Behavioral brain teaser: Which of these buttons should you press for the best chance at the most money?

Originally published at: Behavioral brain teaser: Which of these buttons should you press for the best chance at the most money? | Boing Boing



So, $2million then?


I press neither and you give me $500k.



Playing along, my understanding of probability is each shot is 50%. And each shot is individual, not cumulative. So I’d have a good chance of getting at least 50 milllion, but I also could get nothing.

So me in my position, I’d take one shot and collect the million and, properly invested, never have to work another day in my life. And then take the next shot at the $50 million. And I’d probably do the same no matter how many times I get to hit both buttons: the first one always for 1 million.

Now to see how that might line up with their expectations and counsel…

Edit: better answer below :slight_smile:

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$1M vs $2M wouldn’t make a huge difference in my life over the long run, so if I get two presses then the first one is going to be the 50/50. If I get $50M, then I’ll go for another $50M in the second press (no one needs $100M, but I’ll take it someone’s giving it away). On the other hand, if I fail to get $50M on the first press, I’d take the guaranteed $1M on the second, because I wouldn’t want to walk away with nothing.


Oh, I like your thinking. Hell yeah, try for the $50 million first.


Green button first. If I win $50M, press it again for a chance at $100M. If I lose, press the red for a guaranteed $1M. This is the optimum strategy with a 50% chance of $1M, 25% chance of $50M and 25% chance of $100M.
Red then green has a 50% chance of $1M and 50% chance of $51M.
Two green presses has 25% chance of $100M, 50% chance of $50M and 25% chance of nothing.
Two red presses has 100% chance of $2M.


Hit the $1 million FIRST!

THEN go for the $50 million coin flip.

…lock in set-for-life mode, then go for the extended family & next generation too.

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This isn’t the 90’s…I don’t think I could just retire if a million popped into my bank account. I mean I could make it work, but not really enjoy it. Sure if I grew it over 5 or 10 years I’d probably retire 10 years early.

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Nice breakdown, and indeed optimal, but ignores the human at the wheel.

…gotta be a 1970s study out there showing how many people will hit & miss the $50M first, then hover over that Double-or-Nothin! second press

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Didn’t you post this yesterday?

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Oh, not retire & do nothing. …it’s a shame $1M wouldn’t even payoff my house after taxes.

But $1M wisely managed (i.e. keep the mortgage, invest the winnings) can absolutely free up your life choices for the foreseeable future


I think you have the probabilities wrong in the green+green/green+red route - there are only three outcomes:

  • green (lose) + red (win)
  • green (win) + green (lose)
  • green (win) + green (win)

So 33% chance of $1M, 33% of $50M, 33% of 100M. So the odds are better for the big money than you thought!

ETA No, you were right! With the first press you have a 50% chance of just winning $1M. There are three outcomes but they’re not weighted evenly.

My set-for-life mode is going to require a tad more than that.

This isn’t the 50’s.

$1,000,000 in 1950 → 2022 | Inflation Calculator.

Give me $12,000,000 and it’ll definitely lock in set-for-life mode. :grin:

Granted, we may have different definitions of “set” or “for life”. :wink:


If $1M lands in my lap unexpectedly, I’m going to buy one nice but not extravagant indulgence (maybe two, one for me and one for my wife), then put the rest away for retirement. I have far enough to go that I’d likely get some reasonable growth and have a nice padding to either retire a few years early or just live a little nicer after I do retire.

Wait a minute, the first time this was posted you only had one press, now you have two?

For me it’s still the guaranteed 1 million first for the reasons talked about in the other topic.

Pressing the second button twice does not change your chances, it’s still 50/50 each press.

All these posts about 25% and 33% chance at one million confuse me and I don’t think they’re correct.

There is a 100% chance at 1 million and now in this version 100% chance at 2 million and that’s not a chance, it’s a sure thing. Or 100% sure thing at 1 million and still 50% chance at 50 million.

I guess there is a 50% chance at 100 million but then there’s also a 100% chance at zero if you waste both chances on the 50 million.

I still go with 100% sure thing 2 million because then I retire immediately and invest the rest so our daughter can retire early or when we die which ever comes first.


For those curious about arguing odds of various tactics:
Red-Red: 100% $2M
Red-Green: 50% $1M, 50% $51M
Green-Red: 50% $1M, 50% $51M
Green-Green: 25% $0, 50% $50M, 25% $100M
Green, Then Red if loss and Green if win: 50% $1M, 25% $50M, 25% $100M

While there’s no “loss” in this experiment (since all money is gained), there is the feeling of loss if you don’t hit that 50-50 shot on the green. So if you hit green once, there is the potential of “losing” $1M if it doesn’t give you $50M, and doubly so if you hit green twice and lose both times.

The real interesting part here is how $1M is such an interesting amount, because it tells you more about how much wealth a person has, which is the unstated premise in all these tests about “risk tolerance”. You’d probably see much more uniform results with a 1B/50B or a $1/$50 contrast.


That’s a lousy deal for you.

If you hit red first, or second for that matter, won’t it always be 1 million 100%?

As a matter of fact shouldn’t the 1 million always be 100% no matter when you press it? Why is it showing 50% for 1 million in all of your scenarios?