# 100% chance at $1.08M or 97% at $36M?

**URL:** <https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402>\
**Category:** In My Humble Opinion\
**Created:** [November 22, 2017, 2:03pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402 "2017-11-22T14:03:31Z")\
**Posts on this page:** 20\
**Page:** 4

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [November 22, 2017, 6:59pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/61 "2017-11-22T18:59:05Z")

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> [@](#):
>
> Quoth **Machine Elf** :
> 
> In that scenario, the expected value of the first choice is only $994K; you’d have to have some kind of risk fetish to take that option instead of the for-sure $1M. Most people pay to reduce their risk, not increase it.

There’s an entire city in the Nevada desert built from the money of people who do pay to increase their risk. Call it a “fetish” if you want, but it’s not uncommon.

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**Author:** ![puzzlegal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/puzzlegal/32/3827_2.png) [@puzzlegal](https://boards.straightdope.com/u/puzzlegal)\
**Post date:** [November 22, 2017, 6:59pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/62 "2017-11-22T18:59:50Z")

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> [@bucketybuck](#):
>
> So I don’t carry knowledge of the number of plane crashes around in my head, fair enough, but I would have thought it obvious that whatever the percentage was didn’t matter to the important point, which was the fact that there is already a risk to taking a flight, same as there is to any journey…

You must never fly. The difference between 0.000007 and 0.03 is huge. Much more important than the difference between 0.97 and 1.00. If there were a 3% chance of a commercial jet crashing, I would likely be dead right now. And almost no one would fly. That’s a super-risky thing to do just to travel quickly. So whatever your point was supposed to be, I couldn’t follow it. “There’s some risk” is true of absolutely everything.

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**Author:** ![bucketybuck](https://avatars.discourse-cdn.com/v4/letter/b/898d66/32.png) [@bucketybuck](https://boards.straightdope.com/u/bucketybuck)\
**Post date:** [November 22, 2017, 7:09pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/63 "2017-11-22T19:09:56Z")

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> [@puzzlegal](#):
>
> You must never fly. The difference between 0.000007 and 0.03 is huge. Much more important than the difference between 0.97 and 1.00. If there were a 3% chance of a commercial jet crashing, I would likely be dead right now. And almost no one would fly. That’s a super-risky thing to do just to travel quickly. So whatever your point was supposed to be, I couldn’t follow it. “There’s some risk” is true of absolutely everything.

I fly. Usually for short distances before jumping out, but thats a different story.

Honestly, after reading this thread I’m not sure “risk aversion” is a strong enough description. At least the poll restores my faith somewhat.

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**Author:** ![Snarky\_Kong](https://avatars.discourse-cdn.com/v4/letter/s/a183cd/32.png) [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)\
**Post date:** [November 22, 2017, 7:09pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/64 "2017-11-22T19:09:58Z")

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> [@blondebear](#):
>
> I’ll take the million, or 600K, or whatever it ends up being after taxes. Bird in the hand and all that.

Sure, but a bird in the hand is worth two in the bush, it’s not worth 36 in the bush.

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**Author:** ![Tamerlane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tamerlane/32/7602_2.png) [@Tamerlane](https://boards.straightdope.com/u/Tamerlane)\
**Post date:** [November 22, 2017, 7:36pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/65 "2017-11-22T19:36:51Z")

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> [@DrDeth](#):
>
> Yep. It would pay off the mortage, and make my eventual retirement worry free.

That’s really what sells it for me. $37 million would make me rich, which would be awful nice. But $1 million would _guarantee comfort_ in retirement, which I am fast approaching. I’m already set up reasonably well, but in my case a million in cash would push that over the edge into no-real-worries-land. A guarantee of that is worth just a bit more than an excellent chance at rich.

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**Author:** ![Surreal](https://avatars.discourse-cdn.com/v4/letter/s/eada6e/32.png) [@Surreal](https://boards.straightdope.com/u/Surreal)\
**Post date:** [November 22, 2017, 8:02pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/66 "2017-11-22T20:02:46Z")

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I’m quite risk-averse (I’ve always held a very low percentage of equities in my portfolio for my age), but I’d still try for $36 million.

In fact even if the odds were 50/50 I’d probably still opt for $36 million, because $1.08 million just isn’t enough to change my quality of life substantially.

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**Author:** ![Corry\_El](https://avatars.discourse-cdn.com/v4/letter/c/ecae2f/32.png) [@Corry\_El](https://boards.straightdope.com/u/Corry_El)\
**Post date:** [November 22, 2017, 8:03pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/67 "2017-11-22T20:03:54Z")

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> [@Chronos](#):
>
> There’s an entire city in the Nevada desert built from the money of people who do pay to increase their risk. Call it a “fetish” if you want, but it’s not uncommon.

And you could describe the risk of many bets in Vegas as something like putting down $1 for a somewhat less than \<1/36, somewhat less than 2.78%, chance of winning $36 net. More people would probably go to casino’s if word spread it was even a 6% chance rather than maybe 2%. Here it’s a 97% chance of winning, yet a not small % of respondents say they wouldn’t take it. Again one outcome has expected value $1mil. The other one has expected value $34.9 mil (.97\*36) and ~30% would take the first to avoid that very small risk. WOW, to me. But utility of wealth is a personal variable. And again on scale, if you asked the question among poor people in poor countries, where ever having anything like 1mil even over a lifetime was a remote possibility, and staying in their current state of poverty is significantly shortening their life expectancy, I’d understand it better.

I used to frequent a good (for some purposes) financial forum to read, Bogleheads. Many (also almost all middle class developed world and mainly American) people there express sort of similarly exaggerated financial risk aversion\*. My theory is it’s due to people perhaps wanting to believe if their financial situation is firmly in order, they somehow are in control of their destiny in general. They can cling to that certitude to not think of all the bad things that could still happen if you’re financially secure (in the way of painful disease, dementia, you name it). If you are ‘certain’ your money will last till you’re 100, that somehow makes it likely you’ll ever get close to 100, in a life worth living. Again just my theory of the subconscious machination for extreme financial risk aversion, as in turning down this deal, for non-impoverished people.

\*there it’s a little weirder though, in that the forum zeitgeist downplays stock market risk (‘it always comes back’, well in other countries in the longer run of history actually no it doesn’t always, it has in the _US_ stock market in last century or so) on one hand, yet posters sometimes compete to name lower and lower safe % of nest egg to withdraw each year in retirement based on sometimes ridiculously optimistic (from POV of living) life expectancy, ‘I know the general LE is less than 80 but my parents are already in their 90’s, I figure 110 for me…’ etc but lifespan of relatives is actually not that strong a predictor of your own.

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**Author:** ![wolfman](https://avatars.discourse-cdn.com/v4/letter/w/a8b319/32.png) [@wolfman](https://boards.straightdope.com/u/wolfman)\
**Post date:** [November 22, 2017, 8:10pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/68 "2017-11-22T20:10:20Z")

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I’m pretty sure I’d go for the 36 million, Because I am a major pessimist and self-blamer. If I took the sure thing I would spent the rest of my life looking at is as having lost 35 million rather than gaining 1 million.

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**Author:** ![markdash](https://avatars.discourse-cdn.com/v4/letter/m/ba8739/32.png) [@markdash](https://boards.straightdope.com/u/markdash)\
**Post date:** [November 22, 2017, 10:01pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/69 "2017-11-22T22:01:08Z")

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I’m normally quite risk averse, but I’m not THAT risk averse.

$1m is a goodly sum of money but in the end it would get my wife and I a nicer house and some retirement savings. Whereas the $36m is life-changing not only for our generation, but for 2 generations beyond as well.

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**Author:** ![Mr\_Shine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mr_shine/32/464_2.png) [@Mr\_Shine](https://boards.straightdope.com/u/Mr_Shine)\
**Post date:** [November 22, 2017, 10:26pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/70 "2017-11-22T22:26:52Z")

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> [@pulykamell](#):
>
> Actually, they are a little confusing, or at least I see the potential for immediate confusion. I had to double check to make sure I read the options and the hypothetical correctly. The confusing part is both options and outcomes contain the numbers 37 and 1, but don’t correspond to each other. If you’d go for the $37 million, you have to choose the second option, which contains the phrase “$1 million,” while the “take the $1 million” option is the one with the number 37 in it.

There is no $37 million. There never was any $37 million. Roulette pays back 36\*stake ($36 million as in the OP). any references to $37 million in the thread are a failure to read the OP. The poll options list the advantage of each option (more chips or higher value chip) so is consistent.

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**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\
**Post date:** [November 22, 2017, 11:12pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/71 "2017-11-22T23:12:36Z")

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> [@puzzlegal](#):
>
> You must never fly. The difference between 0.000007 and 0.03 is huge. Much more important than the difference between 0.97 and 1.00. If there were a 3% chance of a commercial jet crashing, I would likely be dead right now. And almost no one would fly. That’s a super-risky thing to do just to travel quickly. So whatever your point was supposed to be, I couldn’t follow it. “There’s some risk” is true of absolutely everything.

There are studies that show that people overestimate small probabilities and underestimate large ones. In our class I quoted pTerry about this - “million to one shots happen nine times out of ten.”

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**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\
**Post date:** [November 22, 2017, 11:40pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/72 "2017-11-22T23:40:01Z")

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The $36M. Like **Voyager** said, that’s enough for guilt-free first-class and other perks. $1M ain’t, and would only modestly improve my QoL.

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**Author:** ![Mean\_Mr.Mustard](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mean_mr.mustard/32/3865_2.png) [@Mean\_Mr.Mustard](https://boards.straightdope.com/u/Mean_Mr.Mustard)\
**Post date:** [November 22, 2017, 11:56pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/73 "2017-11-22T23:56:15Z")

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Am I the only one who doesn’t know what to do?

My gambler’s mind says go for the big payout, it’s a no-brainer.

But my gut just _knows_ that I would fall in the 3% if I went big. At which point I would sob like a schoolgirl.  
mmm

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**Author:** ![silenus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/silenus/32/166_2.png) [@silenus](https://boards.straightdope.com/u/silenus)\
**Post date:** [November 23, 2017, 1:05am UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/74 "2017-11-23T01:05:02Z")

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Why cry? You aren’t out a dime, no matter how it goes. Your life is the same tomorrow as it was today. Go big! Grab for the “Changing lots of people’s lives” money. If you one of the 3% and lose, you have a story that will get you free drinks for the rest of your life.

Dum vivimus, vivamus!

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**Author:** ![Corry\_El](https://avatars.discourse-cdn.com/v4/letter/c/ecae2f/32.png) [@Corry\_El](https://boards.straightdope.com/u/Corry_El)\
**Post date:** [November 23, 2017, 1:22am UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/75 "2017-11-23T01:22:49Z")

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> [@Mr\_Shine](#):
>
> There is no $37 million. There never was any $37 million. Roulette pays back 36\*stake ($36 million as in the OP).

I might have introduced $37mil in my restatement of the question. The proposal is the same as ‘I give you $1mil, now you can keep it or pay $1mil for a lottery ticket 97% likely to pay off $37mil’. Ie $1mil net or $36mil net, stating it that way to emphasize the fact that the $1mil (approx) really is yours, it’s not ‘house money’ (a generally ridiculous concept), and you really did lose it if you take the bet and lose. In comparison I don’t see why the roulette/chip aspect is particularly important.

Again though however it’s stated I’m wowed that people not in dire poverty would take 100% chance at 1mil over 97% chance at 36mil.

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**Author:** ![Mosier](https://avatars.discourse-cdn.com/v4/letter/m/7ea924/32.png) [@Mosier](https://boards.straightdope.com/u/Mosier)\
**Post date:** [November 23, 2017, 1:23am UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/76 "2017-11-23T01:23:42Z")

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I would take the 37 million option even if they only gave me 18 chips to place, making it closer to 50/50. The jump from where I am to 1 million is smaller than the jump from 1 million to 36 million. With 36 million I could do something actually important like create a scholarship fund or something.

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**Author:** ![Bosda\_Di\_Chi\_of\_Tricor](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bosda_di_chi_of_tricor/32/16845_2.png) [@Bosda\_Di\_Chi\_of\_Tricor](https://boards.straightdope.com/u/Bosda_Di_Chi_of_Tricor)\
**Post date:** [November 23, 2017, 2:04am UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/77 "2017-11-23T02:04:02Z")

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Look up the definition of “Hubris”.

I’ll take the one million, then invest.

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**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\
**Post date:** [November 23, 2017, 2:12am UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/78 "2017-11-23T02:12:24Z")

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> [@Corry\_El](#):
>
> I might have introduced $37mil in my restatement of the question.

No, it looks like it was me with the first response to this thread. I didn’t even realize it until **Mr Shine** ’s last comment, so even though I answered “correctly” (in that my poll answer matched my real answer), I still confused the numbers. Given the amount of people confusing the numbers and answering it wrong, yes, the way the poll is laid out is apparently leading to some confusion in the answers.

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**Author:** ![kaylasdad99](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kaylasdad99/32/3398_2.png) [@kaylasdad99](https://boards.straightdope.com/u/kaylasdad99)\
**Post date:** [November 23, 2017, 3:07am UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/79 "2017-11-23T03:07:40Z")

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> [@TriPolar](#):
>
> I’ll voted for the sure thing. But it just occurred to me I could buy my own 37th chip and get the big payoff.

> [@Shodan](#):
>
> I like the way you think.
> 
> Regards,  
> Shodan

> [@Darren\_Garrison](#):
>
> I take the 36 $1 million chips, walk away from the wheel and cash them out.

> [@Mr\_Shine](#):
>
> You all get nothing!

Why? It’s not like they STOLE Fizzy Lifting Drinks.

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**Author:** ![JPrescott](https://avatars.discourse-cdn.com/v4/letter/j/e36b37/32.png) [@JPrescott](https://boards.straightdope.com/u/JPrescott)\
**Post date:** [November 23, 2017, 3:34am UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/80 "2017-11-23T03:34:10Z")

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I’m living in poverty. Even $30k would be life changing for my family. No WAY would I risk losing.

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