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View Poll Results: Suppose you're offered the flip of a fair coin, with the following provisions: Heads,

Voters
54. You may not vote on this poll
  • Less than $100,000

    4 7.41%
  • $100,000

    6 11.11%
  • $200,000

    8 14.81%
  • $300,000

    11 20.37%
  • $400,000

    9 16.67%
  • $500,000

    11 20.37%
  • $600,000

    1 1.85%
  • $700,000

    0 0%
  • $800,000

    0 0%
  • $900,000

    2 3.70%
  • You can't buy me off. I'm flipping no matter what.

    2 3.70%
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Thread: A study in certainty equivalent, risk aversion, and utility

  1. #1


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    A study in certainty equivalent, risk aversion, and utility

    Will you please vote and help me with a study I'm doing. There will be two polls, of which this is the first.

    Suppose you're offered the flip of a fair coin, with the following provisions: Heads, you win $1 million, tails you get nothing. What is the minimum amount of cash in hand (no questions asked) you'd be willing to accept NOT to play the game?

    Don

  2. #2


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    Quote Originally Posted by DSchles View Post
    Suppose you're offered the flip of a fair coin, with the following provisions: Heads, you win $1 million, tails you get nothing. What is the minimum amount of cash in hand (no questions asked) you'd be willing to accept NOT to play the game?
    $300,000

    (I have to admit that I went back and forth between $250,00 & $300,000)

  3. #3


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    Quote Originally Posted by BJPloppy View Post
    $300,000

    (I have to admit that I went back and forth between $250,00 & $300,000)
    I had some technical trouble. Please vote now.

    Thanks.

    Don

    P.S. Second poll won't appear till we have a good sample of answers to this one.

  4. #4
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    I assume you get to do this once in a lifetime.

  5. #5


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    Option "Less than $100,000" is very misleading. If my choice was only $100 I wouldn't take it. If my choice was $90,000 I would take it.

  6. #6


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    I think the answer to this depends on what the value of the money is to the person the offer is being made to. With such a large reward for winning, the amount taken not to play has to be life changing in some way otherwise there is no reason to accept it. As MWP says, $100k may not be granular enough. There are lower amounts which would be accepted in a heart beat by some.

    I used to think about this when watching the game show "Deal or No Deal". The optimal strategy for the game is always refuse the offer, because the offers are always below EV for the remaining suitcases. However, given that each contestant only gets to play once in their life, they always (wisely, in my opinion) stopped when the offer was for an amount which was significant enough to make difference to their future in some way.

    So, to some extent, the results of this poll will reflect the spectrum of that threshold for the members of this forum.

  7. #7


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    Quote Originally Posted by Midwest Player View Post
    Option "Less than $100,000" is very misleading. If my choice was only $100 I wouldn't take it. If my choice was $90,000 I would take it.
    So, your answer is less than $100,000!

    Don

  8. #8


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    Quote Originally Posted by Gronbog View Post
    I think the answer to this depends on what the value of the money is to the person the offer is being made to. With such a large reward for winning, the amount taken not to play has to be life changing in some way otherwise there is no reason to accept it. As MWP says, $100k may not be granular enough. There are lower amounts which would be accepted in a heart beat by some.

    I used to think about this when watching the game show "Deal or No Deal". The optimal strategy for the game is always refuse the offer, because the offers are always below EV for the remaining suitcases. However, given that each contestant only gets to play once in their life, they always (wisely, in my opinion) stopped when the offer was for an amount which was significant enough to make difference to their future in some way.

    So, to some extent, the results of this poll will reflect the spectrum of that threshold for the members of this forum.
    You don't think I picked the title of the thread out a hat, do you? :-) All the words were chosen carefully to reflect the full nature of the question. First, most here understand that certainty equivalent, in this context, means the amount of money you would accept, with certainty, to avoid taking any risk whatsoever. But that amount, in turn, depends on two things: 1) one's personal aversion to risk, which is a variable, and 2) the utility of the amount of money chosen to that specific individual.

    Some further clarification: In a recent interview, Warren Buffett stated, matter of factly, "money has no utility to me whatsoever." So, presented with this opportunity, it would make little sense for him NOT to flip the coin. On the other hand, a homeless person would consider receiving $100,000 or less as a life-altering event. To him, the utility of even the smallest category offered is so great that gambling would be insane. So yes, the analogy to "Deal or No Deal" is palpable.

    So, again, I don't need any of this to be explained to me. I'm interested in what category your personal answer falls. And yes, of course, it's a one-time event. Do you think I'm asking what you'd do if you could do this every hour on the hour? The terms are clear. This discussion isn't going to turn into what anyone had for breakfast. :-)

    Don

  9. #9


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    Quote Originally Posted by DSchles View Post
    So, your answer is less than $100,000!

    Don
    Yes!

  10. #10


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    Theres No Way, i would take a chance on a 1,000,000 vs. nothing.. 100,000 (or 10%) is all it would take to buy me off..For me 100 Grand is ALOT of money to me and is all i would need to re-invest and live comfortably for years to come..And Although 1,00,000 is 10x as much..It def. wouldnt be 10x as valuable for a person like me..Therefore 100,000 would be the right choice for me.. Its the same reason i always play the "little lotto" and not the Big one..
    Last edited by Jack Jackson; 12-14-2017 at 11:03 PM.
    http://bjstrat.net/cgi-bin/cdca.cgi

  11. #11


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    Very interesting!

    I looked at Deal or No Deal differently. In my mind, leaving with nothing doesn't hurt, in that it doesn't take away from what I have. I guess I don't dwell a lot on what might have been. That said, a free shot at a million is just that. If I lost, I'm no worse off than I am now. If I won, though...

    I was once playing in a positive EV situation, when I won a bonus that was more than the target EV. I continued to play, however, because it was still a positive situation. In theory I could have lost my bonus chasing the origional EV. But I thought if it was positive BEFORE the bonus, it's still positive and went for it.

    If the question was worded differently, i.e. "Would you rather have $X or flip for a million?" I might take X, as it is guaranteed cash. But I would be hard pressed to decide the amount of X.

  12. #12


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    I voted $500k, but in reality, probably somewhere around $450-480k or so. $480k would be life changing money, but neither would $480k nor $1M be enough to retire, so give me the EV. Unless It is a fairly trivial loss of EV. The leverage I can get out of $450-480k is tremendous, so I can accept a little loss in EV to know I'll have that seed money.

  13. #13


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    Me and my family do not currently need the money to live on and nothing would change if I did not win the million. So, I would settle for "$200k (pay off mortgage and other debts).

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