# Game Show Math

I recently saw a couple minutes of “Are You Smarter Than a 5th Grader?” and the experience left me bewildered. Not by the elementary school kids. Let’s say the contestant was named Rick. He was around 40 years old. He had been playing for a while and had reached \$11,500 in winnings. The host then announced that Rick had an opportunity for a Big Bonus Question. The host let Rick know that the question was a 5th grade question in the category “Social Studies,” and then he offered Rick a choice. Here were the alternatives: 1) Rick could quit now and walk away with the \$11,500 in winnings. 2) Rick could try to answer the Big Bonus Question. If he got it right, he would win \$115,000. If he got it wrong, he would walk away with \$2,500. Of course, Rick can’t know the question before he makes his decision. What would you do? Rick decided to quit and walked away with \$11,500. (That’s also what his wife wanted him to do, but that’s another story.)

\$11,500 is not life changing money. \$115,000 can be life changing money. I would go for broke.

I always figured \$2 million was life changing money - anything less and I would still have to work for a living. \$115,000 is some nice help with the mortgage, not life changing.

I don’t mean “quit working” money. I mean, “buy a new house” money, or, let’s take the whole family to Bora Bora money. That can be life changing for middle class people. I am not middle class, and \$115,000 would change my life considerably right now.

I know what you meant, I was just bored and had to post something or go back to dynamic rebalancing strategies…

You’r risking 9k for a potential 100k. Unless you are a total idiot I would think you can answer the question correctly at least 1 out of 10, making it a good bet. Definitely go for it.

…apparantly his wife knows he’s an idiot also because she wanted him to stop too.

You 100% go for it. If you don’t, you’re a total moron. The one thing about game shows that pisses me off is this. You came in with \$0.00 and you’re not paying to be there. So what’s the point of not going for it? But that’s actually a different point from this. This guy is just a moron. Say its a 1 and 10 chance of getting it right like Analyze_This said. .1(115,000) + .9(2,500) = 13,750 I am amazed the game show is set up that way. I wonder if they do any screening for contestants to make sure they’re dumb enough not to screw the network out of their money.

But you have no idea what the question is, so where do you get the 1 in 10 chance? It might be 1 in 1000 chance. I have never seen the show, but it doesn’t sound as if they gave him a chance to pull a number out of a hat. If that were the case, I would agree with you, the guy is an idiot. But the question could be so outrageous, that he would have no chance at all of answering it. In which case he would be better off with the \$11,500.

The game is called “Are You Smarter Than A Fifth Grader”…

also you don’t know contestant’ degree of risk aversion. you take the 13,750 gamble every time if you’re risk neutral but not necessarily if you’re risk averse, which just about everyone is.

Maybe he flunked social studies in high school?

"The one thing about game shows that pisses me off is this. You came in with \$0.00 and you’re not paying to be there. So what’s the point of not going for it? " This logic is not entirely sound. While in this case it certainly seems like the expected value is greater than the alternative, in many cases it’s not so clear what the EV is, and even when the EV is known exactly, there’s still a difference between 100%*(X) and 50%*(2X).

You also have to remember that expected value is really only relevent with situations that have multiple events. While this may come up alot from the show’s perspective, its a single event for each player.

It’s a loss aversion/regret aversion/anchoring thing. If the guy answers the question incorrectly he’ll view it as a loss of \$9,000 and wants to avoid the regret of that loss.

I mean I GET why he would make that decision… I just still think its stupid. If you’re playing with house money, why be risk-averse/regret-averse? No matter what you’re walking out of there with cash. Go big or go home. (especially since these were questions from 5th grade curriculum)

"The one thing about game shows that pisses me off is this. You came in with \$0.00 and you’re not paying to be there. So what’s the point of not going for it? " Sounds a bit like life itself (coming in with nothing and life itself doesnt have a clear cost associated to it). Yet we dont consider the money we collect along the way as house money and risk/regret aversion reigns supreme, given that we are all very unlikely to go “all-in” at any point in our lifetimes.

"The one thing about game shows that pisses me off is this. You came in with \$0.00 and you’re not paying to be there. So what’s the point of not going for it? " Disagree, winning the whole thing may be the only way it makes a difference for you not the same for everyone. Also you are falling into the “House money” or “mental accounting” mistake. I would take the bet too and I think the contestant may be more inclined if the question had been framed - Here you just won 115,000 now you can a) keep the money if you take question and answer correct, b) return 112,500 if you take question and get it wrong or c) dont take the question just return 103,500. Now I sure as hell am going to try to keep it all. Ref: “Why smart people make big money mistakes”