Well, yes. But the expected deviation from the mean is still ≈7.07. And the probability that the outcome will be either 93/107 or 107/93 is (slightly) higher than the outcome being exactly 100.

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fainpul 15 hours ago | parent | next [-]

But those are 2 results. 100 / 100 is more likely than 93 / 107 (or any other specific result) is what I'm saying.

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paddleon 15 hours ago | parent | next [-]

You can tell the difference between

93 heads, 107 tails and

93 tails, 107 heads

but not between

100 heads, 100 tails and

100 tails, 100 heads.

So while those are two results (93/107 and 107/93), they really only count as two separate outcomes if you pre-specify that the first number is heads.

If instead you consider symmetries, where there are 2 ways to get 93/107 and only one wall to get 100/100, then you have more likelihood for the 93/107 outcome because you have two ways to get it.

	▲	an hour ago \| parent [-]
		[deleted]

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kalaksi 15 hours ago | parent | prev | next [-]

I don't think that makes 100 / 100 the most likely result if you flip a coin 200 times. It's not about 100 / 100 vs. another single possible result. It's about 100 / 100 vs. NOT 100 / 100, which includes all other possible results other than 100 / 100.

	▲	andoando 11 hours ago \| parent [-]
		If you flip a coin 200 times, and repeat that a billion times, 100/100 will be more likely than any other ratio. It will be a bell curve with 100/100 as the peak

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Joker_vD 15 hours ago | parent | prev [-]

Depends what you count as a result, I guess. "There is exactly N flips of a single kind" is also a viable definition, just as "The exact sequence of flips was x_0, x_1, ... x_199" is.

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eviks 15 hours ago | parent | prev [-]

Why not go one abstraction further and go expected deviation from deviation? Probably the word "expected" plays a mind trick? "Expected" doesn't mean the probability increases, the easiest way to understand it is just by looking at the probability distribution function chart for coin tosses - you'll immediately see that mean has the highest chance of happenning, so exactly 100 is the most likely outcome