Wednesday, November 13, 2013

The World's Largest Cheat Sheet

Ben Blatt of Slate has created a cheat sheet for The Price Is Right. This would normally go rather unremarked. You have no shortage of people who, when you say you're going to attend a Price Is Right taping, will immediately give you tips on Plinko and Cliffhangers. And ONLY Plinko and Cliffhangers, no matter how much you remind them that they do six pricing games a show and Plinko and Cliffhangers are only two games that don't even get played every day. What is notable here is that Ben has created a cheat sheet, based on game theory, for every pricing game. Even the 50/50 timesaver games nobody likes but everybody acknowledges have to be part of the show, like Double Prices or One Right Price. There are also segments on Contestant's Row, the Showcase Showdown and the Showcase.

Well, okay, almost every pricing game. The newest game, Do The Math, is too new to have gotten a spot on the sheet. But it's a 50/50 game in which you're asked which of two prizes is a given amount more expensive than the other, and the price difference is big enough that it shouldn't be too tough to do by yourself. Check Game, recently returned after a long hiatus, is also left off the list.

The first thing to note is that for some games, game theory can't help, offering no advantage over guessing randomly or just, you know, knowing your damn prices. The second thing to note is that for some games in which game theory is an assist, game theory is actually a worse option than whatever it is the contestants are doing now. Take, for example, Double Cross. Game theory suggests that, of the four possible options presented, you ought to randomly pick either the second or third option, giving a win percentage of 36.9%. The actual contestants, though, have a 73.9% win percentage. The third thing to note is that Plinko, despite all the advice you may get, is one of the games with no game-theory improvement on random guessing (players currently win an average of 3.88 chips out of a possible 4 anyway), and advice on placing the chip is a bit silly. The fourth thing to note is that even on a size small enough to fit on my screen, which is already too big to fit in anything you'd be able to get into the studio and actually use, it's too small to read. You'll basically need to just memorize it.

There are, though, games in which game theory is an improvement on current behavior, and three games for which game theory will present a 100% win percentage. Advice here is what you really need. And Cliffhangers is claimed to be one of those games, but the cheat sheet actually has an error here, listing the maximum allowable margin of error as $30 instead of the $25 it actually is. In any case, conventional wisdom says you ought to go $25/$35/$45, but the cheat sheet suggests that $19 is actually the optimal amount for the first prize, and then the other two prizes ought to be called at $11 higher than whatever the previous prize turned out to be. (The Spelling Bee section also seems a little unclear on the concept- you don't get to see what's behind one card before you pick the next- but the general principle that the R's and 'CAR' cards are most likely hiding in or beyond the mid-20's remains valid and usable.)

The other games where game theory claims a 100% win rate are Clock Game (though everybody knows that strategy), and Now or Then, which relies heavily on the fact that four of the prices are always listed as 'Now' and two as 'Then'. This strategy is shown in a flowchart in the article.

Various caveats aside, here's the flowchart.

No comments: