Good idea. My readers are idiots. Every last one of ’em.

*I was more hoping that you’d be motivated to write a post about the optimal Top Chef structure, choosing the best pieces from TC and TC Masters.*

I have this vague, half-baked post swirling around my head about how the *TCM* star system provided a completely misleading veneer of transparency, kind of like quarterly SEC filings that nobody ever reads…

I was more hoping that you’d be motivated to write a post about the optimal Top Chef structure, choosing the best pieces from TC and TC Masters. An expansion of your (obviously correct) point that they should replace Toby Young with Jay Raynor.

For me, sticking on the topic of judges/critics, I’d vote Gael Greene over Gail Simmons and make James Oseland a frequent (but not permanent) guest judge.

]]>And a clarification, regarding your response of “I don’t think it’s credible to assume that being on the winning team for a relay race Quickfire more than doubles a contestant’s chances of winning the entire competition.”:

I don’t think that being on the winning Quickfire team *causally* doubles a contestant’s chances of winning the competition. But I do think that it reveals the underlying probabilities of the contestant’s winning are higher than the prior (naive) estimate of 1/n.

Obviously my %s were pulled from my butt, but if you had to estimate the probability of the winning chef coming from the set of (Jen C., Jesse, Mattin, and Bryan), what would it be? It must be higher than the unconditional 23.5%, right?

I’d say 40% is a good estimate, which is in line with my 10% per chef number. (Perhaps not surprising, since both the 40% and 10% numbers have the same anal origin.)

Also, I forgot to point out another factor that’s important here, when considering Robin’s chances of winning the Quickfire. The other 4 chefs are using the ingredient that they’ve selected and demonstrated skill with. So it’s not just that Robin would be going up against Jen with a random dish, she’s going up against Jen knowing that Jen will be using a main ingredient for which she’s already demonstrated aptitude.

Unrelated, I wish they could merge the best parts of Top Chef Masters with Top Chef Las Vegas.

]]>The bigger issue is your calculation of the $3,000 payoff. After the winning group of 4 demonstrated clear superiority in kitchen skills relative to the other cheftestants, there’s simply no way you can use the unconditional average to say that Robin has a 1/5 chance to win the competition.

Using your framework, I’d look at it this way:

Going in, each contestant has a 1/17 shot to win. Obviously, this isn’t strictly true, but it’s true from the viewer’s perspective. So if the gold coin *and the winning team* were chosen at random, your math holds. But once we observe non-random selection, we can make inferences about the 4 quickfire participants. Namely, they have a better chance of winning the competition than the other 13 cheftestants. Let’s say that, instead of a 5.88% chance of winning, each of the 4 quickfire semi-winners has a 10% chance to win the competition. That leaves the remaining 13 contestants with a 4.62% chance of winning. If you believe that the chances of winning the competition are roughly equal to the chances of winning the quickfire battle (which seems like a reasonable assumption), that gives the 4 “true” competitors a 22.4% chance each of winning the quickfire, and Robin only a 10.3% chance of winning the quickfire. Which means that Robin’s expected payoff from the quickfire is only $1,552, not $3,000. With an X of $0, that gives an indifference point of $422,069 for the value of winning the competition.

If you believe that the 4 quickfire competitors have a 12% chance of winning the competition, the indifference point drops to $313,846 as a result of Robin’s expected value falling to $1,153. (Again assuming $X=0)

I think Robin made the right decision.

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