British versions have been hosted by Leslie Crowther[?] (of "Crackerjack" fame) and Bruce Forsyth. This article describes the hourlong Bob Barker version.
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 he/she 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 contestant's 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. 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 if the first 2 contestants in a Showcase Showdown can go over, the 3rd contestant automatically makes it to the showcase, but he gets 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. 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 his own showcase, he wins both showcases. 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. One is http://www.tpirsite.com/ . The show's official website is at http://www.cbs.com/daytime/price , but it has a lot of mistakes. Sites made by fans are generally much more accurate. There is also a message board about the show at http://communities.msn.com/ThePriceIsRightUpdateMessageBoard/ .
Note: the Bob Barker version was originally half an hour long, and it featured 3 pricing games. There was no Showcase Showdown; the top 2 winners of the day participated in the Showcase. This was changed in 1975 to the hourlong version which is described above.
Dennis James also hosted a weekly edition, similar to Bob's version, from 1972 to 1976. Bob also took over the weekly show in 1976, but it was cancelled in 1980. The daily show continues to this day. Two new versions were attempted: in 1986 with Tom Kennedy, and in 1994 with Doug Davidson. Both of these quickly died out.
A series of nighttime specials was aired in 1986, and another series aired in 2002. There have also been primetime specials for the show's 25th and 30th anniversaries.
Mark Goodson Productions was bought out by Pearson Television in the mid1990s. (Pearson is now known as Fremantle Media.) Some fans associate this time as the start of a decline in the quality of the show. There are many recent changes that are disliked:
Fremantle has had many failed remakes of other Goodson shows, such as Match Game (1998), Card Sharks (2001), and To Tell The Truth (2000). Two of these have become somewhat popular: Family Feud (1999), and Whammy!: The All New Press Your Luck (2002).
Analysis of Games and Strategy
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?
The strategy in the showcase showdowns is also interesting. When should you choose to spin again? 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 "fiftysix seventyone, two, three, four" will test all prices in the range $5671$5674.
Other Mathematically interesting games:
Dice Game
10 Chances  Informally, there's the "zero rule" which says that if a zero is one of the digits displayed, the zero goes last. Bob Barker sometimes criticizes contestants who violate this. This rule did not apply for all of this game's history, but it has been followed on all recent episodes. Thus, someone who watches the show regularly has a big advantage.
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, 1digit foreknowledge (probably first), 2digit foreknowledge) . 3 Strikes is the one of the few games where the contestant can lose even if they knew the price in advance.
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