Mind Games - Guaranteed $500,000 Or A 50% Chance At $1 Million?

by golbguru on June 8, 2007

You are at some juncture in a television show where you have been given a choice - take $500K right now, or face a situation in which you either win $1 million or you lose it all (well, you get to keep $25,000 but that’s almost like losing it all).

What would you choose?

Personally, this is a no-brainer for me; take the $500K and be happy.

money mind games

However, the dude (Steve) on episode #113 of Are You Smarter Than a 5th Grader, took the 50% chance and lost it all (I am basing this 50 % chance on a two-outcomes basis - either you win it or you lose it. The mathematically true probability of winning the money, is a bit complicated affair to calculate and would be far far less than this). I thought it was a small lesson in “risk perception” there. Perhaps, Steve didn’t have the patience to think it through at the time (public performance pressure and the smell of free money can make people do weird things) - but I am sure he won’t try to make such a bet ever again.

This sort of goes in tune with my post earlier this week about how you would treat a windfall, in which I mentioned a potential tendency to take extra risk (more than reasonable risk) and show excessive optimism, when it comes to free money.

Consider this:

You have managed to accumulate $500,000 in savings. Now, a shrewd friend gives you an honest and genuine investment option - invest it in this so-and-so venture and this will either double your money or you will will get back just $25,000. Would you do it?

Personally, I don’t think many people (in their normal surroundings) will take that risk. Steve’s case was no different - he already had the possession of his $500,000; the money was his to keep and he should have treated it like his hard-earned money - but a combination of factors (most probably the feeling of “free money” and the excessive optimism), made him put his money at risk.

Have you noticed that, in most TV shows, such make-or-break options (options with the highest risk) are usually offered near the penultimate step - around which the participants are at the peak of their optimistic self and most likely to lose it all. :)

Come to think of it, even the gambling industry probably works a lot on this concept. Perhaps (I don’t have any concrete proof here), the worst gambling losses may be occurring when a gambler wins money right at the onset of whatever game he/she is playing. Early wins may be altering the risk perception of a gambler by making him/her overly optimistic on future chances and encourages more gambling. Have you experienced something similar in a casino anytime?

Greed complicates the matters even more.

(Disclaimer: I don’t really *watch* the TV show mentioned above, but sometimes it’s more entertaining than flipping channels ;) )

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{ 27 comments… read them below or add one }

1 Trent 06.08.07 at 5:11 pm

Game shows select for contestants who will be risky like that. That’s why you won’t see an accountant on Deal or No Deal.

2 broknowrchlatr 06.08.07 at 5:50 pm

I’d even take $400k over a 50% chance at $1mm. The first $500k is worth way more than teh second $500k.

3 Super Saver 06.08.07 at 6:20 pm

Golbguru,

It’s only gambling if one doesn’t know the answer. It would have been a 100% chance for $1 million if he knew the right answer, which he didn’t.

Not seeing the choices, I don’t know if I would have gotten the right answer of Explorer I. I would have needed eliminate incorrect answers like Mercury, Sputnik etc to get there.

4 The Digerati Life 06.08.07 at 6:20 pm

I’d fake being a risk taker then if I become eligible as a player, I’ll play conservatively. Wow, that’s a HUGE amount to lose. I bet the dude will regret it to the end of his time. I certainly would!

5 Super Saver 06.08.07 at 6:29 pm

Golbguru,

Here’s another interesting thought.

After answering the Million dollar question, another question is would you keep $50 or risk in on a 50% chance to win $100? Statistically, the answer to both should be the same. So a risk averse game player won’t get past the first correct answer :-)

6 golbguru 06.08.07 at 6:35 pm

Trent: Wow..so there is profiling at these places too? That’s interesting.

broknowrchlatr: I don’t want to say the dollar amount that I would have taken to avoid the 50% chance….it’s much less than $500K and more than $25,000. :)

Super Saver: Probability is counted before the question is put to the guy. For any question in the last round (with no other bells and whistles - like sneak,peek, etc.) the only two options are either his answer is right or his answer is wrong; and hence the probability of the right answer ($1 million) is 50%.

Once the result has been determined the probability is not defined - it becomes a past event so no more “probably outcomes” :)

Also, irrespective of how well you know a certain subject - the host can throw really obscure question at you - the probability that the host will choose a question you know is tending to zero and yet the probability that you answer the question right is 50% (based on two outcomes - right or wrong). I am sure it’s much more complicated than that (considering all the possible wrong answers one can give) but that’s as much as I am willing to stretch it. :)

It’s a bit easier to calculate in case of a multiple choice type questions.

The Digerati Life
: Good luck on the faking part - I am sure they will ask your neighbors and your fellow bloggers before they pick you up ;)

The dude perhaps will laugh it off after many years - but if he is married, his wife is going to make him regret it till the end of time.

7 MoneyNing 06.08.07 at 7:16 pm

He might have got to the 1 million dollar question just because he took risks to get there.

So, we shouldn’t really judge him just by the last question.

8 tanyetta 06.08.07 at 9:07 pm

i would love the opp to decide to take $500K or risk it all. :)

i had to stop watching deal or no deal. i found myself yelling at the tv. i honestly could NOT understand people who would take such chances.

once it hits 6 figures, i’m outta there. period. guess that’s why i’ve never been chosen to go on those shows! I’m too broke to take chances like that :)

9 golbguru 06.08.07 at 9:52 pm

MoneyNing: It’s not really to judge him or anything; it’s just an observation on how things were laid out and how the risk perception plays a part in your decision making, when you get a feeling of “I am winning”.

Even if he had won the $1 million - the measure of risk he would have taken wouldn’t have changed - in that case I would have described his actions as - “he took an unreasonable amount risk, which paid off”. :)

Also, may be my particular line of thoughts , as characterized in the post, is that way because I tend to think of risk in terms of “what will I lose if I take this risk?”, instead of “what will I gain if I take this risk?”.

tanyetta: Yeah, six figures is pretty encouraging to call it quits. So you won’t have a million - but you would be exceptionally happy with what you would win. But then who would provide entertainment for us? and how will I get to write posts like these? ;)

10 agressive saver 06.09.07 at 7:26 am

the real question is if he was in that position again, would he risk the money? i mean at even odds to double your money, you should do it every time. but, if you’re not a professional gambler, chances are that you won’t be in that same position anytime soon, and you should take your gains.

11 Kitty 06.10.07 at 6:56 pm

I saw the same show, and I was almost ready to shout at the guy to take the money.

To be fair, I don’t think it is not really a 50% choice. While you might not remember some obscure fact, if you know that you are really good in the subject, your chances to get the question to which you know the answer is higher. I’d estimate my chances in some subjects - e.g. astronomy are close to 0% (not only don’t I know many facts, those I do know, I know in another language). My chances in math would be close to 100% - given my math background I cannot imagine not knowing the answer to 1-5th grade math question. I’d imagine a professional editor would not walk away if the subject is spelling.

I got bored with Deal or No Deal, but I also think that once the amount crosses six figures it may be time to consider leaving. But a lot depends on how the board looks like. If there are still several large amounts left, even if one or two of these is nocked out, the chances are, the offer will keep going up. I think I’d try to estimate the chances. Still, it is difficult to say what I’d do in real circumstances.

I think the main requirement for these TV shows, by the way, is to have a bubbly personality, so that you jump up and down, laugh, cry, drop to your knees, etc. I am too reserved, so I’d never be considered.

12 Tyler K 06.11.07 at 7:07 am

What you’re actually talking about is risk aversion (or risk tolerance). Accepting the assumption that the odds are exactly 50%, it makes no difference mathematically which choice you make. What you’re talking about is economic “utility”…that is, for you, the first $500,000 is more valuable than the second $500,000. You’ve decided that the contestant has made a mistake not on the actual value of the money (a constant), but your perception of its utility. The choice is actually neutral in terms of expected value.

(Side note: In fact, its possible that your risk aversion has caused you to criticize the contestant’s as incorrect, when in fact YOUR choice would have been the incorrect one. The way you wrote it ["well, you get to keep $25,000 but that’s almost like losing it all"] makes it seem like the choices are either $500,000 guaranteed or $25,000 guaranteed with a 50% chance at $1,000,000. In that case, the mathematically correct choice is the second one. I’ve never seen this show, so I have no idea what the rules actually are.)

13 broknowrchlatr 06.11.07 at 7:23 am

I agree with Tyler’s reasonning for the most part but disagree with the conclusion.

The utility of the money is very important. The $25000 can be taken out of the equasion. If you do so, you are then opting to keep an additional $475k or risk it for a 50% change at $975k. The issue I have is that the utility of the first $475k is still much more than the utility of the second $500k.

Lets pretend the ammount was 10 times as much. Would you argue that anyone should trade $4.75 million for a 50% chance at $9.75 million? Either one means that you basically never have to worry about money again, as long as you manage your money well.

14 golbguru 06.11.07 at 7:33 am

Kitty: “I think the main requirement for these TV shows, by the way, is to have a bubbly personality, so that you jump up and down, laugh, cry, drop to your knees, etc.” …yeah, I hear you…these people really do all such things. :)

Tyler K
: Again, it’s not much of pointing the guy out as “incorrect” - as much of it is an observation on how the *utility* of $500,000 didn’t seem enough for him. I am grossly assuming the fact that $500,000 is a whole lot of money at this time, irrespective of what your net worth is. I totally agree that for some people the utility of $500,000 might be less than what I have in mind. You really have to be an extraordinary individual to risk something equivalent of $500,000 at great odds in order to double it. That’s why I also asked if you would do it if it were your hard-earned money? Would hard-earned $500K created a different picture of “utility” in your mind. So, my line of thoughts is along this line - not really to criticize what the dude did. I would have really understood the risk tolerance if the dude were plenty rich already (already have millions of dollars)- but I don’t think that was the case.

Also, compared to the $500,000 that he had in his hands - the utility of $25,000 is indeed much less.

“…makes it seem like the choices are either $500,000 guaranteed or $25,000 guaranteed with a 50% chance at $1,000,000.” ..That’s right. Although, I don’t quite understand how you calculated the second chance as being “mathematically correct”. It seems to me like some kind of an average return was calculated, or was it?

In my opinion, two events should be compared either on the basis of probability of occurring ( in this case 100% and 50% assumption) - if the returns are equal or they should be compared on the basis of expected returns (if the probability is the same). If things are not that simple (like it was the case with this dude), then someone like me would take the easy way out - look for the utility of the money. :)

15 golbguru 06.11.07 at 7:36 am

broknowrchlatr : Oops, I typed my response to Tyler a bit slower and you beat me to it; I almost said the same thing as you were saying on the utility of the money.

16 Tyler K 06.11.07 at 7:38 am

You’re missing the point, though. The utility of the money is abstract and subjective. The only objective fact is which decision maximizes the expected value of the player’s choice.

17 Tyler K 06.11.07 at 7:46 am

That was to broknowrchlatr, not golbguru. I definitely see what you’re saying, but I think it’s important to keep the math in mind. I personally would also keep the $500,000, but I would also understand that it was a mathematically neutral or incorrect decision (depending on the rules). The point is that it’s subjective and personal, not at all objective.

Although, I don’t quite understand how you calculated the second chance as being “mathematically correct”.

Expected value is the mean of the potential outcomes. The EV of keeping the $500,000 is $500,000 since there’s only one potential outcome. The expected value of the second choice is the mean of the two potential outcomes: $1,025,000 or $25,000, for an EV of $525,000. Without the $25,000, the EV is $500,000, making the EV of either choice exactly equal, which is where risk tolerance comes into play.

18 broknowrchlatr 06.11.07 at 8:13 am

I agree that the second answer is mathematically correct. You are correct that the utility of the money is subjective. But, I have a hard time believing that anyone that would qualify for the show would not have a similar utility. This is true of “Deal or no Deal” as well. I think it is safe to assume that your odds are 100% even there. However, at any point in the show where an offer is made, the offer to stop is lower than the asverage of the remaining cases. Now, part of this is because they want to encourage you to go on. But I think that part of it is that they know that the utility decreases as ammounts go up. So, giving people an offer that is an average would get too many people to stay (the initial average is over $131k)

Maybe if you are a billinnaire and money is no object, then taking the chance is better because it gives a statistically better result.

But, I think that even though it is subjective, the utility of the money is about the same for all contestants. It is likely that either ignorance of this + being motivated by the croud is what causes people to make these decisions.

19 golbguru 06.11.07 at 7:47 pm

Tyler: I understand the expected value a bit better. Thanks. However, from a personal perspective I have trouble with “The utility of the money is abstract and subjective.” - I would rather say the mathematical value is abstract - although it’s not subjective.

The concept of money is abstract, but for a common man it has practical implications - which materialize into “what can $X buy” - that’s not really abstract. Of course, when you say whether it’s a “lot” of money or “less” then yes, money is subjective.

Also, there must be some traps in thinking in terms of mathematically “expected value” - what happens when the odds are decreased and the winning amount is increased? For example, in the example of the post, what if the odds were taken to 0.005% and the winning amount was correspondingly increased to so that the EV is the same? I bet, risk tolerance start playing a bigger role in the equation, even though mathematically things were equal. :)

20 Corndogdriver 06.11.07 at 8:23 pm

A smaller-scale yet still interesting example is “The Cash Cab” where people answer questions while being driven to their destinations in a real cab. At the end, they’ve usually won around 400-600 bucks and are offered a chance at double or nothing. The host makes the offer with actual cash in his hand and it’s fairly rare that someone takes him up on it - even if they’ve seriously kicked booty on the questions so far.

21 MoneyNing 06.15.07 at 6:15 pm

golbguru: I heard that at the heat of the moment, it’s very easy to focus on “how much you can win” instead of “how much I could lose” since people don’t feel like the $500k is his/her money yet. I wish I had a chance to do this, so I can tell you how it feels and I hope that I can make a rational decision then.

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23 Max G 07.30.12 at 7:38 pm

Stupidest gamble of that Dude’s life. He will regret this decision forever.

24 Online Mastering 08.06.12 at 12:17 am

or you could just play the lottery ahahah

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