# Fair coin $2000 for $600
**URL:** https://boards.straightdope.com/t/fair-coin-2000-for-600/927886
**Category:** In My Humble Opinion
**Created:** [December 12, 2020, 11:41am UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886 "2020-12-12T11:41:10Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@CardboardBoxx](https://boards.straightdope.com/u/CardboardBoxx)
#### Post date: [December 12, 2020, 11:41am UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/1 "2020-12-12T11:41:10Z")
You’ve been targetted by a popular gameshow that picks random people off the street and offers them cash for questions. You get 6 right, for $600. They then offer you a chance to boost it to $2000 on one toss of a fair coin. Do you take the $600 and walk away or go for the $2000?
The coin is absolutely 100% reliably fair.
_Poll ([view on site](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/1))_
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### Author:  [@What\_Exit](https://boards.straightdope.com/u/What_Exit)
#### Post date: [December 12, 2020, 2:17pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/2 "2020-12-12T14:17:16Z")
$600 is a nice windfall. 100% chance to take it home.
50% chance for an extra $1400 but 50% chance of nothing. I would chicken out and take the $600, but I’m not a gambler.
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### Author:  [@kayaker](https://boards.straightdope.com/u/kayaker)
#### Post date: [December 12, 2020, 2:20pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/3 "2020-12-12T14:20:30Z")
Let it ride. Baby needs a new pair of shoes. Winner, winner, chicken dinner.
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [December 12, 2020, 2:21pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/4 "2020-12-12T14:21:17Z")
I’m not a gambler, either, but those odds are just too good. A high positive expectation, risking money that I don’t need? Absolutely.
The analysis changes if that’s all the money I have and rent’s due tomorrow, or something like that. But that’s not the situation presented.
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### Author:  [@needscoffee](https://boards.straightdope.com/u/needscoffee)
#### Post date: [December 12, 2020, 2:35pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/5 "2020-12-12T14:35:15Z")
The OP doesn’t specify whether you’d lose everything if you lose the toss.
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### Author:  [@What\_Exit](https://boards.straightdope.com/u/What_Exit)
#### Post date: [December 12, 2020, 2:49pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/6 "2020-12-12T14:49:03Z")
I believe he is implying that, otherwise there is no reason to choose.
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### Author:  [@needscoffee](https://boards.straightdope.com/u/needscoffee)
#### Post date: [December 12, 2020, 2:57pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/7 "2020-12-12T14:57:42Z")
Obviously. Or it could be a trick.
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### Author:  [@TriPolar](https://boards.straightdope.com/u/TriPolar)
#### Post date: [December 12, 2020, 3:07pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/8 "2020-12-12T15:07:16Z")
This. As long as I don’t have a serious need for $600 it’s worth gambling. I’ll lose I’m sure, but I’ll feel justified in going with the odds.
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### Author:  [@CardboardBoxx](https://boards.straightdope.com/u/CardboardBoxx)
#### Post date: [December 12, 2020, 4:35pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/9 "2020-12-12T16:35:05Z")
You’ve been targetted by a popular gameshow that picks random people off the street and offers them cash for questions. You get 6 right, for $6. They then offer you a chance to boost it to $20 on one toss of a fair coin. Do you take the $6 and walk away or go for the $20?
The coin is absolutely 100% reliably fair.
_Poll ([view on site](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/9))_
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### Author:  [@CardboardBoxx](https://boards.straightdope.com/u/CardboardBoxx)
#### Post date: [December 12, 2020, 4:35pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/10 "2020-12-12T16:35:44Z")
You’ve been targetted by a popular gameshow that picks random people off the street and offers them cash for questions. You get 6 right, for $6000. They then offer you a chance to boost it to $20000 on one toss of a fair coin. Do you take the $6000 and walk away or go for the $20000?
The coin is absolutely 100% reliably fair.
_Poll ([view on site](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/10))_
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### Author:  [@TriPolar](https://boards.straightdope.com/u/TriPolar)
#### Post date: [December 12, 2020, 5:02pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/11 "2020-12-12T17:02:08Z")
I said I’d go for the $20000, but I might feel different on any given day.
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### Author:  [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)
#### Post date: [December 12, 2020, 6:03pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/12 "2020-12-12T18:03:14Z")
> [@TriPolar](#):
>
> This. As long as I don’t have a serious need for $600 it’s worth gambling. I’ll lose I’m sure, but I’ll feel justified in going with the odds.
That’s my thinking too. As long as I can “afford” to lose the $600, I’d risk it for an even chance to more than double it.
I’m in good enough financial shape that the marginal utility of the dollar amounts pretty closely matches their cash value.
But if went up to higher amounts (as in the latest version of the poll), that might not be the case. I’m not sure for myself where the threshold is, but I’d keep $6 million rather than risk it on a chance to win $20 million.
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### Author:  [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)
#### Post date: [December 12, 2020, 6:36pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/13 "2020-12-12T18:36:14Z")
> [@Thudlow\_Boink](#):
>
> That’s my thinking too. As long as I can “afford” to lose the $600, I’d risk it for an even chance to more than double it.
>
> I’m in good enough financial shape that the marginal utility of the dollar amounts pretty closely matches their cash value.
>
> But if went up to higher amounts (as in the latest version of the poll), that might not be the case. I’m not sure for myself where the threshold is, but I’d keep $6 million rather than risk it on a chance to win $20 million.
That’s about me. For the reasons both you and @Chronos laid out.
$6K vs $20K, I’d take the coin flip without hesitation. Add 3 zeros and my decision definitely changes. But 60K/200K? Aye, there’s the rub.
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### Author:  [@Andy\_L](https://boards.straightdope.com/u/Andy_L)
#### Post date: [December 12, 2020, 8:33pm UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/14 "2020-12-12T20:33:57Z")
> **[Risk aversion](https://en.wikipedia.org/wiki/Risk_aversion)**
>
> Pages for logged out editors learn more
>
> In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome. Risk aversion explains the inclination to agree to a situation with a more predictable, but possibly lower payoff, rather than another situation with a highly unpredictable, but possibly high...
This article talks about why these questions are not getting the same answers…
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### Author:  [@jtur88](https://boards.straightdope.com/u/jtur88)
#### Post date: [December 13, 2020, 4:15am UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/15 "2020-12-13T04:15:21Z")
Quit when you’re ahead. I walk away with the windfall of $600.
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### Author:  [@peccavi](https://boards.straightdope.com/u/peccavi)
#### Post date: [December 13, 2020, 4:28am UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/16 "2020-12-13T04:28:59Z")
All these situations tend to separate those who understand gambling and odds from those who don’t. If you don’t gamble, you concentrate on what you are risking ($600 that you didn’t walk in with) rather than return ratio versus win/loss ratio.
Consider this scenario: You are offered this bet 100 times in a row. If you take the “smart” risk averse choice each time, you end up with $60,000. But if the coin is truly fair and you take the bet every time, you will walk away with more than double that. In fact, the coin has to go against you for more than 3/4 of the tosses before you walk away with less than the risk averse decision.
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### Author:  [@Colibri](https://boards.straightdope.com/u/Colibri)
#### Post date: [December 13, 2020, 5:08am UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/17 "2020-12-13T05:08:50Z")
> [@peccavi](#):
>
> All these situations tend to separate those who understand gambling and odds from those who don’t.
I think most people here understand the odds perfectly well, and you are misunderstanding the point of the successive polls. What’s important to most people isn’t the odds, it’s how much difference a particular amount of money will make in their life.
For me, I would take the bet automatically up to $6,000/$20,000, since $6,000 would be a nice windfall but wouldn’t change my life significantly. I would have to think harder at $60,000/$200,000 but probably take the bet because the larger number would change my life more significantly. At $6 million/$20 million my choice would again be automatic in NOT taking the bet, since given my age and life style $6 million would be more than I could spend in the rest of my life, and $20 million wouldn’t offer me any additional benefits. It doesn’t matter what the odds are if the larger amount is of no greater utility to me.
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### Author:  [@peccavi](https://boards.straightdope.com/u/peccavi)
#### Post date: [December 13, 2020, 5:16am UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/18 "2020-12-13T05:16:47Z")
> [@Colibri](#):
>
> It doesn’t matter what the odds are if the larger amount is of no greater utility to me.
Ah, but let’s take the hypothetical I posed- 100 flips, but you have to choose bet or walk at the start. You take the bet, right? What about 50 flips? 10 flips? 5 flips? 2 flips?
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### Author:  [@Colibri](https://boards.straightdope.com/u/Colibri)
#### Post date: [December 13, 2020, 5:17am UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/19 "2020-12-13T05:17:31Z")
> [@peccavi](#):
>
> > [@Colibri](#):
> >
> > It doesn’t matter what the odds are if the larger amount is of no greater utility to me.
>
> Ah, but let’s take the hypothetical I posed- 100 flips, but you have to choose bet or walk at the start. You take the bet, right? What about 50 flips? 10 flips? 5 flips? 2 flips?.
That’s not the question.
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### Author:  [@peccavi](https://boards.straightdope.com/u/peccavi)
#### Post date: [December 13, 2020, 5:20am UTC](https://boards.straightdope.com/t/fair-coin-2000-for-600/927886/20 "2020-12-13T05:20:00Z")
> [@Colibri](#):
>
> That’s not the question
Neither is $6 million versus $20 million (not in the OP, at least).
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