<p>The basis game: A number between 1 and 100 (presumably an integer) is randomly generated. You, along with other people, choose a number between 1 and 100, without knowledge of the other numbers chosen. The person who chose the number closest to the randomly generated number wins.</p>

<p>Assume for the questions that the other people are humans and not perfectly playing machines. </p>

<p>Q1.: What is the optimal number to choose? </p>

<p>Q2.: What is the optimal number to choose if we are also fine with getting second place ?</p>

<p>Part 2: We iterate this 5 times, without any knowledge of prior rounds (as in, we don't know who won in the prior rounds, and we don't know what others have chosen in the prior rounds. We can consider these rounds to be done simultaneously).</p>

<p>Q3: What is the optimal number to choose if we want to maximize our chances of winning at least one round?</p>

<p>Q4: What is the optimal number to choose if want to maximize our chance of either getting first or getting second in at least one round?</p>

CC BY-SA 3.0
2015-06-22T12:42:54.473Z
Welcome to Cognitive Sciences. Apart from Q1, the remainder seems more suitable for Crossvalidated. SE : http://stats.stackexchange.com/
AliceD
CC BY-SA 3.0
2015-06-22T19:17:05.287Z
@AliceD It's not about statistics. Maybe economics.SE (tag `behavioral-economics`). Anyway, I recall experiments leading to the winner who chooses something around 1/3 of the interval.
Anton Tarasenko
CC BY-SA 3.0
2015-06-22T19:51:52.163Z
Hmm, I suppose I should have mentioned that you should take human psychology into account for all of them. I have changed the question a bit.
Name
CC BY-SA 3.0
2015-06-22T19:58:10.607Z
Would that fit this place better? Thank you for the welcome. I shall also look into the other stack exchanges.
Name
CC BY-SA 3.0
2015-06-23T06:55:12.560Z
It is similar to the 2/3 of the Average game: https://en.wikipedia.org/wiki/Guess_2/3_of_the_average, but has some differences.  This one is called The Closest Wins game.  There is a paper that discusses the optimal strategy for this game http://www.calpoly.edu/~aamendes/GTweb/GuessingGamesAug22.pdf - basically it depends on the number of players, and becomes very difficult to solve for >4 players.
Arnon Weinberg
CC BY-SA 3.0
2016-06-01T18:47:01.060Z
I'm voting to close this question as off-topic because this is on calculation of chance and should go to CrossValidated.SE
AliceD
<game-theory>
Optimal way to choose a number to be close to a randomly generated number
Name
# Optimal way to choose a number to be close to a randomly generated number

(Asked by: username_0 on 2015-06-22)

The basis game: A number between 1 and 100 (presumably an integer) is randomly generated. You, along with other people, choose a number between 1 and 100, without knowledge of the other numbers chosen. The person who chose the number closest to the randomly generated number wins.

Assume for the questions that the other people are humans and not perfectly playing machines.

Q1.: What is the optimal number to choose?

Q2.: What is the optimal number to choose if we are also fine with getting second place ?

Part 2: We iterate this 5 times, without any knowledge of prior rounds (as in, we don't know who won in the prior rounds, and we don't know what others have chosen in the prior rounds. We can consider these rounds to be done simultaneously).

Q3: What is the optimal number to choose if we want to maximize our chances of winning at least one round?

Q4: What is the optimal number to choose if want to maximize our chance of either getting first or getting second in at least one round?

**Tags:** game-theory

> **Comments:**
> **username_1**: Welcome to Cognitive Sciences. Apart from Q1, the remainder seems more suitable for Crossvalidated. SE : http://stats.stackexchange.com/  
> **username_2**: @username_1 It's not about statistics. Maybe economics.SE (tag `behavioral-economics`). Anyway, I recall experiments leading to the winner who chooses something around 1/3 of the interval.  
> **username_0**: Hmm, I suppose I should have mentioned that you should take human psychology into account for all of them. I have changed the question a bit.  
> **username_0**: Would that fit this place better? Thank you for the welcome. I shall also look into the other stack exchanges.  
> **username_3**: It is similar to the 2/3 of the Average game: https://en.wikipedia.org/wiki/Guess_2/3_of_the_average, but has some differences.  This one is called The Closest Wins game.  There is a paper that discusses the optimal strategy for this game http://www.calpoly.edu/~aamendes/GTweb/GuessingGamesAug22.pdf - basically it depends on the number of players, and becomes very difficult to solve for >4 players.  
> **username_1**: I'm voting to close this question as off-topic because this is on calculation of chance and should go to CrossValidated.SE  

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