Deal or No Deal Math Question

[kosydar 0]

For those of you familiar with the show.....

Tonight this lady had 4 cases left. The values left were $10, $75, $5,000, and $1,000,000. Her deal was for $201,000, and she took it. My roommate said it was a good deal because there was a 75% chance she would end up with less money than the deal. I say it was a bad deal because she was losing money on average. The total amount she could win is $1,005,085 (sum of the remaining cases). Divide that by the total number of outcomes (4, which all have an equal chance of occuring), and her Expected Value is $251,271.25. Every time she takes the deal for $201,000, she loses $50,271.25. Is my math wrong? I'm not saying I'd necessarily turn down the deal, but from a purely mathematical standpoint I think its a poor deal.

[sweetblazer 0]

yes. Because the total sum is only a million. Thats the absolute most she can get not 1005085. Even though i still think your friends math is wrong a bit.

[Chadd 916]

I tend to agree with your roomate. $200k in the bank is hard to pass up.

[kosydar 0]

I tend to agree with your roomate. $200k in the bank is hard to pass up.

I'd take the $200,000 just because I think the emotions would outweigh the math. But that is a sacrifice.

[kosydar 0]

yes. Because the total sum is only a million. Thats the absolute most she can get not 1005085. Even though i still think your friends math is wrong a bit.

The most she can get is $1 million. But the $250,000 is an average of all the possible results, weighted by the likelihood of each one.

[mack 44]

That's just too much thinking. The amount of money per case is arbitrary when you just figure that it's a 25% across the board.

[ambro 0]

Your math is right, but your roomate's logic is more correct. I don't know the details of the show, but from what it sounds like she picks a case and goes home with however much money is in it, or she walks with the 201,000 that she had. There's a better chance of getting less than that than there is to get the $1,000,000, so I'd side with the roommate. I'm also not a big risk taker, so that may explain my choice.

[MNdgame 0]

Well the whole point of their deals is to make them mathematically better on their side, I think thats what they are trying to do...

[kosydar 0]

Well the whole point of their deals is to make them mathematically better on their side, I think thats what they are trying to do...

Of course the deals will be better for the show's side. However, the next guy who went, the total sum of his remaining four briefcases was really low, something like $160,000. His offer was $40,000, which was mathematically "fair". His EV would be $40,000 so that was fair. However, the original lady's deal was only 80% of her EV. So when there is more on the line, the show offers worse deals for the contestants because A. The sum they are offering is much higher so B. People either won't notice or are much more willing to settle because its a lot more money.

[DeI 18 0]

She only had to pick one more brief case, right? If so, she should have taken a gamble, 3-to-1 odds that it would not be 1,000,000 are pretty good IMO.

[Dangles 0]

The shows offer mathematically shouldn't have been $201 000 which I thought was unfair because when you add them all up and divide by four, you dont get $201K. I found that later on in the show when she was still on a had already taken the deal, the lady had $10 and $1M left. The offer than was $500K; which doesn't explain to me.. why not just take the average of them since thats what the "banker" did for the very last offer when there was two suitcases left?

[D3nZ 0]

I've always said yeas it would be great to get out of there with 200,000$ but you went there empty handed. So even if I would get out of there with 200$ I would have been happy just beeing selected and getting a chance to pay diner for the whole family. So sometimes I don't see their point of beeing such crybabies, you went there empty handed.

[capes921 0]

i don't care what the math was, it was the smart move because if she opened up the million, her next offer would have been 5000, way too much of a loss to be able to swallow

[Dangles 0]

Yes, but the next case she opened was the $5000 and then the next one after that was $75, so she was down to the $10 and the $1M

[Eagles39 0]

The shows offer mathematically shouldn't have been $201 000 which I thought was unfair because when you add them all up and divide by four, you dont get $201K. I found that later on in the show when she was still on a had already taken the deal, the lady had $10 and $1M left. The offer than was $500K; which doesn't explain to me.. why not just take the average of them since thats what the "banker" did for the very last offer when there was two suitcases left?

After she makes the deal, and she starts choosing the cases she would have chosen the bank can make the deal whatever it wants, because they are not paying that sum.

[stickfixchaska 0]

Yes, but the next case she opened was the $5000 and then the next one after that was $75, so she was down to the $10 and the $1M

Hind sight is 20/20.

Look at it this way...The bank offers $201k. If she does not take the deal, she had a 1 in 4 chance to walk out with 5x as much money($1 mil). Ok, that would be awesome, but at the same time, she would have a 3 in 4 chance of leaving with (at best) 40x LESS money $5k.

The thought of 40x times less money is all the motivation one needs to made a deal.

[Dangles 0]

But you'd think they'd make it realistic. It's obvious the banker already has the money figured out on whatever case she opens.

[Extremo 0]

the reason they offer less than the average is to try and make the contestant go on as far as possible, it makes for more exciting TV. With those boxes I would definitely have taken the $201k. I guess it depends which way you look at it, I mean she had a 1 in 4 chance of winning a million, how many of us have ever been that close?

[Zach11 0]

forget the cases, i just want the babes that open them B)

In this scenerio i woudl have tried to pick one more case since she had a 1 in 4 chance of not picking the 1mil case. If she would have gotten luckey and picked a low $ case the bankers offer woudl have went up considerably.

200K is hard to pass up though

[Leinad 0]

What was in her case?

[Dangles 0]

$10. "Ladies please..."