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Here’s the distribution of the first million digits of the square root of two’s decimal expansion.

Number of digits | is:   0's |  99 818   1's |  98 926   2's | 100 442   3's | 100 191   4's | 100 031   5's | 100 059   6's |  99 885   7's | 100 012   8's | 100 347   9's | 100 126 

If each digit had a Bernoulli chance of coming up (like a 10-sided die), you’d expect to see 10 000 ± 30 times.  And going on with that same assumption, the chance of the least-frequent digit coming up less than 99 000 times would be something like one percent.

What does it mean?  I will meditate on this and expand √2 in different bases besides 10.