AO Survivor II: R1 Reward - Axiom of Choice

[Jeff Probst]

Round 1 Reward Challenge -- The Axiom of Choice
This challenge will serve two purposes. First, it will be used to set the initial teams. Second, your team will earn a reward which will help you in the round 1 Immunity challenge, Invertigo.

The challenge is quite simple. I would like you to choose a non-integral number between 0 and 100.

Your score for the challenge will be SUM{sqrt[abs(X - Xi)]}, where X is your chosen number and {Xi} are all numbers chosen by all players.

If you choose a number which another player has already chosen, I will move your number half the distance toward the mean (the mean before I move any numbers).

If you do not choose a number, I will set it equal to the third quartile of all other numbers chosen. If more than one person does not choose a number, I will randomly order the names and assign the third quartile, third quartile + 0.1, third quartile - 0.1, third quartile + 0.2, etc, to those players.

You may choose your number by sending a PM to me. Once you have chosen your number, you may NOT change it. You may choose your number anytime after this challenge is posted, but you must choose no later than 11:00a ET on June 1. Teams will be announced the morning of June 1, or once all players have chosen their number if earlier, and the first immunity challenge will run the afternoon of June 1.

This is the only time in the game I will explicitly point out something like this...despite initial appearances, this is NOT merely a game of chance nor is their one ideal strategy to picking a good number.

I will also use those scores to rank you and assign you to teams. The five players with the highest scores will be on Team A; the five players with the next highest scores will be on Team B; the six players with the lowest scores will be on Team C.

Team A will win the Reward. The actual Reward will be announced along with the description of the Invertigo challenge and will give Team A an edge in that challenge.

So you could say Axiom of Choice has no real winners. But there are losers. And those losers will be on Team B.

[cubedbee]

Real numbers only?

[Jeff Probst]

Is there a definition of "between" that would allow you to choose a non-real number between 0 and 100 and which would provide a valid result for the score formula? If so, you may choose a non-real number.
No need to reply publicly. If you have a way to game this or any other challenge, you may ask for any additional info you need by PM (assuming you'd rather not have others see your idea).

[cubedbee]

Originally Posted by Jeff Probst

Is there a definition of "between" that would allow you to choose a non-real number between 0 and 100 and which would provide a valid result for the score formula? If so, you may choose a non-real number.

Yes, there is certainly a definition of “between” that would allow non-real numbers. Just like there is a definition of “is” that didn’t make Clinton a liar. Every word has many definitions, some from much more reputable sources than others, and in a game like this, one would think that the definition of “between” should be decided by the authority running the game, not by the individuals playing.

[wat?]

Originally Posted by cubedbee

Yes, there is certainly a definition of “between” that would allow non-real numbers. Just like there is a definition of “is” that didn’t make Clinton a liar. Every word has many definitions, some from much more reputable sources than others, and in a game like this, one would think that the definition of “between” should be decided by the authority running the game, not by the individuals playing.

Could you choose such an example that would qualify, yet does not give away your choice? I'm failing to see outside of the box of semantics right now.

[Jeff Probst]

Originally Posted by cubedbee

Yes, there is certainly a definition of “between” that would allow non-real numbers. Just like there is a definition of “is” that didn’t make Clinton a liar. Every word has many definitions, some from much more reputable sources than others, and in a game like this, one would think that the definition of “between” should be decided by the authority running the game, not by the individuals playing.

Clinton had to make his definition up. You may use any number you wish meeting the stated criteria. If it is not clear how I need to calculate the criteria and scoring formula, I will ask you to cite a reference. I will attempt to accept any generally agreed-upon definitions. My complex analysis is a bit rusty -- if "between", "absolute value", and "square root" are well-defined functions, you are welcome to use imaginary numbers. Likewise for any other class of number.

In most games, you are correct that rules clarifications like this should be set by the authority running the game, and not the individuals playing. In this game, I prefer to let the individual players decide just how create they can be and how ethically creative they want to be when interpreting the rules. As is specifically noted in the rules, "if it's not in the rules, it's fair game."

Some ambiguity will be intentional. Some will be me not foreseeing an option. This is the latter. You are welcome to take advantage of it.

[cubedbee]

Originally Posted by wat?

Could you choose such an example that would qualify, yet does not give away your choice? I'm failing to see outside of the box of semantics right now.

Pretend your on a football field and the coach tells you to go stand between the 50 and your own 60.

Does the coach mean to actually stand on white sideline, between the numbers 50 and 60?

Or does he want you to stand anywhere on the field that is bounded by the 50 yard line on the left and the 60 yard line on the right?

Both are valid interpretations of the word “between”, but both give very different results.

[Judge Dredd]

I think most football players would have no clue where their own 60 yrd line is.

[4sigma]

Originally Posted by Judge Dredd

I think most football players would have no clue where their own 60 yrd line is.

It's between the 50 yrd line and the endzone.

[wat?]

Originally Posted by cubedbee

Pretend your on a football field and the coach tells you to go stand between the 50 and your own 60.

Does the coach mean to actually stand on white sideline, between the numbers 50 and 60?

Or does he want you to stand anywhere on the field that is bounded by the 50 yard line on the left and the 60 yard line on the right?

Both are valid interpretations of the word “between”, but both give very different results.

Cool.

I meant pick a non-real number, though.