Choosing a Game Show Briefcase

[quote]LiveFromThe781 wrote:

they know whats been eliminated though, hes referring to a show where the whereabouts of the case are known. the “bankers” offer a wager to buy the briefcase based on the likelihood the player has it because they open up so many cases. the difference is that the million dollars isnt always a million, there could only be a 400,000 and 20,000 case, im basing this off my recolection of only seeing the show once or twice, but im pretty sure thats how they do it.[/quote]

I’ve seen the show. The original problem as stated in this thread involves there being only two cases left, one of which contains a million dollars. Whatever two amounts are left in play, you’re equally likely to have as you are to have the other, assuming you haven’t quit before then.

[quote]etaco wrote:
Your expected value is essentially 500k so if that is all we’re going on then you should reject any offer less than that.[/quote]

How do you figure? The average value of a briefcase at the beginning of the game is well below that, hence the shitty offers you get from the banker.

[quote]LiveFromThe781 wrote:

they know whats been eliminated though, hes referring to a show where the whereabouts of the case are known. the “bankers” offer a wager to buy the briefcase based on the likelihood the player has it because they open up so many cases. the difference is that the million dollars isnt always a million, there could only be a 400,000 and 20,000 case, im basing this off my recolection of only seeing the show once or twice, but im pretty sure thats how they do it.[/quote]

I’ve seen the show. The original problem as stated in this thread involves there being only two cases left, one of which contains a million dollars. Whatever two amounts are left in play, you’re equally likely to have as you are to have the other, assuming you haven’t quit before then.

I would punch Howie Mandel in the face then fuck number 17.

I would love to fo on that show. I’d be a prick by making the game really boring for the viewers.
I’d select case no1, and then open every case in order 2,3,4 and so on.
Has anyone done this before? I mean, you have the same chance anyway. I don’t really have lucky numbers.

[quote]Doyle wrote:
I would love to fo on that show. I’d be a prick by making the game really boring for the viewers.
I’d select case no1, and then open every case in order 2,3,4 and so on.
Has anyone done this before? I mean, you have the same chance anyway. I don’t really have lucky numbers.[/quote]

Yes someone did this before.

It was just as exciting.

(That is it was still boring as bat shit).

[quote]LiveFromThe781 wrote:
reject anything less than 500k? why?

i would accept 400k if it boiled down to a 50:50 with 1M

50% says i get nothing
100% says i get 400k (or whatever it is after taxes)

you might feel shitty after if you had the 1M in your briefcase but reality is you made the right choice because that just could easily have said $1.

risk aversion is all fine in theory but when you have 3 kids to put through college at home, gas & electric bills plus food to put on the table how do you explain to them your economics course said itd be wiser to take the shot at 1 million because they didnt offer you 10% more than they “should” have.[/quote]

Your response dovetails nicely with some interesting research that won somebody a Nobel price for economics.

When you’re faced with the following decision:

  1. Take a 50/50 shot at profiting $1 million, or
  2. Take a 100% shot at profiting $400,000,

most people will go with option 2. Now, the logical option is option 1, because you will earn more money on average. But people don’t like putting their profit at risk.

However, rephrasing the question to

  1. Take a 50/50 shot at turning a $1 million loss into a break even, or
  2. Take a 100% chance of a $400,000 loss,

most people will take option 1. They will take Option 1 despite the fact that it’s the logically incorrect answer: you will lose more money on average taking Option 1 over Option 2. Yet most people do.

The hypothesis is that people are risk-averse when there’s a chance of losing profit, but take risks when there’s a chance of eliminating loss.

Very interesting research, and I found it amusing that Live just unknowingly demonstrated it for us.

[quote]thesixteenth wrote:
jtrinsey wrote:
I am doubting myself, so somebody smarter than me tell me where this line of mathematical logic falters:

1.) Your initial probability of choosing the $1,000,000 case is (1/26)

2.) The probability of it being in either case at the end is 1, or 100%, however you prefer. It has to be in one of the two cases.

3.) If the probability of it being in your case is (1/26), and the probability it is in both cases combined is 1… then why is the probability of the other case not (25/26)?

But then I am confusing myself because then it seems that you could do the same thing for the $1 case. That is why I am thinking it may not matter whether you switch or stay.

Your initial probability is 1/26, but after you eliminate one case, it is then 1/25 that it has the million. And so on and so forth, until it is 1/2. People are confusing this problem with the Monty Hall problem, but it’s different because in that scenario, the host knows which case has the $1 million dollars, whereas in this one, he has no idea. You could have picked it at any time throughout playing the game and eliminating cases, you just happened not to.
[/quote]

This is correct. The Monty Hall problem does not fit this scenario. The last two cases would be a 50/50 chance.

[quote]skaz05 wrote:
I would punch Howie Mandel in the face then fuck number 17.[/quote]

This is also correct.

[quote]etaco wrote:
Your expected value is essentially 500k…[/quote]

How did you come up with that number? It’s around 130,000.

EDIT: Nevermind. I just realized your number is from this 50/50 scenario.

[quote]tGunslinger wrote:
The hypothesis is that people are risk-averse when there’s a chance of losing profit, but take risks when there’s a chance of eliminating loss.
[/quote]

You can see this play out all the time in casinos around the world.

When people lose, they tend to continue playing, hoping for that long shot to bring them out of the hole. They generally lose big.

When people win, they tend to tighten up with their bankroll and place smaller bets.

[quote]malonetd wrote:
tGunslinger wrote:
When people win, they tend to tighten up with their bankroll and place smaller bets.[/quote]

However, how many people win big at the beginning and then lose it by playing recklessly? How many times have you heard the old “I was up huge but left with $20” senario? People never know when to quit gambling. This year I tore it up the first half of the NFL season, and just stopped betting at Week 9 because I knew that I was just bound to start losing. I tracked my picks anyway on a free site and I was correct, I would have lost it all by now.

[quote]tGunslinger wrote:
LiveFromThe781 wrote:
reject anything less than 500k? why?

i would accept 400k if it boiled down to a 50:50 with 1M

50% says i get nothing
100% says i get 400k (or whatever it is after taxes)

you might feel shitty after if you had the 1M in your briefcase but reality is you made the right choice because that just could easily have said $1.

risk aversion is all fine in theory but when you have 3 kids to put through college at home, gas & electric bills plus food to put on the table how do you explain to them your economics course said itd be wiser to take the shot at 1 million because they didnt offer you 10% more than they “should” have.

Your response dovetails nicely with some interesting research that won somebody a Nobel price for economics.

When you’re faced with the following decision:

  1. Take a 50/50 shot at profiting $1 million, or
  2. Take a 100% shot at profiting $400,000,

most people will go with option 2. Now, the logical option is option 1, because you will earn more money on average. But people don’t like putting their profit at risk.

However, rephrasing the question to

  1. Take a 50/50 shot at turning a $1 million loss into a break even, or
  2. Take a 100% chance of a $400,000 loss,

most people will take option 1. They will take Option 1 despite the fact that it’s the logically incorrect answer: you will lose more money on average taking Option 1 over Option 2. Yet most people do.

The hypothesis is that people are risk-averse when there’s a chance of losing profit, but take risks when there’s a chance of eliminating loss.

Very interesting research, and I found it amusing that Live just unknowingly demonstrated it for us.[/quote]

well, i am smarter than the average bear