Here are sample sets that I mailed to ToniXX. No tricks here; no cherry-picking; just straight data. Again, try any of these algorithms yourself, and draw your own conclusions.
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1) Here's just [10d2], rolled over and over again:
11, 14, 14, 10, 19, 12, 11, 18, 15, 15, 15, 10, 18, 10, 17, 15, 20, 10, 20, 14, 15, 10, 19, 11, 16, 12, 10, 17, 19, 11, 20, 20, 20, 11, 10, 16
Seem all right at first glance? 1d2 is a coin flip. 10d2 is ten coin flips. To roll a 20 on 10d2 means to flip heads on a coin ten times in a row. To manage that, the odds are 1 in 1024. The odds of rolling a 10 -- that's ten tails in a row -- is similarly 1 in 1024. Yet in the above 36 attempts, I managed to roll either 10 or 20 twelve times -- 33% of the time! Of the remainder, 11 or 19 -- results of comparable supposed rarity -- showed up eight times.
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2) Stat generator history entries:
3/14/2012 10:06:26 AM, Emmett, Sinister Shroom:
Stats: STR:17, INT:17, WIS:16, DEX:15, CON:13, CHR:16
3/16/2012 2:07:41 PM, Ihsahn, Sinister Shroom:
Stats: DEX:17, INT:17, WIS:16, STR:15, CON:13, CHR:16
3/19/2012 1:25:23 AM, Zafalia Sojafa, Sinister Shroom:
Stats: WIS:17, DEX:17, INT:16, CHR:15, STR:13, CON:16
That was the *very next stats roll* made that day, with *exactly* the same stats, in *exactly* the same order.
Two stats rolls later:
3/23/2012 10:33:35 AM, Veneficus, Incursion into Newiron:
Stats: STR:17, DEX:17, CON:16, CHR:15, WIS:13, INT:16
Again, the same exact stats, in exactly the same order.
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3) Using [3d6][3d6][3d6][3d6][3d6][3d6]:
07 05 18 08 05 18 -- Two 18's
05 03 16 06 03 16 -- Two 3's
03 18 14 05 18 15 -- Two 18's and 3
18 17 13 04 17 14 -- 18/17/17 and a 4
14 13 09 16 13 10 -- Average Joe
With rolls like these I should be playing the lottery.

Really, really wild results here.
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4) Using [1d100][1d100][1d100][1d100][1d100][1d100], I generated several sets of numbers. Then I took those sets and sorted them by the first number in each set. Here are the results, along with the steps between each number in the series:
02 93 71 11 92 75: -9, -22, -60, -19, -17
06 97 75 15 96 78: -9, -22, -60, -19, -18
15 07 85 24 06 88: -8, -22, -61, -18, -18
21 12 90 30 11 93: -9, -22, -60, -19, -18
30 22 00 40 21 03: -8, -22, -60, -19, -18
41 33 11 51 32 14: -8, -22, -60, -19, -18
42 34 12 52 33 15: -8, -22, -60, -19, -18
44 35 13 53 34 17: -9, -22, -60, -19, -17
50 41 19 59 40 23: -9, -22, -60, -19, -17
52 44 22 62 43 25: -8, -22, -60, -19, -18
53 45 23 63 44 26: -8, -22, -60, -19, -18
65 57 35 75 56 38: -8, -22, -60, -19, -18
85 76 54 94 75 57: -9, -22, -60, -19, -17
86 78 56 95 77 59: -8, -22, -60, -18, -18
89 80 58 98 79 62: -9, -22, -60, -19, -17
96 88 66 06 87 69: -8, -22, -60, -19, -18
In other words, the second number is always 8 or 9 less than the first number; the third number is always 22 less than the second number; and so forth.