The Price Is Right

This is a game show based on the contestants guessing the price of various prizes. One of the nice features is that, since the pricing games involve only one contestant, you're almost always rooting for the contestant to win. Also, this article describes the 60-minute verison. There were some 30-minute versions, but none has lasted more than a year since the '70s. (Editor's note: the 60-minute version was itself 30 minutes long for the first three years, as well as the second through approximately ten weeks of the fourth year.)

The game starts in "contestants row", where 4 contestants bid on the price of a small prize, like a TV or sofa. Each contestant bids in turn, and whoever is closest without going over wins. If all contestants go over, then each gets another bid. If a contestant is exactly right, he/she gets a $500 bonus (used to be $100).

The winner gets to play a "pricing game", where they can win a bigger prize, like a car, a trip, or cash. A new contestant is chosen for "contestants row" and the process repeats a total of 6 times.

After the 3rd and 6th pricing games, there is a "showcase showdown", so that 2 finalists can be determined for the showcase. The contestants, in order from the one who won the least to the top winner, spin a wheel with 20 sections marked $.05 to $1. After the first spin, the contestant has a chance to stay or spin again. The contestants' score is the sum of the two spins (or 1 spin if he/she decides to stay). The goal is to have the highest score without going over $1. Any contestant who goes over $1 is immediately eliminated. There is a rule that the wheel must go "all the way around" when spinning, to make it hard to aim for a specific square of the wheel.

If a contestant gets $1 in the "showcase showdown", he/she wins $1,000 and gets a "bonus spin". A score of $1 on the bonus spin yields a $10,000 bonus, and $.05 or $.15 (located below and above $1) yield a $5,000 bonus. The bonus spin starts with the wheel on the $.05, so that the contestant is never denied money for failing to get the wheel all the way around.

If 2 contestants are tied, there is a spinoff consisting of one spin only each. The $1,000 bonus and a bonus spin can still be earned in a spinoff. If two contestants tie with $1, there is a spin that is simultaneously a bonus spin and spinoff. However, a contestant cannot win more than one $1,000 bonus. (Yes, I actually saw this happen. Two contestants tied for $1, and then they tied on the bonus spin for a 2nd spinoff. On the 2nd spinoff, one contestant got $1 again, but did not get another $1,000.) Until the late '70s, however, there was no "bonus spin", and contestants simply won a $1,000 bonus every time they spun $1 (so if two people tied at $1 and had a spinoff, they could win another $1,000 bonus by spinning $1 again). Another interesting possibility is that the first 2 contestants in a showcase showdown can go over. The 3rd contestant automatically makes it to the showcase, but they get one spin to try to get $1 and win $1,000.

The 2 winners of the showcase showdowns make it to the showcase. One showcase is shown, and the contestant with greatest winnings so far has the option to "bid or pass". After the bid is placed, the 2nd showcase is shown. The showcase usually involves several prizes connected by a little story, but the older episodes tend to have better stories. The goal, as usual, is to be the closest without going over. If both contestants go over, nobody wins the showcase. If the winner is within $250 of (used to be less than $100 away from) the price of their showcase, they win both showcases. (At least once, both contestants were within $100 of the actual price; in fact, one of the bids was $1 closer than the other!) If the two contestants are exactly the same distance from the actual prices (in other words, if there is a tie), each wins his own showcase. (This has happened exactly once.) If there is a tie where the difference is within $250, both contestants win both showcases. (This has never happened.)

There are many fine "Price is Right" sites on the internet, so there's no point in reproducing all that information here. One is http://www.cbs.com/daytime/price It can also be accessed at http://www.tpir.tv/ There is also a message board about the show at http://communities.msn.com/ThePriceIsRightUpdateMessageBoard/

Some of the Price is Right games are mathematically interesting.

The strategy for the contestants row game is interesting. Suppose the price is uniformly distributed between $1 and $1,000? What is the optimal bidding strategy? I remember seeing an article on this once.

The strategy in the showcase showdowns is also interesting. When should you choose to spin again? I remember seeing an article on this once, but a simple computation or computer simulation will yield the answer.

The "Clock Game" gives the contestant 30 seconds to deduce the price of a 2 prizes. (first one, and then with leftover time the other) The contestant makes a guess, and the host says "higher" or "lower". Any contestant who knows binary search will win easily. Further, you're allowed to cheat in the pronunciation. For example saying "fifty-six seventy-one, -two, -three, -four" will test all prices in the range $5671-$5674.

Other Mathematically interesting games:

Dice Game

10 Questions (Editor's note: there is no such game as "10 Questions." Perhaps the person who wrote this was thinking of "Ten Chances.")

Race Game (like Mastermind)

Plinko (what are the odds of winning $10k assuming the board randomizes perfectly?)

3 Strikes (odds of winning assuming perfect foreknowledge of price, 1-digit foreknowledge (probably first), 2-digit foreknowledge)