Game Show: The Wall

I caught this NBC gameshow already in progress last night. Apparently, two person teams of players answer questions, then get to choose one of seven gates to drop a basketball sized ball down a two story "Plinko" board. At the bottom are a variety of money amounts in slots at the bottom. Slot amounts can vary from $1 to $1,000,000. If they answer correctly, the amount that the ball lands in is added to their total, if incorrect, the amount is subtracted (but they cannot go below zero).

In the first part of the game, one of the players is shown the possible answers to the multiple choice questions, then asked which slot to place the ball (or balls, as a "triple" option is available). Meanwhile, the other player is in an isolation booth, and has to answer the multiple choice question that will determine whether the balls will be added or subtracted to their total. There are a few rounds like this, and the number of balls or the amount in the "really big" slot going up each time (in the final round, the big slot is worth one million dollars).

At the conclusion of the "ball" part of the game, the player in the isolation booth is given a 'contract' that has a guaranteed amount on it. The amount of the offer depends on something that happened in the beginning of the show that I missed, and $20k for each question they answered correctly. The isolated player, who does not know what happened on the Plinko has to decide whether the team will take the guarantee, or tear up the contract and take the results of the Plinko.

The team last night got up to $1.1 Million, but ended the game with $0 on the wall. Unfortunately, the isolated player tore up the contract that was worth a little over $35k, so they ended up with nothing. It didn't help that the isolated player got every multiple choice question wrong, so all those balls were negative to their total.

The question for the poll is, what strategy would you use if you were the player in the isolation booth?

Ah, another game show where they will stretch out the nothing segments to reduce prizes awarded.


I would have to know more about who is answering the questions and what kind of questions are normal. If it is people I do not know, I would take the contract. If I knew my crew, I would take the wall.

I watched about 15 minutes in the middle of an episode and couldn't figure out what was going on. I need to watch it from the beginning to have anything to say.

Quote: Wizard

I watched about 15 minutes in the middle of an episode and couldn't figure out what was going on. I need to watch it from the beginning to have anything to say.

That source of all wisdom has a pretty good overview:

https://en.wikipedia.org/wiki/The_Wall_(game_show)

The show seems like a rehash of possibly the oldest game show idea in the book--Prisoner's Dilemma. If you're the player in the booth, your decision is going to be dependent on whether you think your partner is a smart person or a moron. If you think they probably butchered the Round 2 and 3 multiple choice questions, you take the contract.

There's also a leftover rehash of the Deal or No Deal trope. You have to assume that the EV of the contract is lower than the EV of proceeding onward--in this case, taking the player bank. But a player who has observed his partner's poor performance during Round 1 may be inclined to grab whatever contract is offered--which means that the show host will be inclined to offer less in that contract.

So the fact of the matter is that as with most variations of Prisoner's Dilemma, you can't make an intelligent decision in the initial iteration. In this case, you have to know to what extent the player's (the one who answers the questions in later rounds) performance affects the offer in the contract--as that is the only information that the isolated player has to guide his decision. So you could make a much better decision after, say, the 30th show. Multiple iterations of cooperation-based games allow the formulation of an optimal strategy.

It's not the prisoner's dilemma, as you actions in the booth are in isolation from the actions of the player outside. It doesn't matter how good or bad your team is... the person in the booth is the only one answering questions. According at least to the source of all wisdom.

The further to the right you drop a ball the better the result will be, on average, but the ball dropper only gets to guess how well the booth player will do, and the booth player only gets to guess how well they really did.

The final offer is based on the first round + 20 grand per correct question. They don't know how much the additional is, just it's at least what they went in with.

So very little information except based on knowing how well you did in the booth, and hoping the giant plinko machine was kind to you.

I don't know how the "base" amount of the final offer is determined, as I didn't catch that part of the show, but the one I did see was around $35k. Even if they got all the questions right, the final offer would potentially be ~$120k max? About half the slots are over $100k. The other half were like $1 or $10.

The "big" money slot was positioned closer to the right edge of the board, so selecting drop gates 6 or 7 would put the ball almost directly over it. I assume the most common distribution for a ball entering the plinko is straight down.

Quote: TheCesspit

It's not the prisoner's dilemma, as you actions in the booth are in isolation from the actions of the player outside.

So very little information except based on knowing how well you did in the booth, and hoping the giant plinko machine was kind to you.

That's exactly what the Prisoner's Dilemma is. Each prisoner doesn't know about the other prisoner's choice, and only has past history to go on; if there's no past history, that's where the dilemma lies.

Quote: stinkingliberal

That's exactly what the Prisoner's Dilemma is. Each prisoner doesn't know about the other prisoner's choice, and only has past history to go on; if there's no past history, that's where the dilemma lies.

The outside the booth player makes no choices, but has information. There is no collaboration/betrayal matrix, or benefit for betraying the other person. I've seen other game shows that do use the prisoner's dilemma. The players do know each other well (seem to be couples or friends) and they can have agreed to always do plan X. Only one person has a choice to take the offer or take the bank. Both players get to share either the bank or the contract.

I don't believe this show, from the set up and what I've read and seen, is the prisoner's dilemma.

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The contract is the amount they earned in round 1, plus $X per correct question (I believe X is 20,000, but not sure if that varies)... but with no way of knowing how may questions they got right before making the choice. So you could have an idea 'I have $30,000, plus I reckon I got 3 questions right, so $90,000.... now is that more or less than the random chance amount from outside'.

Though it's not quite random... the player outside can manipulate the odds of getting a higher payout for each right answer (or bigger penalty for wrong question) by how far right they place the ball, but as the big amounts are flanked by $1's, then it's very swingy.

I think if your confident you got over 50% of the question right, and 50% of the questions are in subjects your partner knows you know about, you take random. Otherwise you take the guarantee. Of course, the Dunning-Kroeger effect comes into play, where you may not know how badly you did, and have a greater level of confidence in those subjects you know a little about.

Quote: Ayecarumba

I don't know how the "base" amount of the final offer is determined, as I didn't catch that part of the show, but the one I did see was around $35k. Even if they got all the questions right, the final offer would potentially be ~$120k max? About half the slots are over $100k. The other half were like $1 or $10.

The "big" money slot was positioned closer to the right edge of the board, so selecting drop gates 6 or 7 would put the ball almost directly over it. I assume the most common distribution for a ball entering the plinko is straight down.

Yes, it's like a Pascals triangle for the distribution. And at the edges, one side of the distribution is heavily weighted to the edge.

This based on watching a couple of clips and reading the outline on wikpedia and another site. I may have got some subtleties wrong. There are extra bonus and penalty balls just chucked in regardless of your question answering, so it adds to the swing. I believe $120-190k was the max theoretical offer.

In the episode I watched, the last round, in which one slot was worth $1 Million, consisted of four "green" balls which add to the total, four "red" balls that subtract, and four "white" balls that turned green or red depended on getting the answer to the questions right or wrong. The four red balls had to be launched from the same gate as the four green balls.

The sequence for the player on stage was
1) Select one of the seven gates to release a green ball. The ball would be dropped and the amount in the landing slot would be added to the team's potential "Wall Total".
2) Repeat three more times. After the four green balls, the team I saw had $1.1 million.
3) Question balls: The stage player got to see the answers, then decide which gate to start the ball(s) from. It is "ball(s)" because the player on stage was given the option to "Double Up" (launch two balls simultaneously from the same slot), then "Triple Up" (launch three balls simultaneously) I don't know if you only get this option when the prior question is answered incorrectly?. The risk is that a wrong answer has the potential to wipe all the winnings off the board quickly, since all the balls would be red. On the other hand a $3 million dollar collection would be possible if the player on stage decided to triple up, the isolated player got the question correct, and all three balls ended up in the same $1 million slot.
4) Four mandatory red balls. There is nothing to decide here, as four red balls are dropped, one at a time, in the same sequence and gates as the first four green balls. As the position and amounts in the slots did not change, it is natural to assume that in the long run, these four red balls will cancel the amount earned in the first four green ball drops. In the episode that I saw, the first four green balls earned 1.1 million, and the last four red balls subtracted ~900,000. Unfortunately, the isolated player missed every question, so all the "swing" balls were red, and took out the $200,000 potential "Wall Total" (by like $2,000).

It turns out the team had decided ahead of time to take their chances on the wall no matter what, and the isolated player followed through by tearing up the contract for $35k. They walked away with nothing.

Questions were like:
-- Which of these four Space Shuttles flew the last mission?: Atlantis, Endeavor, Enterprise, Discovery
-- How many double stitches are on a major league baseball? : 108, 118, 128, 138
-- Which is the tallest?: Washington Monument, Seattle Space Needle, Eiffel Tower, Something else that I can't recall