Sunday, April 30, 2006

colbert mocks bush

Last night, Stephen Colbert gave a speech mocking President Bush at the White House Correspondents Dinner, which Bush attended. The video (a 3 parter on YouTube on Google Video) is pretty long, but quite funny. It's getting some "blogosphere" buzz... will it go viral like Jon Stewart's "Crossfire" appearance?

Tuesday, April 04, 2006

deal expectations

NBC has a game show called Deal Or No Deal in which the contestant picks one of 26 suitcases containing amounts of money ranging from $.01 to $1,000,000. After picking the suitcase, the contestant slowly eliminates the other suitcases, revealing their amounts. The contestant is periodically offered a "deal" to trade in their suitcase for some amount of money.
If you've eliminated a lot of the high paying suitcases, you get offered a low deal. If you've eliminated all but the most valuable suitcases, you get offered a pretty sweet deal. If you decline all the deals to the very end, you get the amount of money in the mystery suitcase.

It seems like a clear case of probabilistic expectation, so I was curious if the "deal" offers were just the expected value of the contestant's suitcase; I don't watch the show often and I don't normally carry a calculator with me, but I was watching last night and had my laptop with me, so I decided to quickly calculate some odds.

When we tuned in, the current contestant was down to 3 suitcases: $.01; $400k; and $750k. Ignoring the one cent suitcase, that's 1/3 * 400k + 1/3 * 750k or an expected value of $383k. Her deal? $375k. Pretty close. (She took the deal; her suitcase was worth $400k, so she only lost out on $25k. Chump change =).

One contestant later, they were down to 8 suitcases with one worth $750k. The offer given to the contestant was $21k. Now $750k / 8 is almost $100k, so the deal value was clearly below expectation. The contestant eliminated two more (low value) suitcases, and her deal got bumped up to $63k. One more low value suitcase down and her deal went up to $96k (her suitcase now had expected value $150k). She took that deal.
They then walked through what would have happened had she had continued the game. She kept eliminating suitcases until there were 2 suitcases (the one she'd picked and one last mystery case) and they said her offer would have been $400k. $25k above expectation.

So it looks like the game has an increasing expectation multiplier that actually hits >1. I guess if I'm ever on the show, I'll work my way down to 2 suitcases and then take the deal -- proving once and for all that mathematicians make piss poor gameshow contestants. Now if only they'd bring back Let's Make a Deal...