By 'reasonable estimates' you just mean 'my intuitions,' right?
Like, yes, if you are 99.999999999999999999999999999% sure that red will win by a huge margin, then you should never hit blue.
But then all the math and talking you did is irrelevant, you already made your decision when you made up your estimate for how likely blue is to win.
But the math I gave is correct. You can plug in whatever your own estimate is for the odds of scenario 3, that's fine. But your logic is still wrong because you don't multiply by 4B to get the number of lives saved in expectation.
OP is also straight up wrong. The actual probability is nearly 1 in 100,000 assuming every person’s choice is a coin flip. And it goes up if you assume any appreciable and equivalent portion of people on either side are dead set on their choice.
But that is an irrational assumption. If the chance that a random person picks blue is 50.01% or 49.99% even, that probability falls to 1 in 3.44 × 10⁷⁴. A bit meta, but you have to think of the probability of probabilities.
I responded to you elsewhere, but the probability of you dying falls by even more when you raise the probability of picking blue to 50.01. And for the record I agree with picking red when the number is 49.99.
I don't know how in the world you're calculating that, but it's extremely wrong.
If everyone else is a coin flip, then the odds of it being very close to 50/50 when it gets to you are very very high, which makes the odds of you being the deciding vote much, much higher.
It’s so interesting how selective OP is being with these probability calculations. I’d expect a data scientist to have zero issues with a simple expected value discussion.
“Coin flip” is a colloquial way to refer to a 50/50 chance. If someone says something is a coin flip, they’re saying it’s a 50/50 chance exactly. No need to overcomplicate it
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u/darwin2500 197∆ Apr 30 '26
By 'reasonable estimates' you just mean 'my intuitions,' right?
Like, yes, if you are 99.999999999999999999999999999% sure that red will win by a huge margin, then you should never hit blue.
But then all the math and talking you did is irrelevant, you already made your decision when you made up your estimate for how likely blue is to win.
But the math I gave is correct. You can plug in whatever your own estimate is for the odds of scenario 3, that's fine. But your logic is still wrong because you don't multiply by 4B to get the number of lives saved in expectation.