Expected value doesn't mean jack shit if the game can only be played once.
> Expected value (also known as EV, expectation, average, or mean value) is a long-run average value of random variables.
If you can only press a button once - you should take the guaranteed money in almost all circumstances (assuming you have finances that look like most Americans - if you're already a millionaire... do what you want, this game doesn't matter much to you).
Basically - This is a dire misunderstanding of how statistics works in general. The population at large might be better off pressing the 50% at 50 million button (because then you are running this game many times and you will likely achieve the expected value) - but as an individual, who can only roll the dice once, you are much better off just taking the immediate and guaranteed win.
And that's not even accounting for the drop off in marginal value of each dollar as you accumulate them - that first million is far more impactful than the next 49.
> Expected value (also known as EV, expectation, average, or mean value) is a long-run average value of random variables.
If you can only press a button once - you should take the guaranteed money in almost all circumstances (assuming you have finances that look like most Americans - if you're already a millionaire... do what you want, this game doesn't matter much to you).
Basically - This is a dire misunderstanding of how statistics works in general. The population at large might be better off pressing the 50% at 50 million button (because then you are running this game many times and you will likely achieve the expected value) - but as an individual, who can only roll the dice once, you are much better off just taking the immediate and guaranteed win.
And that's not even accounting for the drop off in marginal value of each dollar as you accumulate them - that first million is far more impactful than the next 49.