2. Guess f of the Average
Rules
This game will be played in three rounds. Please do not discuss anything game-related or post in thread until all rounds are complete.
Each player submits a number on the closed interval [0,100] to the mod. DO NOT COPY ANY OTHER PLAYERS IN THE PM OR CLAIM YOUR NUMBER TO ANY OTHER PLAYER.
Whoever submitted the number closest* to f(A) where A is the average of all numbers submitted scores 9 points. If there is a tie for the winner, each tied player scores 9 points, MINUS 1 per additional player who tied with them, to a minimum of 1 point total.
Note: your submission does not need to be an integer, or even a rational number. It must be a real number, and you must be able to describe it unambiguously. If there are more than 100 decimal digits, I will cut it off after the 100th digit after the decimal point.
Functions
Each round, the function f(x) will change:
Round 1 f(x)=0.99x
Round 2 f(x)=10000/(x^2-100x+2600)
Round 3 f(x)=50sin(3πx/200)+50
I'll accept submissions for each round at ~24 hour intervals and post results for the round at the end of that time frame, but if your submissions are not dependent on the results from previous rounds, you may submit numbers for all three rounds at once. If I receive all submissions for a particular round early, I will post the results early, unless at least one player requests that I don't.
*The closest number x to y is the one which minimizes the absolute value of the difference, |x-y|.
The following post will have a link and an image of the graph for the round 2 and 3 functions.