'Survivor' Game Theory
I wanted to get this shot in before tonight's finale of 'Survivor'. I love this show and have been watching it religiously since season 2. The reason I like it isn't for the drama or the "reality TV" aspect, it's because I think Mark Burnett and co. have created the world's most complicated strategy game.
Think about it. Chess is 100% strategy, but is sufficently less complicated because of the finite movements. Hold 'em poker is more complex because of the human reading/betting/bluffing angle, but still has the pretty important luck factor (at least over the short run). "Survivor" has very little luck -- only producer controlled things like tribe placement and challenge selection (and the mysterious, never used 'purple rock'). It also has the very sophisticated factor of human deception and alliances. That factor throws the game complexity off the map (and really into the realm of game theory as I understand it).
It's too bad the producers always cast the show with a bunch of dimwits. The case could easily be made that the smartest/best player in "Survivor" history was Richard Hatch in the first season. Nobody since has shown a very good ability to manipulate people or use what I would consider to be a complex, well-thought out strategy. Maybe this is editing. Maybe it's exhaustion. But I think it's stupidity. It would be really great to get a bunch of (in shape) poker/chess/backgammon professionals on the show to see what happens.
All of which is to say -- Thursday night, "Survivor" contestant Cindy made what may be the worst decision in the show's history. Of course, nobody has been given the same choice as her before. For those who aren't fans, (but are still reading -- good for you!) Cindy was given a $25K Pontiac SUV for winning a challenge, with the choice of either taking the car or giving the other 4 contestants the same car each. She chose to keep the car. Of course, there are other reasons why she shouldn't have, as this article points out. But let me just take the tack of why it was a bad idea from the possible cash return alone.
Let's compare this to a poker tournament for a second. If you have 5 people left at the table and the prizes remaining are $100, $10, $8, $7, and $6; assuming everyone has equal stacks of chips and equal skill, there is $131 prize money left in the game -- approximately $18 a person. Advancing from 5th place to 4th place in this situation gets you from $18 a person 'game equity' to close to $31 a person. Getting from 5th place and still alive to 4th place and still alive isn't just the $1 difference in the guaranteed payout, it's the equity in having the shot at the bigger prizes up the ladder. The assumptions above are big, of course, even for poker. "Survivor" has a bigger complexity in terms of human elements, and there is no way of knowing (especially with questionable editing) how secure players felt or who is really a better player.
BUT, for the sake of this discussion, let's assume that all the remaining players are equal. And (this is a big one) -- giving the other players the car guarantees you'll stay around for one more day, is that a good call from a money perspective? I think so. Let me take some shots at the math, and vague assumptions about probability:
1) Giving up the car means they won't vote you out that night.
2) If you don't give up the car, your chance of elimination goes up slightly that night -- from 20% to 40% let's say.
3) There is no effect on subsequent votes (for now, we'll leave it at just this vote).
The numbers above for the hypothetical poker tournament aren't pulled out of thin air. If you add 3 0's to each of them, they are the "Survivor" prizes. So given that, getting from 5th place and still alive to 4th and still alive increases your 'game equity' from $187857.14 to $313750. A more than $125K difference. If you go home it's a differnce from $60K to $313750. A $250K difference. Divide this by 5 for the aforementioned 20% more chance you go home, and it's still more than the $25K value of the car. The only way it's not a bad decision from this standpoint is if either you think there is no negative effect on the other players voting, or you don't think you have a chance of winnning the $1M prize (if your upside is 2nd place, there is just a $40K difference in prize possiblity).
This brings me to the second reason this was a terrible idea. THE JURY. Assume you think you do have a chance to win. If you make it to the final 2, 3 of the people voting whether or not you should win are people you gave a car to. You need 5 votes to make the leap from 2nd place -- $100K to 1st -- $1M. Are those votes each worth $220K? Does giving them a car sway 3 of them to some degree? Does it sway the other 6 on the jury at all? Can we quantify that at all? Probably not, but it doesn't seem like a trivial consideration to me.
So what really happened? Cindy got voted out that night. It is easy to write all this in hindsight, that she could have saved herself and bought herself some of the shaky concept of 'game equity'. Maybe my knowlege of game theory is off. But either way, wasting your chance at 1 million dollars for a $25K Pontiac hardly seems worth it.
