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?