[flir]

> a random stream of bits should have almost as many ones as zeros

almost??

[xvedejas]

I think this is the correct way to phrase it. Just because the probabilities of each are both 50% doesn't mean it's more likely than not to get the same number of ones and zeros. It would just mean you're equally likely to get a few more ones as you are to get a few more zeros. But the counts are unlikely to be very far apart.

[082349872349872]

But in absolute (not relative terms) the counts will tend to diverge over time.

[eru]

Yes. You expect the absolute difference in numbers of 0s vs 1s to grow roughly with the square-root of the total number of digits produced.

[philipswood]

In the limit, yes.

But for the first few bits maybe "almost".

[alex_smart]

With n random bits, you will likely have approximately \sqrt{n} more ones than zeros (or vice versa).

[thisisauserid]

You aren't suggesting that something random should be predictable, right?

[0xFF0123]

"Almost" suggests it is predictably fewer

[KTibow]

"Around" might be better

[AlecSchueler]

It suggests roughly the same amount, could be higher or lower.

[niles]

Around would do that more effectively. Almost is more similar to nearly, and I agree commonly used for lower.

[flir]

I read "almost as many" as "not quite as many". In other words, fewer.

My mental model is that an unbiased random stream of 1's and 0's should converge on 50% 1's and 50% 0's over time, not 49% 1's and 51% 0's.

Looks like it's a language ambiguity thing I'm not quite getting.

[ruune]

Over time, it should be almost 50/50, yeah. What if you got 10000001 random numbers? There's no way it's exactly 50/50 with an uneven amount. It's almost 50/50

[madeofpalk]

To converge on 50% implies 49%\51% prior. Almost even.

[b112]

Yes, almost. They will approach equal as the count approaches infinity.

So if ypu ever see a random pick equate to 50/50, the end of the universe is upon us.

[eru]

The ratio of occurrences of 0s and 1s will go to one in the limit. But the absolute difference of occurrences will diverge. (It grows roughly like the square-root of the number of digits.)

[AlexAltea]

Nit, their ratio (bits set/unset) will approach 1 as the count approaches infinity, but the values themselves will not approach equal. https://gist.github.com/AlexAltea/3aa96efc41f59e80631c346908...

[Rebelgecko]

If a random streams length is odd, they'll never be the exact same.