficult - how do you guess what an average person thinks is a winning numer? Or, more directly, what a group of average people think are winning numbers? And then, having hopefully figured out what the other people will guess, you have to come up with a number that will beat them. It’s a meta-guessing game like Nickel Pushing or Snakes & Diamonds.