Even if you shoot only once, you still have a higher chance of hitting something slightly off the middle than the perfect 100/100. And this because that's one point-precise result (100/100) vs. a cumulated range of individually less-probable results, but more probable when taken as a whole.

For a fair coin, hitting 100/100 is ~5%, vs. ~30% falling in [97; 103] \ {100}. You can simulate here: https://www.omnicalculator.com/statistics/coin-flip-probabil...

▲

tshaddox 14 hours ago | parent | next [-]

> you still have a higher chance of hitting something slightly off the middle than the perfect 100/100

That's because "something slightly off the middle" is a large group of possible results. Of course you can assemble a group of possible results that has a higher likelihood than a single result (even the most likely single result!). But you could make the same argument for any single result, including one of the results in your "slightly off the middle" group. Did you get 97 heads? Well you'd have a higher likelihood of getting between 98 and 103 heads. In fact, for any result you get, it would have been more likely to get some other result! :D

▲

zdragnar 14 hours ago | parent [-]

> But you could make the same argument for any single result

Isn't that the point? The odds of getting the "most likely result" are lower than the odds of getting not the most likely result. Therefore, getting exactly 100/100 heads and tails would be unlikely!

▲

tshaddox 13 hours ago | parent | next [-]

But as I said, getting any one specific result is less likely than getting another other possible result. And the disparity in likelihoods is greater for any one specific result other than the 50% split.

▲

alwa 12 hours ago | parent | prev [-]

I think the disagreement is about what that unlikeliness implies. "Aha! You got any result? Clearly you're lying!"... I'm not sure how far that gets you.

There's probably a dorm-quality insight there about the supreme unlikeliness of being, though: out of all the possible universes, this one, etc...

	▲	zdragnar 10 hours ago \| parent [-]
		Let's look at the original quote: > "Remember, if you flip a coin 200 times and it comes heads up exactly 100 times, the chances are the coin is actually unfair. You should expect to see something like 93 or 107 instead". Inverting the statement makes it read something like this: You are more likely to not get 100/100 than you are to get exactly 100/100 ...which is exactly what I was saying. Nobody is arguing that there is a single value that might be more likely than 100/100. Rather, the argument is that a 100/100 result is suspiciously fair.

▲

e12e 13 hours ago | parent | prev [-]

Should that be 25% for 97..193 excluding 100?

	▲	shakow 12 hours ago \| parent [-]
		“[97; 103] \ {100}” means the interval [97; 103] without the set {100}; so no, still ~30%.