Price is Right Contestants Row
Before I get to the main topic, an update. Last week I wrote about the process to getting tickets to Burning Man. On Wednesday, I took my chances with the Main Sale. As you may recall, the last hoop to jump through was to be ready to buy tickets at exactly noon on March 30. I was ready. In fact, I had three browsers ready with the link to the sale. To be honest, I’m not sure if this improved my odds, but other sources on Burning Man recommend doing this.
To make a long story short, I did not get a ticket. This was to be expected. At least I tried. Unlike in 2019, the image you see below on my screens was updated about half an hour after the start of the sale that tickets were sold out. You may wonder if I clicked “back,” which the screen says would not help. I did not.
So, it doesn’t look like I will make it to Burning Man this year. That’s okay. I have quite a few other vacation ideas.
Onto the main topic, which is Contestants Row on The Price is Right. This game is played six times on every show. For those who don’t already know, here are the rules:
- Four players are chosen to compete in playing the next pricing game.
- An item is shown, which will usually have a value between $1,000 and $2,000. For example, a nice bicycle.
- The players, in a specified order, will make a bid on the value of the item.
- The player whose bid comes closest to the actual value, without going over, wins the item and gets to play the next pricing game.
- If all four players overbid, then they rebid, in the same order, being told to not bid more than the lowest bid the previous round. This will continue until there is a round where at least one player does not overbid.
What should be your strategy in this game, assuming you know nothing about the value of the prize?
Most contestants on the show have terrible strategy. Let’s say you are the last to bid and the previous bids are $1,500, $1,600 and $2,400. The best bids, again knowing nothing about the value of the item, would be:
- $1: This covers a $1499 range - values from $1 to $1499, although prizes are never close to $1.
- $1601: This covers an $800 range – values from $1,600 to $2,399.
- $2401: This covers an infinite range – values from $2,400 to infinity.
You see players all the time making bids that give up range unnecessarily. In the example above, $2000. That gives up the range from $1600 to $1999, compared to a bid of $1600, for nothing.
No rule of thumb will cover every situation. Just try to cover as wide range as possible, especially in the range where prizes tend to fall.
What if four logicians were playing, you may ask? Let’s assume the logicians know nothing about the value of the prize. To make explanations easier, let’s assume that the contestants may make bids to the penny.
Let’s start with a simple situation where the value of the prize is random and chosen from a uniform distribution from $0 to $1000. There is obviously a positional advantage to going last. I won’t get into the math, but here is how the four logicians should bid, in order from first to last to bid:
- Player 1: $777.80
- Player 2: $555.57
- Player 3: $333.33
- Player 4: $0.01, $333.34, $555.57, or $777.79.
The key is the first three players want to put all subsequent players nearly to an indifference point. They each want to cut off as much space as possible, without motiving a subsequent player to bid $0.01 more than them.
If they bid in this way, player 4 will have a 33.3% chance of winning, regardless of the four possible bids I listed for him. Each of the other players will have a 22.2% chance of winning. I added one or two pennies to the bids of players 1 and 2, to make sure players 3 and 4 didn’t bid over them by $0.01.
However, this is an unrealistic example, as the value of prizes tend to follow more of an exponential distribution. To make it more realistic, assume the value of the prize is chosen randomly from an exponential distribution with a mean of $1,000.
Without getting into the math, here are the optimal bids under the assumption above:
- Player 1: $1,504.08
- Player 2: $810.98
- Player 3: $405.47
- Player 4: $0.01, $405.48, $810.99, or $1,504.09
The probabilities of winning will be the same as under the first case, 33.3% to player 4 and 22.22% to all the others.
That is all for this week. Until next time, may the odds be in your favor.