Strategies for Success in the Price is Right ‘Then or Now’ Game

I have a passion for game shows outside of gambling, particularly intrigued by the game theory elements they present. One show that captivates me is ‘The Price is Right.’ I'm inspired to pen a book that outlines the mathematically optimal strategies for each game on this show, all while being oblivious to the prices involved.

In this edition of the newsletter, I'll focus specifically on one game, ‘Now or Then.’

Here are the rules:

1. Imagine a circular board resembling the Trivia Pursuit wheel, divided into six segments. For clarity in our discussion, let's assign numbers to these segments.
2. Each price featured will either be the current value, or reflect a price from approximately a decade ago.
3. The player may pick any slice.
4. Contestants need to determine if the item in the chosen segment corresponds to the price of 'Now' or 'Then.'
5. To secure a victory in this game, the contestant must correctly identify three consecutive segments on the wheel (for example, segments numbered 4, 5, and 6).
6. Although the show doesn't emphasize it, traditionally there are four items marked as 'Now' and two items marked as 'Then.'

With the above points in mind, it's possible to ensure a win in this game without prior knowledge of any prices. Pay particular attention to rules 2 and 6; I suspect that few contestants are aware of both.

Here is a Youtube example.

Pay attention at the 3:52 mark where Drew emphasizes that in order to win, the player must correctly identify the pretzels, but he adds “You have the freedom to choose any segment.”

Link to fan site: https://priceisright.fandom.com/wiki/Now....or_Then

The answers will be uncovered below the images captured from the show.

Here is the answer:

To begin, select any three adjacent segments and assume they are all 'Now.' For instance, choose segments 6, 1, and 2 at the top.

Here's the approach to take based on what occurred with the first three segments.

1. If all three were NOW, then you win!
2. If at least two of those segments are from the 'Then' category, then the remaining segments must represent the 'Now' prices. Secure your win by marking the other three segments as 'Now.'
3. If there's one 'Then' segment located at either end (slice 2 or 6), choose any value for the two segments nearest to that 'Then' segment. If you locate the second 'Then' segment, the last one must be 'Now.' If you don’t find the second 'Then,' the final 'Then' must occupy the last segment. Note that this scenario was exemplified in the earlier video I mentioned, but the contestant failed to heed Drew’s advice about seeking information from segments other than the critical one.
4. If one 'Then' segment is positioned in the middle (slice 1), then opt for 'Now' for slices 3 and 5. Should both be 'Now,' you can clinch victory by selecting 'Then' for slice 4. If one is 'Then,' go with 'Now' for slice 4 to win.

In essence, the key lies in recognizing that there are two slices marked as 'Then' and effectively narrowing down their positions.

For next week’s newsletter, I’m going to disclose the upcoming question now, allowing you an entire week to ponder and engage with it!

Imagine all 435 voting members of the U.S. House of Representatives participating in a Zoom meeting, scheduled from 9 a.m. to 10 a.m. Attendance for the entire hour isn't necessary; members can join and leave at any random moment within that hour.

What is the probability that at least one Representative's time overlaps with every other Representative on the call? In simpler terms, this means encountering the visuals of all other members during their respective time slots, though not necessarily at the same moment.

Written by: Michael Shackleford