# Thread: Success in Survivor - A Mathematical Model

1. Originally Posted by Lil_Cutie
There was a thread about this awhile back, during last season, I think it was called "Missed Opportunities" and the writer mentioned that Liz should have tried to align herself with Amber. Here's the thing though, maybe she did try and it wasn't shown and Amber refused because she was very positive that she was in a tight alliance with Colby.
I remember Amber was asked this question on The Early Show once she was booted. She had said she was afraid that the Kucha members would run back to Tina, Keith and Colby and they'd get rid of her right away. This could have worked in Kucha's favor 3 different ways.

2. Thanks for that analysis, tmcrae! Those are interesting statistics, and I know they took a fair bit of effort to compile.

Interesting, but if you line these up by score, Brian Hedick could be termed Survivor's best player, ever. By the end of the game, I couldn't stand him, but allow that he played the *game* incredibly well. And interesting that his #2 Clay came in 15th.

1.. Brian (S5)…….54.484
2.. Colby (S2)…….53.639
3.. Kim J. (S3)…….47.917
4.. Kelly (S1) …….46.918
5.. Lex (S3)…….46.402
6.. Neleh (S4)…….45.617
7.. Jenna (S6)…….44.511
8.. Mathew (S6)…….44.150
9.. Ethan (S3)…….43.275
10. Tina (S2)…….42.922
11. Kathy (S4)…….42.851
12. Paschal (S4)…….42.429
13. Rob (S6)…….41.184
14. Rudy (S1) …….40.977
15. Clay (S5)…….40.910

3. Seems like early on, it was better to be a solid second or third place rather then come in first (point wise).

4. *Aside

Seeing Colby's name just now reminded me...Is that him in that new quadro-razor commercial?

5. Once again Tmcrae, great work, the mathematical model was utilzed very well. I have one point to add, Overall Variable, and only one person can qualify for that, that would be Rich Hatch, he invented the game, and all subsequent winners utilized a vriation of his plan. That variable can only be added to the score of one person. So, even though he was not in the top 15 according to the model, he indeed was probably the best. As much as I hate to admit it!!

6. Originally Posted by CharlaFan
I think that if somebody dosn't get a vote against them(untill they get voted out) it could be because they are a terrible player. Case in point Rodger(S2) or Jan(S6) which both are rated high on your lists and did finish high on the show just because they were dead ducks.
I had considered that CF. But in the end, I looked at all the possible reasons there might be for not getting a vote at TC. They are:

1. Popularity or Likeability - People who are genuinely likeable will more than likely get fewer votes than those who are reviled. Tina (S2) and Ethan (S3) are good examples of this.

2. "Under The Radar" - The tribemate hasn't drawn a lot of attention (positive or negative) to themselves. Their strategy involves sitting back, not ruffling any feathers and allowing the game to unfold. See Neleh (S4).

3. Voting Bloc Member - The tribemate is part of a voting bloc. The larger and more powerful your voting alliance is, the fewer the votes there will be to cast against you. The Tagi Alliance from (S1) is a good example of how a strong voting alliance can positively affect this measure. Up until they had to start voting alliance members out in Episode 12, Susan (the eventual bootee), Kelly and Richard had only three, zero and two votes cast against them respectively. Rudy, the other alliance member, drew some fire early in the game but once he made the merge, he garnered only two votes in his last eight TC's.

4. Non-threatening - The tribemate is not viewed as a threat (physically or mentally) to the other players still in the game. These are the people you want around, as they will be less likely to jeopardize your chances of winning it all. You're right, CF. Jan (S5) was most definitely dragged along by Brian and Clay as she was easily manipulated and posed no threat whatsoever to either of them so perhaps she shouldn't have placed as high on the list as she did. However, I bet if you asked Mathew and Rob (S6), they'd probably admit that they really didn't view Jenna as a big threat. Trouble is, when it came time to vote her out she had this nasty habit of winning immunity, which is something I'm quite sure neither of them banked on. How sweet it would have been if Jan could have done the same to Brian and Clay!

In the final analysis, I think the measure of "Tribal Council Votes Against" is a good one when it comes to looking at strong players in the game of Survivor. Remember, if you've never had a vote cast against you during TC, you are guaranteed a spot in the Final 2. Well, barring the "Purple Rock Of Death" of course...

7. Originally Posted by Liant
good job tmcrae

as with any quantitative analysis, there are always some flaws. For example, Richard throwing the final immunity challenge hurts his ranking in your analysis, but was a great strategic move to move him into the final 2.

Also, once the final 2 survivors are in place, there is nothing quantitative that can be measured as to how they will be placed. It's totally in the hands of the jury & therefore a number of differing events go in to how the jury selects the winner.

However, in terms of a quantitative analysis based on previous shows, this looks very good.
Thanks, Liant. You're right in saying that Richard should be given credit for his early exit from the final IC. But the problem is, that may not be the way it is perceived by everyone else. For example, when he first did that, I was a little shocked until I realized his strategy. Richard knew if Rudy won that he would take Richard to the Final 2 because of their alliance. He also knew (or at least was pretty sure) that Kelly would also take him to the Final 2, since he felt that she viewed her chances of winning to be much better with him by her side than with Rudy. If Kelly would have taken Rudy along instead of Richard, Richard's plan would have backfired and he would have deserved to be "hurt" in my analysis by not winning the final IC.

What this comes down to is whether Richard's throwing of the final IC could be correctly classified as a brilliant move, or a ballsy one.

8. I really enjoy any mathematical analysis of this game, whether it be for prediction purposes, or for quantifying how "good" a previous Survivor was. What really fascinates me about the game, though, is whether it is possible to apply game theory to the game as an actual Survivor and come out on top.

A couple of problems here though: most basic game theory models assume that all participants are completely rational and will always make decisions based on what the best strategy is in terms of odds and net paybacks. The emotional factor, however, complicates any working model you could have.

On the bright side, the "social conventions" factor, i.e the fact people tend to vote against people that piss them off and people that don't work hard enough (at least early) are complications of the game model but can be reasonably quantified when making decisions, as the odds of social conventions applying to the game of Survivor - with the participants having so recently been part of "society" prior to arriving on the island - are quite high.

Another problem is that even if you factor in social conventions and detect emotions in other people's choices, your competitors will often have characteristics that you simply cannot know, (such as Sandra blowing Trish's plan in the latest episode. How could Trish know Sandra was a snitch?). Also, the competitors, even the rational ones are likely to not know game theory (or at least very basic game theory, which I am discussing), and many models that you might have devised in the past that assume competitors are making optimum decisions, just as you are, will no longer work.

And so in the end you are left with what I see as one last possibility to properly apply game theory to Survivor and that is: quantifying your pros and cons for every decision, calculating probabilities for any related events to occur (such as alliances being forged between given competitors etc.), and incorporating induction in your judgment of other contestants' potential behaviors (sometimes you can't ignore your hunches, especially in a chaotic game such as this).

All this approach would do, however, is increase your chances of doing well. It could not, of course, give you a sure way of winning. I think your luxury item would also have to be a pen/pencil and a rather large notepad. Potential flaw: Your fellow survivors blowing up on you when finding out that you quantified your assessment of their actions. i.e. leaving around a notepad with "Mark's chances of finding out that I just backstabbed him: 28.6%" written on it.