Using Game Theory to Win the Price is Right
On an afternoon off from school while watching “The Price is Right”, Ben Blatt realized that if the contestants applied game theory to the game show they could improve their chances of winning. Most of the time the contestants on the show just use their intuitions and randomly guess at the price of items. Blatt points out that in most cases the contestant loses more often than they should.
The games covered in this course so far have been simultaneous games where both players reveal their strategy at the same time however, the games in the “Price is Right” are not. Contestants are able to see their opponent’s strategy depending on what turn they get to play. Since the games are not simultaneous contestants could potentially devise dominant strategies. Blatt uses the constant’s row segment as an example of this. Contestants in a row make guesses at the cost of an item one by one and whoever gets closest to the price without going over wins. By the time it is the last contestants turn to guess they have a couple of strategies to choose from. They can guess below the price the other contestants guessed, in between the prices the others guessed, or above what the others guessed. Blatt points out that the dominant strategy is to always guess above since you maximize your chances of winning.
What some contestants fail to realize that hinders their chance at winning is that the games are not random. This means that there is a certain way to play such that the contestant maximizes their chance of winning. For example in the game Squeeze Play, contestants have to remove a middle digit from a 5 to 6 digit number. The digits left over make up the price of an item. This could be considered a simultaneous game in which one player is the contestant and the other is the game maker. The contestant wins if he guesses the same digit that the game maker guesses and the game maker wins if the contestant doesn’t. The key to this game though is that the game maker isn’t randomly selecting a digit. Statistically, in a game with 5 digits the game maker selects the third digit 49.8 percent of the time. Knowing the game makers strategy the contestants on the show could ideally win 49.8 percent of the time instead of thinking that all digits are weighed the same.