A simple new game show on NBC, but surprisingly interesting. The premise:
The player is shown 26 identical briefcases (held by models with lots of cleavage, but that’s irrelevant). Each is secretly labelled randomly with a dollar value, between $.01 and $1Million, roughly doubling: .01, $1, $2, $5, $10…$100k, $250k, $400k, $750k, $1M. The player picks a briefcase at random to keep as “his”, without knowing its value.
The player then chooses 5 of the remaining briefcases, which are then opened to reveal their value.
The player is then offered a deal: swap their briefcase for x dollars. If they decline, they get to pick a few more briefcases to be revealed; followed by another offer.
Each subsequent offer can vary depending on the dollar values remaining. If the contestant has picked (and therefore eliminated) high dollar values, the offer could go down. If they’ve eliminated low dollar values, the offer could go up.
It’s been a while since I took Permutations & Probability. Would the “expected value” of the player’s briefcase be determined as: sum of all unrevealed dollar amounts divided by # briefcases remaining? And if the “deal” exceeds that dollar amount, should the player accept it?
My roommates and I only caught the tale end of it last night since the Apprentice came on just after it but i had known about it and simply not been pulled to tune in. Your description sounds right, but the math might be difficult to do in your head.
For example, say there are 2 cases left: $1,000 and $1,000,000. The expected value is $500,500. Now say the banker offers $500,000. This is less than the expected value of the game, but I would take the deal, because to me $500,000 is worth more than half of what $1,000,000 is worth.
Right… I think you’re getting at ‘the marginal value of money’, where the lifestyle change of getting 50,000 may be greater, or maybe less, than the difference in lifestyle from 350,000 to 400,000, or something like that.
Another complicating value (though related) is risk management… ‘how much is it worth to you not to throw the dice’ – whether there’s value in taking slightly less than the average, simply because it reduces uncertainty.
The show from what I’ve seen seems to rely on people not understanding basic “greater than/less than” level math. Every time I’ve seen the show it’s come down to a situation where there are six or seven dollar amounts left and the banker offers a dollar amount greater than 5 of them but significantly less than the last one. And every time they’ve refused the offer. Do they not get what a bad decision that is? Well, obviously they don’t, or they’re just completely blinded by greed.
Well, what you’re describing sounds like a player optimizing his expected value, and might not be dumb at all. The other way to look at it is that with his next selection, he has a 4/5 chance of removing one of the LOWER priced cases and so his offer will go up.
Essentially, the dilemma is capture in the first couple posts here. . .the banker could always offer exactly the expected value, but he likes to fudge with it based on several factors. . .like someone said, the marginal value of money to you, what’s happened with your recent choices. Lots of stuff.
If a player had the opportunity to play the game 1000 times, say, he would always be best served by going with a strategy of maximizing his expected value. Given that he’s only playing once, though, I’m sure he has qualms about leaving $450,000 on the table on a 50/50 chance of getting $1M versus $1.
It’s pretty easy to see what a bad bet that is, but I couldn’t turn it down.
No matter which dollar values are still left when it’s down to 5-6 cases, it’s hard for me to wrap my mind around the idea that that person is close to winning the $1M. There’s still a 1/26 chance of the chosen case holding the million dollars. You pick your case in the beginning, and you can’t change it. How bogus. I’m bad with probability. Does this figure in?
I, personally, would refuse to play until they replace the 26 useless women-as-props with 26 useless hot male underwear models.
The main thing that bothers me about this show, besides the generally melodramatic atmosphere, is the fact that the contestants act like they really need to think and agonize when picking cases to open. If it were me, I’d really annoy the producers: “I have to open six cases? OK, gimme 1-6.”
The chance that you have the million dollar case CHANGES based on what you’ve seen.
The chance that you picked it in the beginning is still the same, but after things have been revealed to you, something called “conditional probability” kicks in.
What’s the probability a person picked the million dollar case? 1/26
What’s the probability a person picked the million dollar case GIVEN (that is, “conditioned on the fact”) that I’ve revealed 10 cases and none had the million dollars? 1/16
ha, first time playing and i did the flash version…i picked the million dollar case…i’d personally have stopped when they offered me 89000 dollars, but it worked out if i wanted to be greedy.
I played the flash game twice, took the bankers offer both time and made out like a bandit. My briefcase held $200 then $5 - I accepted $14,000 and $17,000.
My husband can do the math in his head, and last time the show was on, he would sit there and predict every single time within 5K what the banker’s offer was going to be. He was telling people to not deal when I thought they should deal, and he was right every single time.
I need to find out how to get him on the show. He’d drive them crazy.
I’m sure the atmosphere has a lot to do with it, but seriously, how could you ever felt like you lost in this show (unless you’re REALLY heavily in debt?) “Oooooh, how disappointing! My briefcase has $500,000, but I made a deal for $112,000! Boo fucking hoo. G’bye, debts! Hello, financial freedom!”
See? I’m not sure of your frame of reference, but I can’t imagine feeling burned by settling for $290K EVER, even if my case held $1M.
I think the key to the show (or any game show…only more so with this one, because it’s not that hard to get many thousands of dollars out of it) is to just caaaaaaalm down and realize that if the rest of America thinks you’re a rube for taking the deal for $70,000, big whoop. You’re $70K richer. You can milk the show for thousands upon thousands of dollars simply by playing it safe. Basically, you only really lose if you go for broke.
IOW, I’ll take my $290K deal and grin all the way to the bank.
