Patterns in Pi

Five "heads" in a row! The next toss is likely a "tails." The gambler's fallacy rests on the erroneous assmption that small subsets will correlate highly with the universal set. Thinking Fast and Slow by Daniel Kahneman (reviewed  on Necessary Facts here) demolishes this confusion of "intuitive" for "calculative" reasoning.

The following appear in pi to 100,000 places, (here). These numerical facts are highly suggestive -- and totally irrelevant.
The following runs appear:
00000
11111
22222
33333
55555 (twice)
66666
99999 (three)
999999
(But 44444, 77777, and 88888 do not appear at all.   President Obama insists that this is unjust and Gov. Romney insists that these are the ones that create jobs.)

The following single digits appear. (Should the government pass laws to equalize these  disparities?)

0 125 of 10004
1 167 0f 10143
2 131 of 9908
3 81 of 10028
4 92 of 9970
5 29 of 10028
6 138 of 10030
7 133 of 10028
8 25 of 9978
9 94 of 9910

The following strings appear:
02468 (four times)
13579 (twice)
12345
23456
34567 - 3 times
56789 - 2 times
43210 - once and none others like 98765

31415 - pi itself
31416 - pi rounded
271828 - e the base of natural logarithms

000001 once but none of the others from 000002, …,  000009)

1776 - 15 times
1492 - 5 times

2997 (the speed of light in a vacuum in meters per second) 9 times
29978 (once)
66260 - Planck's constant (662608) once
66261 - Planck's constant once

17321 - the square root of 3, once
24495 - the square root of  6 once
26458 - the square root of  7 once
33166 - the square root of  11 (twice) (but none of the others below 10)
20500 (The White House ZIP code, once.)

Does order exist, or do we project order? Or is the truth stated entirely differently from either of those?

ALSO ON NECESSARY FACTS
Engines of Creation
The Genius of Design
Teaching Ethics to Engineering Students
Where all the Children are Above Average