# How to Win the Price is Right ‘Then or Now’ Game

One of my interests outside of gambling is game shows. In particular, I love the game theory aspect of many of them. In particular, ‘The Price is Right.’ I would love to write a book about the mathematically optimal way to play every game on that show without any knowledge of prices.

Here are the rules:

1. There is a circular board with six slices, like a Trivia Pursuit wheel. For purposes of discussion, let's number the slices like this.
2. Each price will be either the accurate price “Now” or at some time about ten years in the past.
3. The player may pick any slice.
4. The player must guess whether the item in the selected slice displays the price specific to "Now" or "Then."
5. The player must get three consecutive slices on the wheel correct (for example, slices 4, 5, and 6) to win the game.
6. It is not stated on the show, but there have been traditionally four “Now” items and two “Then.”

Keeping the above information in mind, there is a way to guarantee winning this game without knowing the price of anything. Rules 2 and 6 are critical. I think few contestants know both rules.

Notice at the 3:52 point how Drew correctly states that the player must get the pretzels right to win; but he then adds “However, you can go anywhere you want.”

The answer is revealed below the images taken from the show

Drew explains the rules to the Now or Then game

Bob returns to the show for a visit

Meet the new male models

First, pick any three slices in a row and guess “Now” for all of them. For example, the top three, which are 6, 1, and 2.

Here is how to proceed, according to what happened with the first three slices.

1. If all three were NOW, then you win!
2. If any two were THEN, then the rest must be NOW. Lock in a win by picking NOW for the other three slices.
3. If you get one THEN on either end (slice 2 or 6), guess anything for the two slices closest to the THEN slice. If you find the other THEN, the remaining slice must be NOW. If you don’t find the other THEN, then the last THEN must be the last slice. Note that this was the situation in the example video I mentioned above, but the player didn’t follow Drew’s hint by fishing for information on slices other than the needed one.
4. If you get one THEN in the middle (slice 1), then pick NOW for slices 3 and 5. If they are both NOW, then you will win by picking THEN for slice 4. If one is THEN, then pick NOW for slice 4 for the win.

In other words, it’s all about knowing there are two THEN slices, and narrowing down the location of them.

For next week’s newsletter, I’m going to give you the question now so that you may have a whole week to enjoy working on it!

Suppose all 435 voting members of the U.S. House of Representatives join in on the same Zoom call, which is scheduled for 9 a.m. to 10 a.m. However, it is not required to attend the entire call, just any part of it. Each member randomly picks an exact moment to enter and leave the call somewhere within that one-hour range.

What is the probability that at least one Representative overlaps every other Representative on the call? In other words, seeing the face of every other member during his or her time on the call but not necessarily all at the same time.