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> that first million is far more impactful than the next 49. This is in fact the reason you should take the million. How many times you get to play the game i

> that first million is far more impactful than the next 49. This is in fact the reason you should take the million. How many times you get to play the game is irrelevant. Your whole life is filled with potential but uncertain payoffs, and you should maximise expected utility every time (where utility is not the same as dollars).

Bootvis 4y ago
No it’s not, if you play the game 20 times you’re almost certain to win 50 million and probably a lot more. Unless your utility function is flat after 20 million it does matter.
- orlp 4y ago
  If you play the game 20 games you'll still be better off pressing the 1 million button 5-10 times, at the start if you don't know in advance how many presses you get, or at the end if you do and haven't won big yet.
  - gweinberg 4y ago
    You've only got a one in a million chance of losing 20 times in a row. If you lose 19 times in a row, sure you can take the sure million on the last try. But it doesn't make any sense to take the sure million at the beginning.
- ghaff 4y ago
  It's an interesting question (assuming you know the number of times you get to play up front). In reality, with these numbers, the best strategy for most people who aren't already very wealthy would probably be to get a sure-fire nest egg and then play the odds. If you have to play the same every time, I'm not sure. Again, with these numbers, the utility function is looking pretty flat after $20 million for the vast majority of people. And "almost certain" != certain.
- anigbrowl 4y ago
  if you play the game 20 times you’re almost certain to win 50 million You can get any result you want if you just rewrite the problem conditions ◔_◔
  - Bootvis 4y ago
    I replied to someone claiming that you should always go for certainty no matter how many games you play. If you get to play the game 49 times it doesn’t make much sense to go for certainty 49 times because 2^-49 (or 2^-20) is really small.
- jstanley 4y ago
  After you've pushed "give me $1 million" on your first go, your utility function looks very different to how it did before (assuming you're not already a millionaire).
UncleMeat 4y ago
Not so. It can be throughly reasonable to make a choice that has lower expected value but has a distribution that fits your needs more closely.
- CrazyStat 4y ago
  If one option doesn't fit your needs then it has lower utility.
  - UncleMeat 4y ago
    Then this is worthless as a decision making system since your decisions will always already be the one that maximizes expected utility via this unknowable transformation.
    - CrazyStat 4y ago
      No, that doesn't follow. You might be acting in a short-sighted or impulsive way that doesn't maximize your utility. You can't just post-hoc declare that your true utility function is whatever would have led you to the decision you made.

Bootvis 4y ago

No it’s not, if you play the game 20 times you’re almost certain to win 50 million and probably a lot more. Unless your utility function is flat after 20 million it does matter.

orlp 4y ago
If you play the game 20 games you'll still be better off pressing the 1 million button 5-10 times, at the start if you don't know in advance how many presses you get, or at the end if you do and haven't won big yet.
- gweinberg 4y ago
  You've only got a one in a million chance of losing 20 times in a row. If you lose 19 times in a row, sure you can take the sure million on the last try. But it doesn't make any sense to take the sure million at the beginning.
ghaff 4y ago
It's an interesting question (assuming you know the number of times you get to play up front). In reality, with these numbers, the best strategy for most people who aren't already very wealthy would probably be to get a sure-fire nest egg and then play the odds. If you have to play the same every time, I'm not sure. Again, with these numbers, the utility function is looking pretty flat after $20 million for the vast majority of people. And "almost certain" != certain.
anigbrowl 4y ago
if you play the game 20 times you’re almost certain to win 50 million You can get any result you want if you just rewrite the problem conditions ◔_◔
- Bootvis 4y ago
  I replied to someone claiming that you should always go for certainty no matter how many games you play. If you get to play the game 49 times it doesn’t make much sense to go for certainty 49 times because 2^-49 (or 2^-20) is really small.
jstanley 4y ago
After you've pushed "give me $1 million" on your first go, your utility function looks very different to how it did before (assuming you're not already a millionaire).

UncleMeat 4y ago

Not so. It can be throughly reasonable to make a choice that has lower expected value but has a distribution that fits your needs more closely.

CrazyStat 4y ago
If one option doesn't fit your needs then it has lower utility.
- UncleMeat 4y ago
  Then this is worthless as a decision making system since your decisions will always already be the one that maximizes expected utility via this unknowable transformation.
  - CrazyStat 4y ago
    No, that doesn't follow. You might be acting in a short-sighted or impulsive way that doesn't maximize your utility. You can't just post-hoc declare that your true utility function is whatever would have led you to the decision you made.