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 (150 Kb) 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
405 4.19777 × 10−12 1.19404 × 10−11 83749281426
406 6.40005 × 10−12 1.83404 × 10−11 54524292271
407 9.71801 × 10−12 2.80585 × 10−11 35639877297
408 1.46961 × 10−11 4.27546 × 10−11 23389315392
409 2.2134 × 10−11 6.48886 × 10−11 15411038332
410 3.3201 × 10−11 9.80895 × 10−11 10194767051
411 4.95995 × 10−11 1.47689 × 10−10 6770982074
412 7.37974 × 10−11 2.21486 × 10−10 4514949621
413 1.09356 × 10−10 3.30842 × 10−10 3022588158
414 1.61392 × 10−10 4.92235 × 10−10 2031551342
415 2.37227 × 10−10 7.29462 × 10−10 1370873305
416 3.47287 × 10−10 1.07675 × 10−9 928721412
417 5.06356 × 10−10 1.58311 × 10−9 631669850
418 7.35307 × 10−10 2.31841 × 10−9 431329649
419 1.06347 × 10−9 3.38189 × 10−9 295692882
420 1.53191 × 10−9 4.9138 × 10−9 203508587
421 2.1978 × 10−9 7.1116 × 10−9 140615380
422 3.14046 × 10−9 1.02521 × 10−8 97541411
423 4.4694 × 10−9 1.47215 × 10−8 67928067
424 6.33516 × 10−9 2.10566 × 10−8 47491007
425 8.94376 × 10−9 3.00004 × 10−8 33332914
426 1.25758 × 10−8 4.25762 × 10−8 23487286
427 1.76121 × 10−8 6.01883 × 10−8 16614523
428 2.45664 × 10−8 8.47547 × 10−8 11798757
429 3.41295 × 10−8 1.18884 × 10−7 8411546
430 4.72257 × 10−8 1.6611 × 10−7 6020109
431 6.5086 × 10−8 2.31196 × 10−7 4325334
432 8.93426 × 10−8 3.20539 × 10−7 3119748
433 1.2215 × 10−7 4.42688 × 10−7 2258925
434 1.66338 × 10−7 6.09026 × 10−7 1641966
435 2.25607 × 10−7 8.34633 × 10−7 1198131
436 3.04777 × 10−7 1.13941 × 10−6 877647
437 4.10089 × 10−7 1.5495 × 10−6 645370
438 5.49594 × 10−7 2.09909 × 10−6 476396
439 7.33626 × 10−7 2.83272 × 10−6 353017
440 9.75389 × 10−7 3.80811 × 10−6 262597
441 1.29167 × 10−6 5.09978 × 10−6 196086
442 1.70372 × 10−6 6.8035 × 10−6 146983
443 2.2383 × 10−6 9.0418 × 10−6 110597
444 2.92894 × 10−6 1.19707 × 10−5 83536
445 3.8175 × 10−6 1.57882 × 10−5 63338
446 4.9559 × 10−6 2.07441 × 10−5 48206
447 6.4083 × 10−6 2.71524 × 10−5 36829
448 8.25355 × 10−6 3.5406 × 10−5 28243
449 1.05881 × 10−5 4.59941 × 10−5 21741
450 1.35292 × 10−5 5.95233 × 10−5 16800
451 1.7219 × 10−5 7.67423 × 10−5 13030
452 2.18285 × 10−5 9.85708 × 10−5 10144
453 2.75627 × 10−5 0.000126133 7928
454 3.46659 × 10−5 0.000160799 6218
455 4.34276 × 10−5 0.000204227 4896
456 5.41892 × 10−5 0.000258416 3869
457 6.73511 × 10−5 0.000325767 3069
458 8.33801 × 10−5 0.000409147 2444
459 0.000102817 0.000511965 1953
460 0.000126286 0.000638251 1566
461 0.000154502 0.000792754 1261
462 0.000188279 0.000981032 1019
463 0.000228537 0.001209569 826
464 0.000276313 0.001485883 673
465 0.000332764 0.001818647 549
466 0.000399174 0.002217821 450
467 0.000476958 0.002694779 371
468 0.000567661 0.003262441 306
469 0.000672963 0.003935404 254
470 0.000794669 0.004730073 211
471 0.000934706 0.005664779 176
472 0.001095112 0.006759891 147
473 0.001278016 0.008037907 124
474 0.001485626 0.009523533 105
475 0.001720199 0.011243732 88
476 0.001984011 0.013227743 75
477 0.002279325 0.015507068 64
478 0.002608349 0.018115417 55
479 0.002973191 0.021088608 47
480 0.00337581 0.024464418 40
481 0.003817964 0.028282383 35
482 0.004301151 0.032583533 30
483 0.00482655 0.037410084 26
484 0.005394966 0.04280505 23
485 0.006006767 0.048811816 20
486 0.006661825 0.055473642 18
487 0.00735947 0.062833112 15
488 0.008098434 0.070931546 14
489 0.008876811 0.079808356 12
490 0.009692028 0.089500384 11
491 0.010540821 0.100041205 9
492 0.011419222 0.111460427 8
493 0.012322569 0.123782996 8
494 0.013245514 0.13702851 7
495 0.014182065 0.151210575 6
496 0.01512563 0.166336205 6
497 0.01606908 0.182405285 5
498 0.01700483 0.199410115 5
499 0.017924931 0.217335046 4
500 0.018821177 0.236156223 4
501 0.019685223 0.255841446 3
502 0.020508709 0.276350155 3
503 0.021283392 0.297633546 3
504 0.022001284 0.31963483 3
505 0.022654787 0.342289617 2
506 0.023236827 0.365526444 2
507 0.023740979 0.389267424 2
508 0.024161587 0.413429011 2
509 0.024493868 0.437922879 2
510 0.024734004 0.462656883 2
511 0.024879214 0.487536097 2
512 0.024927806 0.512463903 1
513 0.024879214 0.487536097 2
514 0.024734004 0.462656883 2
515 0.024493868 0.437922879 2
516 0.024161587 0.413429011 2
517 0.023740979 0.389267424 2
518 0.023236827 0.365526444 2
519 0.022654787 0.342289617 2
520 0.022001284 0.31963483 3
521 0.021283392 0.297633546 3
522 0.020508709 0.276350155 3
523 0.019685223 0.255841446 3
524 0.018821177 0.236156223 4
525 0.017924931 0.217335046 4
526 0.01700483 0.199410115 5
527 0.01606908 0.182405285 5
528 0.01512563 0.166336205 6
529 0.014182065 0.151210575 6
530 0.013245514 0.13702851 7
531 0.012322569 0.123782996 8
532 0.011419222 0.111460427 8
533 0.010540821 0.100041205 9
534 0.009692028 0.089500384 11
535 0.008876811 0.079808356 12
536 0.008098434 0.070931546 14
537 0.00735947 0.062833112 15
538 0.006661825 0.055473642 18
539 0.006006767 0.048811816 20
540 0.005394966 0.04280505 23
541 0.00482655 0.037410084 26
542 0.004301151 0.032583533 30
543 0.003817964 0.028282383 35
544 0.00337581 0.024464418 40
545 0.002973191 0.021088608 47
546 0.002608349 0.018115417 55
547 0.002279325 0.015507068 64
548 0.001984011 0.013227743 75
549 0.001720199 0.011243732 88
550 0.001485626 0.009523533 105
551 0.001278016 0.008037907 124
552 0.001095112 0.006759891 147
553 0.000934706 0.005664779 176
554 0.000794669 0.004730073 211
555 0.000672963 0.003935404 254
556 0.000567661 0.003262441 306
557 0.000476958 0.002694779 371
558 0.000399174 0.002217821 450
559 0.000332764 0.001818647 549
560 0.000276313 0.001485883 673
561 0.000228537 0.001209569 826
562 0.000188279 0.000981032 1019
563 0.000154502 0.000792754 1261
564 0.000126286 0.000638251 1566
565 0.000102817 0.000511965 1953
566 8.33801 × 10−5 0.000409147 2444
567 6.73511 × 10−5 0.000325767 3069
568 5.41892 × 10−5 0.000258416 3869
569 4.34276 × 10−5 0.000204227 4896
570 3.46659 × 10−5 0.000160799 6218
571 2.75627 × 10−5 0.000126133 7928
572 2.18285 × 10−5 9.85708 × 10−5 10144
573 1.7219 × 10−5 7.67423 × 10−5 13030
574 1.35292 × 10−5 5.95233 × 10−5 16800
575 1.05881 × 10−5 4.59941 × 10−5 21741
576 8.25355 × 10−6 3.5406 × 10−5 28243
577 6.4083 × 10−6 2.71524 × 10−5 36829
578 4.9559 × 10−6 2.07441 × 10−5 48206
579 3.8175 × 10−6 1.57882 × 10−5 63338
580 2.92894 × 10−6 1.19707 × 10−5 83536
581 2.2383 × 10−6 9.0418 × 10−6 110597
582 1.70372 × 10−6 6.8035 × 10−6 146983
583 1.29167 × 10−6 5.09978 × 10−6 196086
584 9.75389 × 10−7 3.80811 × 10−6 262597
585 7.33626 × 10−7 2.83272 × 10−6 353017
586 5.49594 × 10−7 2.09909 × 10−6 476396
587 4.10089 × 10−7 1.5495 × 10−6 645370
588 3.04777 × 10−7 1.13941 × 10−6 877647
589 2.25607 × 10−7 8.34633 × 10−7 1198131
590 1.66338 × 10−7 6.09026 × 10−7 1641966
591 1.2215 × 10−7 4.42688 × 10−7 2258925
592 8.93426 × 10−8 3.20539 × 10−7 3119748
593 6.5086 × 10−8 2.31196 × 10−7 4325334
594 4.72257 × 10−8 1.6611 × 10−7 6020109
595 3.41295 × 10−8 1.18884 × 10−7 8411546
596 2.45664 × 10−8 8.47547 × 10−8 11798757
597 1.76121 × 10−8 6.01883 × 10−8 16614523
598 1.25758 × 10−8 4.25762 × 10−8 23487286
599 8.94376 × 10−9 3.00004 × 10−8 33332914
600 6.33516 × 10−9 2.10566 × 10−8 47491007
601 4.4694 × 10−9 1.47215 × 10−8 67928067
602 3.14046 × 10−9 1.02521 × 10−8 97541411
603 2.1978 × 10−9 7.1116 × 10−9 140615380
604 1.53191 × 10−9 4.9138 × 10−9 203508587
605 1.06347 × 10−9 3.38189 × 10−9 295692882
606 7.35307 × 10−10 2.31841 × 10−9 431329649
607 5.06356 × 10−10 1.58311 × 10−9 631669850
608 3.47287 × 10−10 1.07675 × 10−9 928721412
609 2.37227 × 10−10 7.29462 × 10−10 1370873305
610 1.61392 × 10−10 4.92235 × 10−10 2031551342
611 1.09356 × 10−10 3.30842 × 10−10 3022588158
612 7.37974 × 10−11 2.21486 × 10−10 4514949621
613 4.95995 × 10−11 1.47689 × 10−10 6770982074
614 3.3201 × 10−11 9.80895 × 10−11 10194767051
615 2.2134 × 10−11 6.48886 × 10−11 15411038332
616 1.46961 × 10−11 4.27546 × 10−11 23389315392
617 9.71801 × 10−12 2.80585 × 10−11 35639877297
618 6.40005 × 10−12 1.83404 × 10−11 54524292271
619 4.19777 × 10−12 1.19404 × 10−11 83749281426

Mathematical Details

View the complete table (150 Kb)

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by John Walker