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Sunday, March 04, 2007

"Amazing Race" Game Theory

One of our guilty night-owl pleasures is watching Amazing Race reruns on the Game Show Network. They're currently running Amazing Race 5, and an interesting situation developed in a recent episode.

The situation is that there are five teams left; it's fairly late in the race to win $1M. The teams are in India, and the first task involves making mud bricks at a brick yard. There is also a "fast forward" task that allows the first team to accomplish it to skip the rest of the race tasks and go directly to the "pit-stop" finish-line for that heat of the race.

All five teams are at the brick yard, so it's clear that nobody has gone for the Fast Forward. One team decides to use it as they're not having much luck making mud bricks (it's harder than it sounds): a man and woman team that are models. They go to the fast forward site and realize that the task is to have their heads shaved!

Now, they have one of those "net gain" choices that economists love. If they shave their heads, they complete the fast-forward task and likely win this heat. If they don't, they have to go back to the brickyard and finish the bricks, and likely finish last and be eliminated. Also, since they're models, and their hair is clearly part of their "professional appearance", they could win the heat, but lose the overall race, and be unemployable as models for several months while they grow their hair back.

If they win the heat, their "expected gain" for each of them is $125K ($1M split in half, with 4 teams left). It is probably higher than that; they'd also be in first place and likely with a several hour lead over the next team. OTOH, since they'd lose precious time in their modeling careers, they also have nontrivial actual loss.

At the end of the day, they actually bailed on the Fast Forward and lost the heat. Also, it happened that it was a "non-elimination heat" so they weren't eliminated, but they are significantly behind the other teams.

Since I'm conservative on such things, I probably would have bailed as well; losing my livelihood for several months, especially in a career as ephemeral as modeling, wouldn't be worth it.

So, what would you do?

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