RetroPsychoKinesis Experiments Probability Table

Abridged Edition


Each of the RetroPsychoKinesis experiments at this site explores the ability of a subject to influence the content of of a sequence of 1024 previously-generated bits, created by a hardware random number generator based on radioactive decay, to yield a statistically significant bias toward one or zero bits in the sequence.

The following table gives the statistics for all possible results from a run of 1024 random bits. Please refer to the probability and statistics page for the mathematical details underlying this table. Fields in the table are as follows:

One Bits
The number of one bits in the run of 1024 bits. Note that the results are symmetrical around the mean value of 512, and hence probabilities are identical for runs with equal excesses of zeroes and ones.

Probability
Probability of obtaining this result in a given run of 1024 bits. Note that even the most probable result, 512, only has about a 2.5% chance of occurring, but that the sum of the probabilities for results between 500 and 524 indicate a run has better than a 56% probability of falling in that range.

Cumulative Probability
Probability of obtaining a result that far or further from the mean of 512 in a given run. Mathematically, the sum of probabilities of results between this result and the closer edge of the bell curve, or the area under the curve from the given point to the closer edge.

Frequency in Runs
The number of runs you can expect to make before obtaining a result this far from the mean due to chance. Inverse of the cumulative probability.

In order to speed up downloading, this table contains only probabilities for runs with between 405 and 619 one bits. This covers the centre of the bell curve and includes all results expected to occur by chance in fewer than 100 thousand million runs. You can view a complete table which includes probabilities for all possible runs, but the file is large (150K) and takes quite a while to download and display. The odds against a run of 1024 bits not appearing in the range covered by the abridged table are more than 64,000 million to one.

One
Bits
Probability Cumulative
Probability
Frequency
in Runs
4054.19777 × 10-121.19404 × 10-1183749281426
4066.40005 × 10-121.83404 × 10-1154524292271
4079.71801 × 10-122.80585 × 10-1135639877297
4081.46961 × 10-114.27546 × 10-1123389315392
4092.2134 × 10-116.48886 × 10-1115411038332
4103.3201 × 10-119.80895 × 10-1110194767051
4114.95995 × 10-111.47689 × 10-106770982074
4127.37974 × 10-112.21486 × 10-104514949621
4131.09356 × 10-103.30842 × 10-103022588158
4141.61392 × 10-104.92235 × 10-102031551342
4152.37227 × 10-107.29462 × 10-101370873305
4163.47287 × 10-101.07675 × 10-9928721412
4175.06356 × 10-101.58311 × 10-9631669850
4187.35307 × 10-102.31841 × 10-9431329649
4191.06347 × 10-93.38189 × 10-9295692882
4201.53191 × 10-94.9138 × 10-9203508587
4212.1978 × 10-97.1116 × 10-9140615380
4223.14046 × 10-91.02521 × 10-897541411
4234.4694 × 10-91.47215 × 10-867928067
4246.33516 × 10-92.10566 × 10-847491007
4258.94376 × 10-93.00004 × 10-833332914
4261.25758 × 10-84.25762 × 10-823487286
4271.76121 × 10-86.01883 × 10-816614523
4282.45664 × 10-88.47547 × 10-811798757
4293.41295 × 10-81.18884 × 10-78411546
4304.72257 × 10-81.6611 × 10-76020109
4316.5086 × 10-82.31196 × 10-74325334
4328.93426 × 10-83.20539 × 10-73119748
4331.2215 × 10-74.42688 × 10-72258925
4341.66338 × 10-76.09026 × 10-71641966
4352.25607 × 10-78.34633 × 10-71198131
4363.04777 × 10-71.13941 × 10-6877647
4374.10089 × 10-71.5495 × 10-6645370
4385.49594 × 10-72.09909 × 10-6476396
4397.33626 × 10-72.83272 × 10-6353017
4409.75389 × 10-73.80811 × 10-6262597
4411.29167 × 10-65.09978 × 10-6196086
4421.70372 × 10-66.8035 × 10-6146983
4432.2383 × 10-69.0418 × 10-6110597
4442.92894 × 10-61.19707 × 10-583536
4453.8175 × 10-61.57882 × 10-563338
4464.9559 × 10-62.07441 × 10-548206
4476.4083 × 10-62.71524 × 10-536829
4488.25355 × 10-63.5406 × 10-528243
4491.05881 × 10-54.59941 × 10-521741
4501.35292 × 10-55.95233 × 10-516800
4511.7219 × 10-57.67423 × 10-513030
4522.18285 × 10-59.85708 × 10-510144
4532.75627 × 10-50.0001261337928
4543.46659 × 10-50.0001607996218
4554.34276 × 10-50.0002042274896
4565.41892 × 10-50.0002584163869
4576.73511 × 10-50.0003257673069
4588.33801 × 10-50.0004091472444
4590.0001028170.0005119651953
4600.0001262860.0006382511566
4610.0001545020.0007927541261
4620.0001882790.0009810321019
4630.0002285370.001209569826
4640.0002763130.001485883673
4650.0003327640.001818647549
4660.0003991740.002217821450
4670.0004769580.002694779371
4680.0005676610.003262441306
4690.0006729630.003935404254
4700.0007946690.004730073211
4710.0009347060.005664779176
4720.0010951120.006759891147
4730.0012780160.008037907124
4740.0014856260.009523533105
4750.0017201990.01124373288
4760.0019840110.01322774375
4770.0022793250.01550706864
4780.0026083490.01811541755
4790.0029731910.02108860847
4800.003375810.02446441840
4810.0038179640.02828238335
4820.0043011510.03258353330
4830.004826550.03741008426
4840.0053949660.0428050523
4850.0060067670.04881181620
4860.0066618250.05547364218
4870.007359470.06283311215
4880.0080984340.07093154614
4890.0088768110.07980835612
4900.0096920280.08950038411
4910.0105408210.1000412059
4920.0114192220.1114604278
4930.0123225690.1237829968
4940.0132455140.137028517
4950.0141820650.1512105756
4960.015125630.1663362056
4970.016069080.1824052855
4980.017004830.1994101155
4990.0179249310.2173350464
5000.0188211770.2361562234
5010.0196852230.2558414463
5020.0205087090.2763501553
5030.0212833920.2976335463
5040.0220012840.319634833
5050.0226547870.3422896172
5060.0232368270.3655264442
5070.0237409790.3892674242
5080.0241615870.4134290112
5090.0244938680.4379228792
5100.0247340040.4626568832
5110.0248792140.4875360972
5120.0249278060.5124639031
5130.0248792140.4875360972
5140.0247340040.4626568832
5150.0244938680.4379228792
5160.0241615870.4134290112
5170.0237409790.3892674242
5180.0232368270.3655264442
5190.0226547870.3422896172
5200.0220012840.319634833
5210.0212833920.2976335463
5220.0205087090.2763501553
5230.0196852230.2558414463
5240.0188211770.2361562234
5250.0179249310.2173350464
5260.017004830.1994101155
5270.016069080.1824052855
5280.015125630.1663362056
5290.0141820650.1512105756
5300.0132455140.137028517
5310.0123225690.1237829968
5320.0114192220.1114604278
5330.0105408210.1000412059
5340.0096920280.08950038411
5350.0088768110.07980835612
5360.0080984340.07093154614
5370.007359470.06283311215
5380.0066618250.05547364218
5390.0060067670.04881181620
5400.0053949660.0428050523
5410.004826550.03741008426
5420.0043011510.03258353330
5430.0038179640.02828238335
5440.003375810.02446441840
5450.0029731910.02108860847
5460.0026083490.01811541755
5470.0022793250.01550706864
5480.0019840110.01322774375
5490.0017201990.01124373288
5500.0014856260.009523533105
5510.0012780160.008037907124
5520.0010951120.006759891147
5530.0009347060.005664779176
5540.0007946690.004730073211
5550.0006729630.003935404254
5560.0005676610.003262441306
5570.0004769580.002694779371
5580.0003991740.002217821450
5590.0003327640.001818647549
5600.0002763130.001485883673
5610.0002285370.001209569826
5620.0001882790.0009810321019
5630.0001545020.0007927541261
5640.0001262860.0006382511566
5650.0001028170.0005119651953
5668.33801 × 10-50.0004091472444
5676.73511 × 10-50.0003257673069
5685.41892 × 10-50.0002584163869
5694.34276 × 10-50.0002042274896
5703.46659 × 10-50.0001607996218
5712.75627 × 10-50.0001261337928
5722.18285 × 10-59.85708 × 10-510144
5731.7219 × 10-57.67423 × 10-513030
5741.35292 × 10-55.95233 × 10-516800
5751.05881 × 10-54.59941 × 10-521741
5768.25355 × 10-63.5406 × 10-528243
5776.4083 × 10-62.71524 × 10-536829
5784.9559 × 10-62.07441 × 10-548206
5793.8175 × 10-61.57882 × 10-563338
5802.92894 × 10-61.19707 × 10-583536
5812.2383 × 10-69.0418 × 10-6110597
5821.70372 × 10-66.8035 × 10-6146983
5831.29167 × 10-65.09978 × 10-6196086
5849.75389 × 10-73.80811 × 10-6262597
5857.33626 × 10-72.83272 × 10-6353017
5865.49594 × 10-72.09909 × 10-6476396
5874.10089 × 10-71.5495 × 10-6645370
5883.04777 × 10-71.13941 × 10-6877647
5892.25607 × 10-78.34633 × 10-71198131
5901.66338 × 10-76.09026 × 10-71641966
5911.2215 × 10-74.42688 × 10-72258925
5928.93426 × 10-83.20539 × 10-73119748
5936.5086 × 10-82.31196 × 10-74325334
5944.72257 × 10-81.6611 × 10-76020109
5953.41295 × 10-81.18884 × 10-78411546
5962.45664 × 10-88.47547 × 10-811798757
5971.76121 × 10-86.01883 × 10-816614523
5981.25758 × 10-84.25762 × 10-823487286
5998.94376 × 10-93.00004 × 10-833332914
6006.33516 × 10-92.10566 × 10-847491007
6014.4694 × 10-91.47215 × 10-867928067
6023.14046 × 10-91.02521 × 10-897541411
6032.1978 × 10-97.1116 × 10-9140615380
6041.53191 × 10-94.9138 × 10-9203508587
6051.06347 × 10-93.38189 × 10-9295692882
6067.35307 × 10-102.31841 × 10-9431329649
6075.06356 × 10-101.58311 × 10-9631669850
6083.47287 × 10-101.07675 × 10-9928721412
6092.37227 × 10-107.29462 × 10-101370873305
6101.61392 × 10-104.92235 × 10-102031551342
6111.09356 × 10-103.30842 × 10-103022588158
6127.37974 × 10-112.21486 × 10-104514949621
6134.95995 × 10-111.47689 × 10-106770982074
6143.3201 × 10-119.80895 × 10-1110194767051
6152.2134 × 10-116.48886 × 10-1115411038332
6161.46961 × 10-114.27546 × 10-1123389315392
6179.71801 × 10-122.80585 × 10-1135639877297
6186.40005 × 10-121.83404 × 10-1154524292271
6194.19777 × 10-121.19404 × 10-1183749281426

Mathematical Details

View the complete table (150K)

Table of Contents

RetroPsychoKinesis Project Home


by John Walker
kelvin@fourmilab.ch