Agains statistics on high bit, with seeds now 8035872 and 10427991. The former seems to indicate again preponderance of 1s in batches of 165 at a time. Not so for latter seed.

RNGwalkhighbit-a.out.txt

Examining batches of 165 bits from \pdfuniformdeviate 2
If more 1s than 0s count 1, else count 0.

There seems to be preponderance of case "more 1s than 0s" in case of seed 08035872,
situation looks more random for 10427991, when averaging over all possible
initial shifts.


+++++++++++++++++++++++
10000 runs of 165 draws
+++++++++++++++++++++++

(shift=1, seed=08035872) 0:4892, 1:5108
(shift=1, seed=10427991) 0:5018, 1:4982

(shift=2, seed=08035872) 0:4880, 1:5120
(shift=2, seed=10427991) 0:4953, 1:5047

(shift=3, seed=08035872) 0:4869, 1:5131
(shift=3, seed=10427991) 0:4975, 1:5025

(shift=4, seed=08035872) 0:4854, 1:5146
(shift=4, seed=10427991) 0:4975, 1:5025

(shift=5, seed=08035872) 0:4879, 1:5121
(shift=5, seed=10427991) 0:4990, 1:5010

(shift=6, seed=08035872) 0:4867, 1:5133
(shift=6, seed=10427991) 0:4983, 1:5017

(shift=7, seed=08035872) 0:4845, 1:5155
(shift=7, seed=10427991) 0:4992, 1:5008

(shift=8, seed=08035872) 0:4840, 1:5160
(shift=8, seed=10427991) 0:4969, 1:5031

(shift=9, seed=08035872) 0:4849, 1:5151
(shift=9, seed=10427991) 0:4972, 1:5028

(shift=10, seed=08035872) 0:4851, 1:5149
(shift=10, seed=10427991) 0:4972, 1:5028

(shift=11, seed=08035872) 0:4869, 1:5131
(shift=11, seed=10427991) 0:4982, 1:5018

(shift=12, seed=08035872) 0:4888, 1:5112
(shift=12, seed=10427991) 0:5007, 1:4993

(shift=13, seed=08035872) 0:4909, 1:5091
(shift=13, seed=10427991) 0:4991, 1:5009

(shift=14, seed=08035872) 0:4889, 1:5111
(shift=14, seed=10427991) 0:4995, 1:5005

(shift=15, seed=08035872) 0:4897, 1:5103
(shift=15, seed=10427991) 0:5011, 1:4989

(shift=16, seed=08035872) 0:4887, 1:5113
(shift=16, seed=10427991) 0:5021, 1:4979

(shift=17, seed=08035872) 0:4877, 1:5123
(shift=17, seed=10427991) 0:5012, 1:4988

(shift=18, seed=08035872) 0:4896, 1:5104
(shift=18, seed=10427991) 0:5041, 1:4959

(shift=19, seed=08035872) 0:4882, 1:5118
(shift=19, seed=10427991) 0:5009, 1:4991

(shift=20, seed=08035872) 0:4879, 1:5121
(shift=20, seed=10427991) 0:4972, 1:5028

(shift=21, seed=08035872) 0:4865, 1:5135
(shift=21, seed=10427991) 0:5004, 1:4996

(shift=22, seed=08035872) 0:4890, 1:5110
(shift=22, seed=10427991) 0:5002, 1:4998

(shift=23, seed=08035872) 0:4895, 1:5105
(shift=23, seed=10427991) 0:5008, 1:4992

(shift=24, seed=08035872) 0:4880, 1:5120
(shift=24, seed=10427991) 0:4997, 1:5003

(shift=25, seed=08035872) 0:4903, 1:5097
(shift=25, seed=10427991) 0:4975, 1:5025

(shift=26, seed=08035872) 0:4917, 1:5083
(shift=26, seed=10427991) 0:4981, 1:5019

(shift=27, seed=08035872) 0:4911, 1:5089
(shift=27, seed=10427991) 0:4967, 1:5033

(shift=28, seed=08035872) 0:4890, 1:5110
(shift=28, seed=10427991) 0:4975, 1:5025

(shift=29, seed=08035872) 0:4879, 1:5121
(shift=29, seed=10427991) 0:4986, 1:5014

(shift=30, seed=08035872) 0:4896, 1:5104
(shift=30, seed=10427991) 0:5009, 1:4991

(shift=31, seed=08035872) 0:4902, 1:5098
(shift=31, seed=10427991) 0:4993, 1:5007

(shift=32, seed=08035872) 0:4890, 1:5110
(shift=32, seed=10427991) 0:4994, 1:5006

(shift=33, seed=08035872) 0:4897, 1:5103
(shift=33, seed=10427991) 0:5009, 1:4991

(shift=34, seed=08035872) 0:4902, 1:5098
(shift=34, seed=10427991) 0:5012, 1:4988

(shift=35, seed=08035872) 0:4877, 1:5123
(shift=35, seed=10427991) 0:4985, 1:5015

(shift=36, seed=08035872) 0:4901, 1:5099
(shift=36, seed=10427991) 0:4977, 1:5023

(shift=37, seed=08035872) 0:4866, 1:5134
(shift=37, seed=10427991) 0:4973, 1:5027

(shift=38, seed=08035872) 0:4882, 1:5118
(shift=38, seed=10427991) 0:4951, 1:5049

(shift=39, seed=08035872) 0:4886, 1:5114
(shift=39, seed=10427991) 0:4962, 1:5038

(shift=40, seed=08035872) 0:4887, 1:5113
(shift=40, seed=10427991) 0:4966, 1:5034

(shift=41, seed=08035872) 0:4878, 1:5122
(shift=41, seed=10427991) 0:4966, 1:5034

(shift=42, seed=08035872) 0:4907, 1:5093
(shift=42, seed=10427991) 0:4970, 1:5030

(shift=43, seed=08035872) 0:4923, 1:5077
(shift=43, seed=10427991) 0:4969, 1:5031

(shift=44, seed=08035872) 0:4898, 1:5102
(shift=44, seed=10427991) 0:4969, 1:5031

(shift=45, seed=08035872) 0:4888, 1:5112
(shift=45, seed=10427991) 0:4967, 1:5033

(shift=46, seed=08035872) 0:4889, 1:5111
(shift=46, seed=10427991) 0:4949, 1:5051

(shift=47, seed=08035872) 0:4851, 1:5149
(shift=47, seed=10427991) 0:4944, 1:5056

(shift=48, seed=08035872) 0:4861, 1:5139
(shift=48, seed=10427991) 0:4902, 1:5098

(shift=49, seed=08035872) 0:4864, 1:5136
(shift=49, seed=10427991) 0:4892, 1:5108

(shift=50, seed=08035872) 0:4871, 1:5129
(shift=50, seed=10427991) 0:4883, 1:5117

(shift=51, seed=08035872) 0:4870, 1:5130
(shift=51, seed=10427991) 0:4884, 1:5116

(shift=52, seed=08035872) 0:4860, 1:5140
(shift=52, seed=10427991) 0:4906, 1:5094

(shift=53, seed=08035872) 0:4879, 1:5121
(shift=53, seed=10427991) 0:4908, 1:5092

(shift=54, seed=08035872) 0:4851, 1:5149
(shift=54, seed=10427991) 0:4899, 1:5101

(shift=55, seed=08035872) 0:4857, 1:5143
(shift=55, seed=10427991) 0:4900, 1:5100


++++++++++++++++++++++
30000 runs of 55 draws
++++++++++++++++++++++

(shift=1, seed=08035872) 0:14865, 1:15135
(shift=1, seed=10427991) 0:15003, 1:14997

(shift=2, seed=08035872) 0:14894, 1:15106
(shift=2, seed=10427991) 0:15022, 1:14978

(shift=3, seed=08035872) 0:14887, 1:15113
(shift=3, seed=10427991) 0:15011, 1:14989

(shift=4, seed=08035872) 0:14917, 1:15083
(shift=4, seed=10427991) 0:14970, 1:15030

(shift=5, seed=08035872) 0:14911, 1:15089
(shift=5, seed=10427991) 0:15022, 1:14978

(shift=6, seed=08035872) 0:14882, 1:15118
(shift=6, seed=10427991) 0:15039, 1:14961

(shift=7, seed=08035872) 0:14893, 1:15107
(shift=7, seed=10427991) 0:15085, 1:14915

(shift=8, seed=08035872) 0:14839, 1:15161
(shift=8, seed=10427991) 0:15095, 1:14905

(shift=9, seed=08035872) 0:14839, 1:15161
(shift=9, seed=10427991) 0:15092, 1:14908

(shift=10, seed=08035872) 0:14913, 1:15087
(shift=10, seed=10427991) 0:15072, 1:14928

(shift=11, seed=08035872) 0:14914, 1:15086
(shift=11, seed=10427991) 0:15086, 1:14914

(shift=12, seed=08035872) 0:14960, 1:15040
(shift=12, seed=10427991) 0:15074, 1:14926

(shift=13, seed=08035872) 0:15031, 1:14969
(shift=13, seed=10427991) 0:15090, 1:14910

(shift=14, seed=08035872) 0:14937, 1:15063
(shift=14, seed=10427991) 0:15133, 1:14867

(shift=15, seed=08035872) 0:14946, 1:15054
(shift=15, seed=10427991) 0:15051, 1:14949

(shift=16, seed=08035872) 0:14938, 1:15062
(shift=16, seed=10427991) 0:15045, 1:14955

(shift=17, seed=08035872) 0:14949, 1:15051
(shift=17, seed=10427991) 0:15045, 1:14955

(shift=18, seed=08035872) 0:14842, 1:15158
(shift=18, seed=10427991) 0:15013, 1:14987

(shift=19, seed=08035872) 0:14889, 1:15111
(shift=19, seed=10427991) 0:14975, 1:15025

(shift=20, seed=08035872) 0:14808, 1:15192
(shift=20, seed=10427991) 0:14971, 1:15029

(shift=21, seed=08035872) 0:14835, 1:15165
(shift=21, seed=10427991) 0:14975, 1:15025

(shift=22, seed=08035872) 0:14895, 1:15105
(shift=22, seed=10427991) 0:14993, 1:15007

(shift=23, seed=08035872) 0:14889, 1:15111
(shift=23, seed=10427991) 0:14965, 1:15035

(shift=24, seed=08035872) 0:14894, 1:15106
(shift=24, seed=10427991) 0:14983, 1:15017

(shift=25, seed=08035872) 0:14927, 1:15073
(shift=25, seed=10427991) 0:15019, 1:14981

(shift=26, seed=08035872) 0:14880, 1:15120
(shift=26, seed=10427991) 0:14990, 1:15010

(shift=27, seed=08035872) 0:14891, 1:15109
(shift=27, seed=10427991) 0:14921, 1:15079

(shift=28, seed=08035872) 0:14917, 1:15083
(shift=28, seed=10427991) 0:14957, 1:15043

(shift=29, seed=08035872) 0:14937, 1:15063
(shift=29, seed=10427991) 0:14954, 1:15046

(shift=30, seed=08035872) 0:14986, 1:15014
(shift=30, seed=10427991) 0:14972, 1:15028

(shift=31, seed=08035872) 0:14994, 1:15006
(shift=31, seed=10427991) 0:15046, 1:14954

(shift=32, seed=08035872) 0:14960, 1:15040
(shift=32, seed=10427991) 0:15024, 1:14976

(shift=33, seed=08035872) 0:14955, 1:15045
(shift=33, seed=10427991) 0:14960, 1:15040

(shift=34, seed=08035872) 0:14973, 1:15027
(shift=34, seed=10427991) 0:14970, 1:15030

(shift=35, seed=08035872) 0:14923, 1:15077
(shift=35, seed=10427991) 0:15067, 1:14933

(shift=36, seed=08035872) 0:14883, 1:15117
(shift=36, seed=10427991) 0:15076, 1:14924

(shift=37, seed=08035872) 0:14864, 1:15136
(shift=37, seed=10427991) 0:15072, 1:14928

(shift=38, seed=08035872) 0:14904, 1:15096
(shift=38, seed=10427991) 0:15052, 1:14948

(shift=39, seed=08035872) 0:14888, 1:15112
(shift=39, seed=10427991) 0:15079, 1:14921

(shift=40, seed=08035872) 0:14872, 1:15128
(shift=40, seed=10427991) 0:15055, 1:14945

(shift=41, seed=08035872) 0:14860, 1:15140
(shift=41, seed=10427991) 0:15078, 1:14922

(shift=42, seed=08035872) 0:14875, 1:15125
(shift=42, seed=10427991) 0:15117, 1:14883

(shift=43, seed=08035872) 0:14917, 1:15083
(shift=43, seed=10427991) 0:15064, 1:14936

(shift=44, seed=08035872) 0:14888, 1:15112
(shift=44, seed=10427991) 0:15048, 1:14952

(shift=45, seed=08035872) 0:14992, 1:15008
(shift=45, seed=10427991) 0:15029, 1:14971

(shift=46, seed=08035872) 0:14898, 1:15102
(shift=46, seed=10427991) 0:14941, 1:15059

(shift=47, seed=08035872) 0:14853, 1:15147
(shift=47, seed=10427991) 0:14933, 1:15067

(shift=48, seed=08035872) 0:14915, 1:15085
(shift=48, seed=10427991) 0:14985, 1:15015

(shift=49, seed=08035872) 0:14876, 1:15124
(shift=49, seed=10427991) 0:14956, 1:15044

(shift=50, seed=08035872) 0:14920, 1:15080
(shift=50, seed=10427991) 0:14977, 1:15023

(shift=51, seed=08035872) 0:14886, 1:15114
(shift=51, seed=10427991) 0:14949, 1:15051

(shift=52, seed=08035872) 0:14897, 1:15103
(shift=52, seed=10427991) 0:14965, 1:15035

(shift=53, seed=08035872) 0:14876, 1:15124
(shift=53, seed=10427991) 0:14993, 1:15007

(shift=54, seed=08035872) 0:14900, 1:15100
(shift=54, seed=10427991) 0:15006, 1:14994

(shift=55, seed=08035872) 0:14829, 1:15171
(shift=55, seed=10427991) 0:15003, 1:14997