I’ll start off by saying congratulations to Rick Bayless for winning *Top Chef Masters*. He was my sentimental favorite, but if I had chosen him I wouldn’t have achieved my perfectly imperfect 0.0% record of predictions for the season. (I’m off to a good start this season too, see below.)

So, *Top Chef: Las Vegas*. Let’s play spot the stereotype: slightly older, slightly insecure female contestant who doesn’t have a chance in hell (Robin), check; arrogant, slightly obnoxiously, but talented, nerd (Eli), check; gimmicky duo, one of whom will be eliminated within three weeks (Michael and Bryan), check; hot-blooded Latino, who cooks “with his heart and his balls” (Hector), check; portly, good-natured goofball (Kevin), check; macho, misogynistic douchebag (Mike), check. (Query: is “misogynistic douchebag” a self-negating insult?)

Speaking of Mike (aka The Douche), which was worse: his irritation that Jennifer C. (nota bene: a *girl*) could keep up with him shucking clams (not beat him mind you, but just keep up) or his blustering when Robin declined to compete in the Quickfire? And speaking of Robin, did she make the right choice? (For a lot more on that, see the end of this post.)

This week’s events gave me good reason to believe the new rules will not have to be significantly amended.

In the Quickfire, the Red Team took about 15 seconds to settle on a plan in which Preeti would shuck the clams. Preeti made it clear to her teammates that she had no idea how to shuck a clam. Kevin, at least, seemed to know how to shuck a clam better than she did (“No, it’s not like an oyster at all!”) Now, was the Red Team prepared to change their plan? Hell no. Did that work out well for them? It did not. And that’s why we have Rule D.

In the Elimination, Jennifer Z. (thank God I don’t have to look at her creepy ear hoops all season) decided to Take a Risk and Wow the Judges with a seitan-stuffed chile relleno. Seitan is never a safe bet. Quoth Kevin: “Who cooks with seitan? Nobody bleeping likes that stuff.” And that’s why we have Rule B.

On a more minor note, at Judges’ Table, Jesse—after finding herself in the bottom for disrespecting a protein (Rule C)—was a great example of Rule E in action. I don’t think she was in serious danger of elimination—that chile relleno was just too bad—but she clearly impressed the Judges by knowing exactly what was wrong with her dish and how it could have been fixed. Eve also had a pretty good explanation at hand (she shouldn’t have added that cream), but got bogged down in a distracting discussion of “complexity” as a vice that seemed to leave the Judges befuddled.

**Predictions: **I had a 1/17 chance of choosing the first to go and a 16/17 chance of at least *not* choosing the Elimination winner. Instead, I chose Kevin who, in spite of being young and Georgian and not formally trained, is apparently a very talented chef. Bzzt.

It’s inherently hard to make predictions this early in the season—it seems like half the cheftestants didn’t even register on screen—but it would be no fun if I didn’t at least try. I was very unimpressed with Eve’s fortitude. I’m guessing she’s going to crack up.

P.S. They got Ferran Adrià?!! [UPDATE 8/25: Oops, I think that’s Joël Robuchon. Not nearly as big a “get.” I got thrown by his not-speaking-English-ness.]

The analysis of Robin’s gold chip dilemma is below the fold.

## The Gold Chip, By the Numbers.

Assume that the expected payoff of competing with immunity is

1/16 * P + X,

where P is the value of winning the competition ($100,000 plus a set of appliances you might not want plus intangibles (bragging rights, *Food & Wine* coverage, business opportunities, etc.)), which we assume Robin would have an equal shot at with the 15 other remaining cheftestants, and X is the value of making it through the first episode, besides just the increased probability of winning the competition (e.g., the value of increased exposure, a shot at future prizes, etc. Low, presumably, but you never know. Maybe the second episode’s Quickfire will have a $30,000 prize).

Assume that the expected payoff of competing in the Quickfire is

1/17 * P + 16/17 * X + $3,000,

where P and X are the same as above, but we now assume Robin has an equal shot at winning the competition/advancing to the next round against *16* cheftestants and an equal shot of winning the Quickfire against 4 (i.e., the expected payoff of the Quickfire is 1/5 * $15,000 = $3,000).

Thus, the expected *decrease* in the payoff of competing in the Quickfire is

(1/16 * P + X) – (1/17 * P + 16/17 * X + $3,000),

or

1/272 * P + 1/17 * X – $3,000.

The question of whether Robin should give up her immunity boils down to whether this number is positive or negative. If it is positive, then competing in the Quickfire will decrease her expected payoff (i.e., she should keep her immunity); if it is negative, it would increase her expected payoff (i.e., she should give up her immunity and compete).

We know that P is at least $100,000, so 1/272 * P is at least $367. In order for it to be worthwhile to keep her immunity, we must conclude that value of P, including intangibles, is significantly more than $100,000 (on the order of $800,000 or more) or that the value of X is on the order of $50,000 or more.

I view both of these propositions as highly unlikely, though the second is more likely than the first. There is an enormous value attached to a respectable, non-first-place run on *Top Chef*, especially to a cheftestant with a winning personality. Indeed, it seems that most, if not all, of the intangible benefit of winning *Top Chef* can be obtained by merely making it about halfway through the competition. Cheftestants like Carla, Fabio, Spike, Lisa, and Sam have arguably gotten more traction in their culinary careers than winners like Ilan and Hung.

In conclusion, I think that Robin made the wrong call. The extremely small leg up she got on a distant Grand Prize was outweighed by a decent chance at a smaller immediate payout. The bottom line is that immunity is not all that valuable at the start of the season, since the chance of getting eliminated is so low.

In other words, she should have listened to The Douche.

I think your math is off here, due to a lack of Bayesian updating. It’s ok to assume that Robin’s chances to win the competition move from 1/17 to 1/16, even though they’re probably not increasing that much – they’re not eliminating people at random, they’re eliminating people from the probabilistic lower tail of the distribution.

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.

Comment by Andy — September 2, 2009 @ 11:17 am

Andy, Thanks for your input! I didn’t realize I was going to be rigorously peer reviewed, so I didn’t state all of my assumptions clearly. It’s true that the situation is more dynamic than my model would suggest, but I think it’s so hard to accurately quantify the priors (as evidenced by the numbers that you have so clearly pulled out of your ass, above) that it’s probably more accurate to just assume everybody’s chances are roughly equal. For instance, 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. Kevin and Michael, obviously two of the top competitors, got knocked out of the Quickfire by Preeti’s incompetence; Jesse, obviously one of the next to go, was on the winning team.

Comment by Chris — September 2, 2009 @ 12:11 pm

I’m always happy to spread my bitterness!

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.

Comment by Andy — September 2, 2009 @ 12:32 pm

Who said anything about causality?

Comment by Chris — September 2, 2009 @ 4:30 pm

Oh, I didn’t mean to imply that you thought there was a causal relation. I was just clarifying (for your readers’ benefit) that *I* didn’t think there was a causal relation.

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.

Comment by Andy — September 2, 2009 @ 4:51 pm

I was just clarifying (for your readers’ benefit) that *I* didn’t think there was a causal relation.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

TCMstar system provided a completely misleading veneer of transparency, kind of like quarterly SEC filings that nobody ever reads…Comment by Chris — September 2, 2009 @ 11:11 pm