jennings rampage

One for Julie Klausner

If you believe Bob Barker, today’s episode of The Price Is Right was historic because it was the first time someone rolled all ones and sixes in the Dice Game, thus automatically winning the brand new car. And while the probability of doing that is 1/81 (1/3^4), making it sort of special, today’s episode of The Price Is Right was important to me because it was the first time I’ve ever seen what I consider to be nearly proper strategic bidding in all six of the preliminary bidding games in Contestants’ Row.

In order to explain the best strategy for bidding in Contestants’ Row, I’ll first need to set up a rudimentary mathematical model to demonstrate how the bidding process works. (When I’m cleaning this essay up for inclusion in my giant collection of essays, I’ll include colorful diagrams. For now, I’ll have to use sentences, and feel free to fashion your own diagrams from these descriptions.)

Think of the winning bid as a single point on a number line of the positive integers, and think of each bid as “staking out” a section of that number line from the point of your bid upwards until you hit another player’s bid. If you bid $500, and another player bid $700, then you win if the actual retail price is greater than or equal to $500 and less than $700. Of course, you can’t go over; if you bid $500 and the actual retail price is $499, you’re fucked.

Let’s think about this game with only two players. The first player would make their bid, which we’ll cryptically call $X. The second and final player has the advantage of knowing the first bid and deciding whether to stake out the section of the number line above that bid or below it. If the second player believes the first player’s bid is too high, he’ll bid $1 and claim the section of the number line from $1 to $X-1; similarly, if he believes that bid is too low, he should bid $X+1 and stake out all higher bids. Of course, by bidding $X+1, the second player gives the first player a chance to win only if his bid was exactly right, so we see that the last player has a clear advantage in this game. Ignoring the cash bonus and the kiss from Bob Barker for a perfect bid, there’s no advantage to trying to nail your bid — go for the win and the chance at the brand new car, and stake out the largest possible section of the number line that you believe has the winning bid contained in it.

The game should be played similarly if there are three players. After the first two players place their bids, we’ll be in one of two scenarios: bids of $1 and $X, or bids of $X and $X+1. At this point, the third player will have the same decision to make based on his opinion of the $X bid, and should stake out the section of the number line where he thinks the actual retail price is hiding. If we’re in the first scenario, the third player will bid either $2 or $X+1; in the second scenario, either $1 or $X+2. Again, the third player has a tremendous advantage, and at least one player will be fucked out of a chance to win.

Now, expanding the game to four players, which is what we see in Contestants’ Row, follows similar logic. There are three scenarios now: bids of $1, $X, and $X+1, bids of $1, $2, and $X, or bids of $X, $X+1, and $X+2. In all these scenarios, the fourth player still has one question: is the highest bid too high or too low? If it’s too low, bid $1 more than the highest bid; if it’s too high, bid $1 more than the lowest bid. This yields four possible scenarios (which I leave to the reader to describe), and at most two players with more than one possible bid on the number line staked out. This game should have little suspense.

Now, I’ve never actually seen the bidding go down like this, so there’s either a problem with my analysis or there’s a problem with the people playing the game. I choose the latter.

I’ll make a rare concession and lower my standard for rationality as it pertains to this game. There may be a psychological barrier to the second or third player bidding $1 or $1 more than another player, knowing that there are still bids to be made, even though it’s still the best strategy available. Perhaps the second and third players believe that they can influence the bids to come by taking a slightly higher or slightly lower bid than they’d want to take. But that fourth player should definitely be bidding either $1 or $1 more than another player, in order to maximize their chances of having the actual retail price in their section of the number line. If they think the prize is $1000, and the lowest bid less than that is $900, there’s no point in pussyfooting — the fourth player should bid $901 and maximize their chances of winning.

This sort of strategy isn’t rare, but it’s not as common as it should be. It should happen 100% of the time, but based on my totally non-scientific pre-caffeine only-half-watching-most-of-the-time observations, it only happens about 40-50% of the time.

We’ve all seen the show, and we all have an idea of what’s going on: when the player with the hypothetical $900 bid is an archetypical sixty-eight year old grandmother of twelve with a hand-sequined t-shirt that reads “I Love Bob,” and the player that would hypothetically want to bid $901 is a staff sergeant in the United States Marine Corps in dress uniform, that Marine knows he’s going to get his ass murmured out of the building if he fucks Grandma. It’s considered bold and courageous to bid $1; it’s considered cold and cowardly to bid $1 more than another player. This game isn’t played in a vacuum; if the Marine bids $901 and the actual retail price is $800 and it didn’t matter, the audience doesn’t apologize for their judgment.

Are we really willing to reduce our chances of winning just to avoid the judgment of a studio full of strangers and the ribbing of your friends back home? What are the standards of sportsmanship on a game show like this? How big is the buffer? Why are we so friendly to a perfect stranger?

But today, I was delighted beyond belief: in the six bidding games, there were a total of ten strategic bids (out of the eighteen total we’d expect), and all six games ended with the fourth player bidding either $1 or $1 more than another player. The crowd wasn’t quite sure what to make of it, but they ate it up when Grandma made a $1 bid to close out the final game. (She lost.) This is clearly progress, and clearly a step in the right direction. Soon, as more contestants play this game correctly and its poor design becomes evident, we can only hope that it will be replaced with a more equitable system to select players for the pricing games out of Contestants’ Row.

Next time: why Plinko is clearly a scam, and when it’s statistically correct to not spin again during the Showcase Showdown. I could write a doctoral thesis on The Price Is Right.