Math games

With not much news this weekend, I scrounged through the Google book cache for game show items. An odd but interesting nugget turned up: Probably not: future prediction using probability and statistical inference by Lawrence N. Dworsky. You probably think this was not light reading, and you're right.

But the book wasn't a complete brick, either. One section called "The Game Show" focused on Deal or No Deal. It rambled through various calculations before concluding:

In summary, playing the game totally by the mathematics makes the choices simple: So long as the expected value is higher than the offer, keep playing. If you got to play the game hundreds of times, this would certainly be the best strategy. If you get to play the game just once, then you have to factor in how you'd feel the next morning: waking up, looking at the check you brought home the night before and deciding how to enjoy your winnings.

I can't resist: well, duh. Of course, the best strategy for playing the game a zillion times is to reject all offers below expected value. It's just that real live contestants don't get to play the game a zillion times.

This is where utility theory comes in. That's big talk for "a bird in the hand is worth two in the bush." Even if the offer is well below expected value, it's genuine money in hand. Losing that money would really sting if the next round of suitcase-openings goes pear-shaped.

Which is what makes the game a lot of fun for me to watch. How far will the contestant push the utility theory envelope? Howie wants to know, now.