Race Game strategy

On The Price Is Right, one of the older and more popular games is the Race Game. On the 40th season premiere, the game was played for a record-breaking four cars.

For those unfamiliar, a quick rundown of the game play:
Given 4 prizes and 4 price tags, place the appropriate tag to the matching prize. You will be shown how many matches are correct, but not which ones. 45 seconds are allotted to make as many changes necessary to get 4 matches. Contestants tend to make 2 to 4 guesses per game.

The Question:
Assume you have no idea what price goes on what prize.
What is the best strategy to win given the time constraint?
How would you handle swapping price tags if after your first guess, you had 0, 1 or 2 right?

They took that video down. Here is a new link. Working on a strategy.

:45 not very long to have a full blown strategy. How many pulls is the max you can get in? 5? It's not like Bonkers where you could get in at least a dozen.

This is the game of MasterMind, but limited to four colors without repeats.


My personal strategy is this: After the first pull, regardless of how many were right, I'd switch only A & B.

Note that the results cannot both be 2 or 3 right, nor 1 then 3, nor 3 then 1.

If both results were zero, then switch the two pairs.
If both results were 1, either C or D was correct. Do a three-way swap.
If the results were 0 then 2, A & B are now right, switch C & D.
If the results were 2 then 0, A & B are originally were right, switch both pairs.

If the results were 1 then 2, one if each pair are now right. Switch one from each pair.
If the results were 2 then 1, one if each pair were right. Switch A & B back, then switch one from each pair.

From this point, consider just the last result and the prior result, and use the rules above.

Quote: Dween

The Question:
Assume you have no idea what price goes on what prize.
What is the best strategy to win given the time constraint?
How would you handle swapping price tags if after your first guess, you had 0, 1 or 2 right?

Are the prices and items so close that you would really have no initial idea what goes where (or at least what doesn't go somewhere)? What is the typical range of prices?

I have tried working on this problem off and on over the years and have never perfected an optimal strategy. Considering it is a fairly simple game, I'm not proud to admit that. Perhaps it is time to take another crack at it.

You know, there are sometimes prizes that are the "obvious" low or high... sometimes there's a large spread, others not. But they have also been using more "exotic" prizes with wildly ranging prices that are hard to peg.

Try this: I picked a random Race Game youtube clip (a recent one).
Price tags:
$849
$1475
$2497
$3600.
(That's a wide spread!)

Prizes were:
55" Samsung 3D LCD TV
3-speed riding lawn mower
LG All-in-one Washer Dryer
An "impressive" treadmill

Are the answers obvious? Maybe you need to watch the clip to visualize the prizes. Even still, could you do it in one go?

Highlight below for answers
3D TV: $3600
Mower: $849..
Washer/Dryer: $1475
Treadmill: $2497

Okay, I've been working on this. My strategy is rather complicated, and would certainly be difficult to implement under the pressure of the show, but the expected number of turns is 3.58333. I can say that with every guess under my strategy the player will have a chance of getting all four right. Here are the odds of each number of turns required

1 4.17%
2 12.50%
3 29.17%
4 33.33%
5 16.67%
6 4.17%

Quote: Dween

You know, there are sometimes prizes that are the "obvious" low or high... sometimes there's a large spread, others not. But they have also been using more "exotic" prizes with wildly ranging prices that are hard to peg.

Try this: I picked a random Race Game youtube clip (a recent one).
Price tags:
$849
$1475
$2497
$3600.
(That's a wide spread!)

Prizes were:
55" Samsung 3D LCD TV
3-speed riding lawn mower
LG All-in-one Washer Dryer
An "impressive" treadmill

Are the answers obvious? Maybe you need to watch the clip to visualize the prizes. Even still, could you do it in one go?

Highlight below for answers
3D TV: $3600
Mower: $849..
Washer/Dryer: $1475
Treadmill: $2497

I didn't watch the video, but I missed all four on my initial guess. However, I think I would have corrected myself in two more turns. I know the TV was one of two, and the washer was one of two, so that was an easy fix. The others I would have guessed, and if wrong, switched.

Do you think the yelling from the audience helps any of the players?

Quote: Ayecarumba

Do you think the yelling from the audience helps any of the players?

Seeing as a player usually has many companions with them, and seeing as just about everyone has a smartphone, couldn't the 2-4 people in their group just price the 4 items up for bids and direct the player?

Quote: Face

Seeing as a player usually has many companions with them, and seeing as just about everyone has a smartphone, couldn't the 2-4 people in their group just price the 4 items up for bids and direct the player?

Probably not. The companions would have to turn on their phones in violation of the show's rules/producer's wishes, search for an item in violation of the show's rules/producer's wishes, relay that information to the contestant onstage in violation of the show's rules/producer's wishes, and not be caught. Why risk a disqualification for cheating when you could win fair and square? By the way, a friend of mine was on TPIR and played that game onstage...

Quote: cclub79

Probably not. The companions would have to turn on their phones in violation of the show's rules/producer's wishes, search for an item in violation of the show's rules/producer's wishes, relay that information to the contestant onstage in violation of the show's rules/producer's wishes, and not be caught. Why risk a disqualification for cheating when you could win fair and square? By the way, a friend of mine was on TPIR and played that game onstage...

Oh. Wasn't privy to the rules. Makes sense and is kind of obvious. Back to the corner I go...

Quote: Ayecarumba

Do you think the yelling from the audience helps any of the players?

No. It is more of a distraction.

The only way it could help is if the contestant had ONE companion, who knew both prices for an initial guess, and understood the strategy enough to give fast advice.

Otherwise, it's more of a time consumer.

Quote: Face

Seeing as a player usually has many companions with them, and seeing as just about everyone has a smartphone, couldn't the 2-4 people in their group just price the 4 items up for bids and direct the player?

I wouldn't be surprised if the studio has cell and WiFi jammers.

I attended a TPIR taping several years ago and we had to check our cell phones outside the studio. Not sure if that has changed in recent years.

The audience yelling makes it more fun but generally it isn't very helpful since everyone is yelling different things. Once in awhile you will get audience consensus on simpler decisions.

I've read stories about folks who go to many tapings and learn the prices of the items since prizes are often repeated. Since then TPIR has started to mix it up by including things such as "2 years of a cell phone plan" or changing the option packages on the cars in an effort to alter the prices.