Author: Dieter Buerssner
Date: 12:59:17 05/21/05
As many of you will have recognized, Pavel is doing a very long match between
Yace Paderborn and Aristarch 4.5. I thought, it should be interesting, to take a
closer look at the statistics. Until now, about 13000 games were played. Yace
was using positional learning. I think, it did not use book learning for the
first 10000 games or so. Possibly it was using book learning later, but I am not
sure. Pavel had intended to use book learning, but it turned out, that by
default Yace book learning will not do anything (by purpose) when the time
control is faster than 5 minutes. The games were played at 2 minutes. I
mentioned this some days ago, and perhaps Pavel has set Yace up to use book
learning even at this fast time control. The results seem to indicate this -
results at later games are clearly better for Yace, than results of former
games. But perhaps, pure positional learning helped here.
Does anybody know the exact details of learning mechanisms in Aristarch?
For the statistics, I used the pgn from Pavel's site:
http://www.pavs.org/new.rar (Pavel, I guess the name of the file could be
improved, for example something like yace_aristarch_20050517).
It turned out, that Yace played a few more games as white, than as black. In the
"sub-matches", always Yace started as white. So, when the last sub-match was an
odd number, Yace also had white in the last game. I deleted all those last games
with black. This were 25 games - of course, it won't really matter in a match of
now 13000 games. After deleting those games, the overall result from Yace point
of view is
6315.0 - 6663.0 ( 48.66%) white + 2732 w= 1591 w- 2166 b+ 1942 b= 1691 b- 2856
One question could be: was the performance about equal during the match, or did
it change significantly. It turns out, that the performance clearly got better
for Yace. Even in earlier stages of the match, where book learning was certainly
off. I give the details (that are hopefully self explaing) at the end of my
post. One can ask: where the games statistically independent. For this, I did
some Monte Carlo simulation of match results. I also give the details at the end
of my post. I am aware, that those results can be got analytically correct
without Monte Carlo simulation, but I was too lazy. With some experience in
Monte Carlo simulations, it is much easier and less error prone to code (I can
give the source code, if anybody should be interested). And of course the
results will be the same. At this place (many more stats at the end), I only
want to pinpoint one result - analysing bunches of 1000 games:
statistics for each bundle of 1000 games
games 1 to 1000: res 44.70% w 47.20% b 42.20% + 33.00% = 23.40% - 43.60%
games 1001 to 2000: res 43.15% w 48.00% b 38.30% + 30.70% = 24.90% - 44.40%
games 2001 to 3000: res 47.85% w 51.50% b 44.20% + 37.40% = 20.90% - 41.70%
games 3001 to 4000: res 46.15% w 49.40% b 42.90% + 33.70% = 24.90% - 41.40%
games 4001 to 5000: res 44.80% w 52.10% b 37.50% + 32.00% = 25.60% - 42.40%
games 5001 to 6000: res 48.40% w 54.60% b 42.20% + 36.20% = 24.40% - 39.40%
games 6001 to 7000: res 48.30% w 52.70% b 43.90% + 35.90% = 24.80% - 39.30%
games 7001 to 8000: res 49.20% w 55.90% b 42.50% + 35.30% = 27.80% - 36.90%
games 8001 to 9000: res 50.55% w 61.50% b 39.60% + 38.20% = 24.70% - 37.10%
games 9001 to 10000: res 48.95% w 53.50% b 44.40% + 35.60% = 26.70% - 37.70%
games 10001 to 11000: res 51.40% w 59.60% b 43.20% + 38.00% = 26.80% - 35.20%
games 11001 to 12000: res 53.30% w 59.20% b 47.40% + 39.10% = 28.40% - 32.50%
games 12001 to 12978: res 55.98% w 61.66% b 50.31% + 43.25% = 25.46% - 31.29%
The result from Yace point of view is almost a strictly monotonic function (with
some random noise of course).
I also give the result of the Monte Carlo simulation for 1000 games. For this
simulation I used individal probabilities for white wins, white draws, white
losses, black wins, black draws and black losses, that were taken from all 12978
games.
Result of chess matches
Player A as white wins 42.1%, draws 24.5% and loses 33.4%
Player A as black wins 29.9%, draws 26.1% and loses 44.0%
Expected result: 48.6593% (as white 54.3612%, as black 42.9573%)
A match of 1000 games was simulated 1000000 times by a Monte Carlo method
result probability p <= res. p > res.
[...]
454.0 - 546.0 ( 45.400%): 0.0776% 0.8435% 99.1565%
454.5 - 545.5 ( 45.450%): 0.0879% 0.9314% 99.0686%
455.0 - 545.0 ( 45.500%): 0.0962% 1.0276% 98.9724%
455.5 - 544.5 ( 45.550%): 0.1060% 1.1336% 98.8664%
456.0 - 544.0 ( 45.600%): 0.1099% 1.2435% 98.7565%
456.5 - 543.5 ( 45.650%): 0.1257% 1.3692% 98.6308%
457.0 - 543.0 ( 45.700%): 0.1342% 1.5034% 98.4966%
457.5 - 542.5 ( 45.750%): 0.1515% 1.6549% 98.3451%
458.0 - 542.0 ( 45.800%): 0.1629% 1.8178% 98.1822%
458.5 - 541.5 ( 45.850%): 0.1694% 1.9872% 98.0128%
459.0 - 541.0 ( 45.900%): 0.1864% 2.1736% 97.8264%
459.5 - 540.5 ( 45.950%): 0.2013% 2.3749% 97.6251%
460.0 - 540.0 ( 46.000%): 0.2068% 2.5817% 97.4183%
460.5 - 539.5 ( 46.050%): 0.2362% 2.8179% 97.1821%
461.0 - 539.0 ( 46.100%): 0.2557% 3.0736% 96.9264%
461.5 - 538.5 ( 46.150%): 0.2698% 3.3434% 96.6566%
462.0 - 538.0 ( 46.200%): 0.2837% 3.6271% 96.3729%
462.5 - 537.5 ( 46.250%): 0.3066% 3.9337% 96.0663%
463.0 - 537.0 ( 46.300%): 0.3138% 4.2475% 95.7525%
463.5 - 536.5 ( 46.350%): 0.3490% 4.5965% 95.4035%
464.0 - 536.0 ( 46.400%): 0.3684% 4.9649% 95.0351%
464.5 - 535.5 ( 46.450%): 0.3989% 5.3638% 94.6362%
465.0 - 535.0 ( 46.500%): 0.4140% 5.7778% 94.2222%
465.5 - 534.5 ( 46.550%): 0.4331% 6.2109% 93.7891%
466.0 - 534.0 ( 46.600%): 0.4698% 6.6807% 93.3193%
466.5 - 533.5 ( 46.650%): 0.4775% 7.1582% 92.8418%
467.0 - 533.0 ( 46.700%): 0.5128% 7.6710% 92.3290%
467.5 - 532.5 ( 46.750%): 0.5339% 8.2049% 91.7951%
468.0 - 532.0 ( 46.800%): 0.5678% 8.7727% 91.2273%
468.5 - 531.5 ( 46.850%): 0.5951% 9.3678% 90.6322%
469.0 - 531.0 ( 46.900%): 0.6262% 9.9940% 90.0060%
469.5 - 530.5 ( 46.950%): 0.6711% 10.6651% 89.3349%
470.0 - 530.0 ( 47.000%): 0.6930% 11.3581% 88.6419%
470.5 - 529.5 ( 47.050%): 0.7224% 12.0805% 87.9195%
471.0 - 529.0 ( 47.100%): 0.7570% 12.8375% 87.1625%
471.5 - 528.5 ( 47.150%): 0.7866% 13.6241% 86.3759%
472.0 - 528.0 ( 47.200%): 0.8234% 14.4475% 85.5525%
472.5 - 527.5 ( 47.250%): 0.8608% 15.3083% 84.6917%
473.0 - 527.0 ( 47.300%): 0.9040% 16.2123% 83.7877%
473.5 - 526.5 ( 47.350%): 0.9236% 17.1359% 82.8641%
474.0 - 526.0 ( 47.400%): 0.9556% 18.0915% 81.9085%
474.5 - 525.5 ( 47.450%): 0.9750% 19.0665% 80.9335%
475.0 - 525.0 ( 47.500%): 1.0172% 20.0837% 79.9163%
475.5 - 524.5 ( 47.550%): 1.0489% 21.1326% 78.8674%
476.0 - 524.0 ( 47.600%): 1.0729% 22.2055% 77.7945%
476.5 - 523.5 ( 47.650%): 1.1213% 23.3268% 76.6732%
477.0 - 523.0 ( 47.700%): 1.1578% 24.4846% 75.5154%
477.5 - 522.5 ( 47.750%): 1.1717% 25.6563% 74.3437%
478.0 - 522.0 ( 47.800%): 1.1762% 26.8325% 73.1675%
478.5 - 521.5 ( 47.850%): 1.2277% 28.0602% 71.9398%
479.0 - 521.0 ( 47.900%): 1.2673% 29.3275% 70.6725%
479.5 - 520.5 ( 47.950%): 1.2777% 30.6052% 69.3948%
480.0 - 520.0 ( 48.000%): 1.3036% 31.9088% 68.0912%
480.5 - 519.5 ( 48.050%): 1.3410% 33.2498% 66.7502%
481.0 - 519.0 ( 48.100%): 1.3474% 34.5972% 65.4028%
481.5 - 518.5 ( 48.150%): 1.3786% 35.9758% 64.0242%
482.0 - 518.0 ( 48.200%): 1.3807% 37.3565% 62.6435%
482.5 - 517.5 ( 48.250%): 1.4000% 38.7565% 61.2435%
483.0 - 517.0 ( 48.300%): 1.4258% 40.1823% 59.8177%
483.5 - 516.5 ( 48.350%): 1.4551% 41.6374% 58.3626%
484.0 - 516.0 ( 48.400%): 1.4634% 43.1008% 56.8992%
484.5 - 515.5 ( 48.450%): 1.4594% 44.5602% 55.4398%
485.0 - 515.0 ( 48.500%): 1.4414% 46.0016% 53.9984%
485.5 - 514.5 ( 48.550%): 1.4790% 47.4806% 52.5194%
486.0 - 514.0 ( 48.600%): 1.4836% 48.9642% 51.0358%
486.5 - 513.5 ( 48.650%): 1.4930% 50.4572% 49.5428%
487.0 - 513.0 ( 48.700%): 1.4979% 51.9551% 48.0449%
487.5 - 512.5 ( 48.750%): 1.4595% 53.4146% 46.5854%
488.0 - 512.0 ( 48.800%): 1.4828% 54.8974% 45.1026%
488.5 - 511.5 ( 48.850%): 1.4748% 56.3722% 43.6278%
489.0 - 511.0 ( 48.900%): 1.4238% 57.7960% 42.2040%
489.5 - 510.5 ( 48.950%): 1.4274% 59.2234% 40.7766%
490.0 - 510.0 ( 49.000%): 1.3972% 60.6206% 39.3794%
490.5 - 509.5 ( 49.050%): 1.4215% 62.0421% 37.9579%
491.0 - 509.0 ( 49.100%): 1.4017% 63.4438% 36.5562%
491.5 - 508.5 ( 49.150%): 1.3924% 64.8362% 35.1638%
492.0 - 508.0 ( 49.200%): 1.3451% 66.1813% 33.8187%
492.5 - 507.5 ( 49.250%): 1.3251% 67.5064% 32.4936%
493.0 - 507.0 ( 49.300%): 1.3163% 68.8227% 31.1773%
493.5 - 506.5 ( 49.350%): 1.2809% 70.1036% 29.8964%
494.0 - 506.0 ( 49.400%): 1.2731% 71.3767% 28.6233%
494.5 - 505.5 ( 49.450%): 1.2563% 72.6330% 27.3670%
495.0 - 505.0 ( 49.500%): 1.2175% 73.8505% 26.1495%
495.5 - 504.5 ( 49.550%): 1.1756% 75.0261% 24.9739%
496.0 - 504.0 ( 49.600%): 1.1709% 76.1970% 23.8030%
496.5 - 503.5 ( 49.650%): 1.1080% 77.3050% 22.6950%
497.0 - 503.0 ( 49.700%): 1.0985% 78.4035% 21.5965%
497.5 - 502.5 ( 49.750%): 1.0682% 79.4717% 20.5283%
498.0 - 502.0 ( 49.800%): 1.0254% 80.4971% 19.5029%
498.5 - 501.5 ( 49.850%): 0.9891% 81.4862% 18.5138%
499.0 - 501.0 ( 49.900%): 0.9789% 82.4651% 17.5349%
499.5 - 500.5 ( 49.950%): 0.9304% 83.3955% 16.6045%
500.0 - 500.0 ( 50.000%): 0.8792% 84.2747% 15.7253%
500.5 - 499.5 ( 50.050%): 0.8741% 85.1488% 14.8512%
501.0 - 499.0 ( 50.100%): 0.8518% 86.0006% 13.9994%
501.5 - 498.5 ( 50.150%): 0.8020% 86.8026% 13.1974%
502.0 - 498.0 ( 50.200%): 0.7881% 87.5907% 12.4093%
502.5 - 497.5 ( 50.250%): 0.7398% 88.3305% 11.6695%
503.0 - 497.0 ( 50.300%): 0.7015% 89.0320% 10.9680%
503.5 - 496.5 ( 50.350%): 0.6746% 89.7066% 10.2934%
504.0 - 496.0 ( 50.400%): 0.6476% 90.3542% 9.6458%
504.5 - 495.5 ( 50.450%): 0.6099% 90.9641% 9.0359%
505.0 - 495.0 ( 50.500%): 0.5795% 91.5436% 8.4564%
505.5 - 494.5 ( 50.550%): 0.5756% 92.1192% 7.8808%
506.0 - 494.0 ( 50.600%): 0.5205% 92.6397% 7.3603%
506.5 - 493.5 ( 50.650%): 0.5137% 93.1534% 6.8466%
507.0 - 493.0 ( 50.700%): 0.4642% 93.6176% 6.3824%
507.5 - 492.5 ( 50.750%): 0.4447% 94.0623% 5.9377%
508.0 - 492.0 ( 50.800%): 0.4224% 94.4847% 5.5153%
508.5 - 491.5 ( 50.850%): 0.3979% 94.8826% 5.1174%
509.0 - 491.0 ( 50.900%): 0.3807% 95.2633% 4.7367%
509.5 - 490.5 ( 50.950%): 0.3640% 95.6273% 4.3727%
510.0 - 490.0 ( 51.000%): 0.3293% 95.9566% 4.0434%
510.5 - 489.5 ( 51.050%): 0.3190% 96.2756% 3.7244%
511.0 - 489.0 ( 51.100%): 0.2911% 96.5667% 3.4333%
511.5 - 488.5 ( 51.150%): 0.2715% 96.8382% 3.1618%
512.0 - 488.0 ( 51.200%): 0.2497% 97.0879% 2.9121%
512.5 - 487.5 ( 51.250%): 0.2314% 97.3193% 2.6807%
513.0 - 487.0 ( 51.300%): 0.2203% 97.5396% 2.4604%
513.5 - 486.5 ( 51.350%): 0.1981% 97.7377% 2.2623%
514.0 - 486.0 ( 51.400%): 0.1904% 97.9281% 2.0719%
514.5 - 485.5 ( 51.450%): 0.1811% 98.1092% 1.8908%
515.0 - 485.0 ( 51.500%): 0.1566% 98.2658% 1.7342%
515.5 - 484.5 ( 51.550%): 0.1553% 98.4211% 1.5789%
516.0 - 484.0 ( 51.600%): 0.1397% 98.5608% 1.4392%
516.5 - 483.5 ( 51.650%): 0.1310% 98.6918% 1.3082%
[...]
As you can see, the extreme results in the actual 1000 games statistics, are
clearly very unlikely. From this already, we can conclude, that the games were
not independent, and that learning did work (in favor of Yace).
Another interesting statistics is already on Pavel's site - results for each
individual ECO code (for white and
black)http://www.pavs.org/opening_statistics.txt
. A smart book cooker might be able to tune the Yace book, based on this
statistic. If anybody really should be interested - I might be able to give even
more detailled statistics. Often many rather different lines yield in the same
ECO code. I could give give some more statistics for such individual lines.
Regards,
Dieter
And now lots of statistics, first from the actual games, then from the Monte
Carlo simulations.
Game statistics:
statistics for each bundle of 200 games
games 1 to 200: res 47.25% w 53.00% b 41.50% + 39.00% = 16.50% - 44.50%
games 201 to 400: res 45.75% w 46.50% b 45.00% + 34.50% = 22.50% - 43.00%
games 401 to 600: res 42.50% w 44.00% b 41.00% + 29.50% = 26.00% - 44.50%
games 601 to 800: res 42.25% w 44.50% b 40.00% + 28.50% = 27.50% - 44.00%
games 801 to 1000: res 45.75% w 48.00% b 43.50% + 33.50% = 24.50% - 42.00%
games 1001 to 1200: res 45.50% w 47.00% b 44.00% + 33.00% = 25.00% - 42.00%
games 1201 to 1400: res 43.75% w 50.00% b 37.50% + 29.50% = 28.50% - 42.00%
games 1401 to 1600: res 38.50% w 45.50% b 31.50% + 28.00% = 21.00% - 51.00%
games 1601 to 1800: res 44.50% w 51.00% b 38.00% + 32.00% = 25.00% - 43.00%
games 1801 to 2000: res 43.50% w 46.50% b 40.50% + 31.00% = 25.00% - 44.00%
games 2001 to 2200: res 45.25% w 49.50% b 41.00% + 30.50% = 29.50% - 40.00%
games 2201 to 2400: res 49.75% w 55.50% b 44.00% + 38.50% = 22.50% - 39.00%
games 2401 to 2600: res 48.75% w 52.00% b 45.50% + 42.00% = 13.50% - 44.50%
games 2601 to 2800: res 47.00% w 49.00% b 45.00% + 40.00% = 14.00% - 46.00%
games 2801 to 3000: res 48.50% w 51.50% b 45.50% + 36.00% = 25.00% - 39.00%
games 3001 to 3200: res 44.50% w 49.50% b 39.50% + 34.50% = 20.00% - 45.50%
games 3201 to 3400: res 48.75% w 51.50% b 46.00% + 36.50% = 24.50% - 39.00%
games 3401 to 3600: res 50.50% w 51.50% b 49.50% + 37.50% = 26.00% - 36.50%
games 3601 to 3800: res 38.75% w 41.50% b 36.00% + 26.50% = 24.50% - 49.00%
games 3801 to 4000: res 48.25% w 53.00% b 43.50% + 33.50% = 29.50% - 37.00%
games 4001 to 4200: res 46.25% w 55.00% b 37.50% + 32.50% = 27.50% - 40.00%
games 4201 to 4400: res 48.50% w 54.00% b 43.00% + 35.00% = 27.00% - 38.00%
games 4401 to 4600: res 43.50% w 54.00% b 33.00% + 32.00% = 23.00% - 45.00%
games 4601 to 4800: res 40.00% w 49.50% b 30.50% + 28.50% = 23.00% - 48.50%
games 4801 to 5000: res 45.75% w 48.00% b 43.50% + 32.00% = 27.50% - 40.50%
games 5001 to 5200: res 49.25% w 57.50% b 41.00% + 36.00% = 26.50% - 37.50%
games 5201 to 5400: res 49.50% w 54.00% b 45.00% + 40.50% = 18.00% - 41.50%
games 5401 to 5600: res 46.75% w 51.00% b 42.50% + 34.00% = 25.50% - 40.50%
games 5601 to 5800: res 47.75% w 57.00% b 38.50% + 36.50% = 22.50% - 41.00%
games 5801 to 6000: res 48.75% w 53.50% b 44.00% + 34.00% = 29.50% - 36.50%
games 6001 to 6200: res 46.50% w 48.00% b 45.00% + 32.50% = 28.00% - 39.50%
games 6201 to 6400: res 42.50% w 48.00% b 37.00% + 29.00% = 27.00% - 44.00%
games 6401 to 6600: res 47.50% w 52.00% b 43.00% + 36.50% = 22.00% - 41.50%
games 6601 to 6800: res 53.75% w 58.00% b 49.50% + 42.00% = 23.50% - 34.50%
games 6801 to 7000: res 51.25% w 57.50% b 45.00% + 39.50% = 23.50% - 37.00%
games 7001 to 7200: res 50.25% w 57.50% b 43.00% + 34.50% = 31.50% - 34.00%
games 7201 to 7400: res 49.50% w 58.50% b 40.50% + 37.00% = 25.00% - 38.00%
games 7401 to 7600: res 44.75% w 47.50% b 42.00% + 29.00% = 31.50% - 39.50%
games 7601 to 7800: res 47.75% w 52.50% b 43.00% + 35.50% = 24.50% - 40.00%
games 7801 to 8000: res 53.75% w 63.50% b 44.00% + 40.50% = 26.50% - 33.00%
games 8001 to 8200: res 48.50% w 61.50% b 35.50% + 37.00% = 23.00% - 40.00%
games 8201 to 8400: res 39.75% w 51.50% b 28.00% + 27.50% = 24.50% - 48.00%
games 8401 to 8600: res 53.50% w 62.50% b 44.50% + 40.50% = 26.00% - 33.50%
games 8601 to 8800: res 55.75% w 64.50% b 47.00% + 42.50% = 26.50% - 31.00%
games 8801 to 9000: res 55.25% w 67.50% b 43.00% + 43.50% = 23.50% - 33.00%
games 9001 to 9200: res 49.75% w 52.50% b 47.00% + 38.00% = 23.50% - 38.50%
games 9201 to 9400: res 54.25% w 60.00% b 48.50% + 39.00% = 30.50% - 30.50%
games 9401 to 9600: res 48.25% w 52.50% b 44.00% + 35.50% = 25.50% - 39.00%
games 9601 to 9800: res 44.25% w 51.50% b 37.00% + 31.00% = 26.50% - 42.50%
games 9801 to 10000: res 48.25% w 51.00% b 45.50% + 34.50% = 27.50% - 38.00%
games 10001 to 10200: res 48.75% w 57.50% b 40.00% + 36.50% = 24.50% - 39.00%
games 10201 to 10400: res 49.75% w 56.50% b 43.00% + 36.00% = 27.50% - 36.50%
games 10401 to 10600: res 55.00% w 64.00% b 46.00% + 43.00% = 24.00% - 33.00%
games 10601 to 10800: res 50.75% w 58.00% b 43.50% + 36.50% = 28.50% - 35.00%
games 10801 to 11000: res 52.75% w 62.00% b 43.50% + 38.00% = 29.50% - 32.50%
games 11001 to 11200: res 55.75% w 61.00% b 50.50% + 39.50% = 32.50% - 28.00%
games 11201 to 11400: res 51.25% w 59.00% b 43.50% + 35.50% = 31.50% - 33.00%
games 11401 to 11600: res 55.00% w 60.00% b 50.00% + 41.50% = 27.00% - 31.50%
games 11601 to 11800: res 52.50% w 60.50% b 44.50% + 39.50% = 26.00% - 34.50%
games 11801 to 12000: res 52.00% w 55.50% b 48.50% + 39.50% = 25.00% - 35.50%
games 12001 to 12200: res 54.75% w 58.00% b 51.50% + 41.00% = 27.50% - 31.50%
games 12201 to 12400: res 53.75% w 60.00% b 47.50% + 39.50% = 28.50% - 32.00%
games 12401 to 12600: res 54.50% w 62.50% b 46.50% + 41.50% = 26.00% - 32.50%
games 12601 to 12800: res 58.50% w 64.00% b 53.00% + 48.00% = 21.00% - 31.00%
games 12801 to 12978: res 58.71% w 64.04% b 53.37% + 46.63% = 24.16% - 29.21%
statistics for each bundle of 500 games
games 1 to 500: res 45.70% w 49.40% b 42.00% + 35.40% = 20.60% - 44.00%
games 501 to 1000: res 43.70% w 45.00% b 42.40% + 30.60% = 26.20% - 43.20%
games 1001 to 1500: res 42.80% w 47.20% b 38.40% + 30.00% = 25.60% - 44.40%
games 1501 to 2000: res 43.50% w 48.80% b 38.20% + 31.40% = 24.20% - 44.40%
games 2001 to 2500: res 47.70% w 51.60% b 43.80% + 36.20% = 23.00% - 40.80%
games 2501 to 3000: res 48.00% w 51.40% b 44.60% + 38.60% = 18.80% - 42.60%
games 3001 to 3500: res 46.60% w 51.20% b 42.00% + 34.40% = 24.40% - 41.20%
games 3501 to 4000: res 45.70% w 47.60% b 43.80% + 33.00% = 25.40% - 41.60%
games 4001 to 4500: res 46.10% w 54.20% b 38.00% + 32.80% = 26.60% - 40.60%
games 4501 to 5000: res 43.50% w 50.00% b 37.00% + 31.20% = 24.60% - 44.20%
games 5001 to 5500: res 48.80% w 54.00% b 43.60% + 37.60% = 22.40% - 40.00%
games 5501 to 6000: res 48.00% w 55.20% b 40.80% + 34.80% = 26.40% - 38.80%
games 6001 to 6500: res 46.10% w 49.60% b 42.60% + 33.20% = 25.80% - 41.00%
games 6501 to 7000: res 50.50% w 55.80% b 45.20% + 38.60% = 23.80% - 37.60%
games 7001 to 7500: res 48.60% w 55.60% b 41.60% + 33.80% = 29.60% - 36.60%
games 7501 to 8000: res 49.80% w 56.20% b 43.40% + 36.80% = 26.00% - 37.20%
games 8001 to 8500: res 46.90% w 58.20% b 35.60% + 35.00% = 23.80% - 41.20%
games 8501 to 9000: res 54.20% w 64.80% b 43.60% + 41.40% = 25.60% - 33.00%
games 9001 to 9500: res 51.80% w 54.80% b 48.80% + 37.60% = 28.40% - 34.00%
games 9501 to 10000: res 46.10% w 52.20% b 40.00% + 33.60% = 25.00% - 41.40%
games 10001 to 10500: res 49.70% w 58.20% b 41.20% + 37.20% = 25.00% - 37.80%
games 10501 to 11000: res 53.10% w 61.00% b 45.20% + 38.80% = 28.60% - 32.60%
games 11001 to 11500: res 53.90% w 58.80% b 49.00% + 38.80% = 30.20% - 31.00%
games 11501 to 12000: res 52.70% w 59.60% b 45.80% + 39.40% = 26.60% - 34.00%
games 12001 to 12500: res 55.30% w 60.00% b 50.60% + 41.60% = 27.40% - 31.00%
games 12501 to 12978: res 56.69% w 63.39% b 50.00% + 44.98% = 23.43% - 31.59%
statistics for each bundle of 1000 games
games 1 to 1000: res 44.70% w 47.20% b 42.20% + 33.00% = 23.40% - 43.60%
games 1001 to 2000: res 43.15% w 48.00% b 38.30% + 30.70% = 24.90% - 44.40%
games 2001 to 3000: res 47.85% w 51.50% b 44.20% + 37.40% = 20.90% - 41.70%
games 3001 to 4000: res 46.15% w 49.40% b 42.90% + 33.70% = 24.90% - 41.40%
games 4001 to 5000: res 44.80% w 52.10% b 37.50% + 32.00% = 25.60% - 42.40%
games 5001 to 6000: res 48.40% w 54.60% b 42.20% + 36.20% = 24.40% - 39.40%
games 6001 to 7000: res 48.30% w 52.70% b 43.90% + 35.90% = 24.80% - 39.30%
games 7001 to 8000: res 49.20% w 55.90% b 42.50% + 35.30% = 27.80% - 36.90%
games 8001 to 9000: res 50.55% w 61.50% b 39.60% + 38.20% = 24.70% - 37.10%
games 9001 to 10000: res 48.95% w 53.50% b 44.40% + 35.60% = 26.70% - 37.70%
games 10001 to 11000: res 51.40% w 59.60% b 43.20% + 38.00% = 26.80% - 35.20%
games 11001 to 12000: res 53.30% w 59.20% b 47.40% + 39.10% = 28.40% - 32.50%
games 12001 to 12978: res 55.98% w 61.66% b 50.31% + 43.25% = 25.46% - 31.29%
statistics for each bundle of 2000 games
games 1 to 2000: res 43.92% w 47.60% b 40.25% + 31.85% = 24.15% - 44.00%
games 2001 to 4000: res 47.00% w 50.45% b 43.55% + 35.55% = 22.90% - 41.55%
games 4001 to 6000: res 46.60% w 53.35% b 39.85% + 34.10% = 25.00% - 40.90%
games 6001 to 8000: res 48.75% w 54.30% b 43.20% + 35.60% = 26.30% - 38.10%
games 8001 to 10000: res 49.75% w 57.50% b 42.00% + 36.90% = 25.70% - 37.40%
games 10001 to 12000: res 52.35% w 59.40% b 45.30% + 38.55% = 27.60% - 33.85%
games 12001 to 12978: res 55.98% w 61.66% b 50.31% + 43.25% = 25.46% - 31.29%
statistics for each bundle of 5000 games
games 1 to 5000: res 45.33% w 49.64% b 41.02% + 33.36% = 23.94% - 42.70%
games 5001 to 10000: res 49.08% w 55.64% b 42.52% + 36.24% = 25.68% - 38.08%
games 10001 to 12978: res 53.54% w 60.14% b 46.94% + 40.09% = 26.90% - 33.01%
Extreme results:
worst result in 100: games 1418 to 1517: 32.000%
best result in 100: games 10566 to 10665: 65.000%
worst result in 200: games 1394 to 1593: 37.500%
best result in 200: games 12597 to 12796: 59.250%
worst result in 500: games 1210 to 1709: 41.100%
best result in 500: games 12377 to 12876: 57.900%
worst result in 1000: games 1019 to 2018: 42.700%
best result in 1000: games 11952 to 12951: 56.250%
worst result in 2000: games 193 to 2192: 43.675%
best result in 2000: games 10876 to 12875: 54.775%
worst result in 5000: games 100 to 5099: 45.260%
best result in 5000: games 7934 to 12933: 52.060%
Now Monte Carlo simulation results. I give the results for 500, 1000, 2000 and
5000 games here.
500 games:
Result of chess matches
Player A as white wins 42.1%, draws 24.5% and loses 33.4%
Player A as black wins 29.9%, draws 26.1% and loses 44.0%
Expected result: 48.6593% (as white 54.3612%, as black 42.9573%)
A match of 500 games was simulated 1000000 times by a Monte Carlo method
result probability p <= res. p > res.
197.0 - 303.0 ( 39.400%): 0.0001% 0.0001% 99.9999%
201.5 - 298.5 ( 40.300%): 0.0002% 0.0003% 99.9997%
202.5 - 297.5 ( 40.500%): 0.0003% 0.0006% 99.9994%
203.0 - 297.0 ( 40.600%): 0.0003% 0.0009% 99.9991%
203.5 - 296.5 ( 40.700%): 0.0001% 0.0010% 99.9990%
204.0 - 296.0 ( 40.800%): 0.0003% 0.0013% 99.9987%
204.5 - 295.5 ( 40.900%): 0.0006% 0.0019% 99.9981%
205.0 - 295.0 ( 41.000%): 0.0006% 0.0025% 99.9975%
205.5 - 294.5 ( 41.100%): 0.0015% 0.0040% 99.9960%
206.0 - 294.0 ( 41.200%): 0.0008% 0.0048% 99.9952%
206.5 - 293.5 ( 41.300%): 0.0010% 0.0058% 99.9942%
207.0 - 293.0 ( 41.400%): 0.0018% 0.0076% 99.9924%
207.5 - 292.5 ( 41.500%): 0.0026% 0.0102% 99.9898%
208.0 - 292.0 ( 41.600%): 0.0022% 0.0124% 99.9876%
208.5 - 291.5 ( 41.700%): 0.0038% 0.0162% 99.9838%
209.0 - 291.0 ( 41.800%): 0.0048% 0.0210% 99.9790%
209.5 - 290.5 ( 41.900%): 0.0039% 0.0249% 99.9751%
210.0 - 290.0 ( 42.000%): 0.0038% 0.0287% 99.9713%
210.5 - 289.5 ( 42.100%): 0.0068% 0.0355% 99.9645%
211.0 - 289.0 ( 42.200%): 0.0072% 0.0427% 99.9573%
211.5 - 288.5 ( 42.300%): 0.0080% 0.0507% 99.9493%
212.0 - 288.0 ( 42.400%): 0.0079% 0.0586% 99.9414%
212.5 - 287.5 ( 42.500%): 0.0113% 0.0699% 99.9301%
213.0 - 287.0 ( 42.600%): 0.0130% 0.0829% 99.9171%
213.5 - 286.5 ( 42.700%): 0.0160% 0.0989% 99.9011%
214.0 - 286.0 ( 42.800%): 0.0188% 0.1177% 99.8823%
214.5 - 285.5 ( 42.900%): 0.0255% 0.1432% 99.8568%
215.0 - 285.0 ( 43.000%): 0.0257% 0.1689% 99.8311%
215.5 - 284.5 ( 43.100%): 0.0276% 0.1965% 99.8035%
216.0 - 284.0 ( 43.200%): 0.0376% 0.2341% 99.7659%
216.5 - 283.5 ( 43.300%): 0.0424% 0.2765% 99.7235%
217.0 - 283.0 ( 43.400%): 0.0468% 0.3233% 99.6767%
217.5 - 282.5 ( 43.500%): 0.0577% 0.3810% 99.6190%
218.0 - 282.0 ( 43.600%): 0.0615% 0.4425% 99.5575%
218.5 - 281.5 ( 43.700%): 0.0728% 0.5153% 99.4847%
219.0 - 281.0 ( 43.800%): 0.0822% 0.5975% 99.4025%
219.5 - 280.5 ( 43.900%): 0.0980% 0.6955% 99.3045%
220.0 - 280.0 ( 44.000%): 0.1104% 0.8059% 99.1941%
220.5 - 279.5 ( 44.100%): 0.1223% 0.9282% 99.0718%
221.0 - 279.0 ( 44.200%): 0.1351% 1.0633% 98.9367%
221.5 - 278.5 ( 44.300%): 0.1532% 1.2165% 98.7835%
222.0 - 278.0 ( 44.400%): 0.1734% 1.3899% 98.6101%
222.5 - 277.5 ( 44.500%): 0.1979% 1.5878% 98.4122%
223.0 - 277.0 ( 44.600%): 0.2222% 1.8100% 98.1900%
223.5 - 276.5 ( 44.700%): 0.2487% 2.0587% 97.9413%
224.0 - 276.0 ( 44.800%): 0.2796% 2.3383% 97.6617%
224.5 - 275.5 ( 44.900%): 0.3048% 2.6431% 97.3569%
225.0 - 275.0 ( 45.000%): 0.3337% 2.9768% 97.0232%
225.5 - 274.5 ( 45.100%): 0.3736% 3.3504% 96.6496%
226.0 - 274.0 ( 45.200%): 0.4051% 3.7555% 96.2445%
226.5 - 273.5 ( 45.300%): 0.4599% 4.2154% 95.7846%
227.0 - 273.0 ( 45.400%): 0.4940% 4.7094% 95.2906%
227.5 - 272.5 ( 45.500%): 0.5398% 5.2492% 94.7508%
228.0 - 272.0 ( 45.600%): 0.5719% 5.8211% 94.1789%
228.5 - 271.5 ( 45.700%): 0.6139% 6.4350% 93.5650%
229.0 - 271.0 ( 45.800%): 0.6994% 7.1344% 92.8656%
229.5 - 270.5 ( 45.900%): 0.7396% 7.8740% 92.1260%
230.0 - 270.0 ( 46.000%): 0.8008% 8.6748% 91.3252%
230.5 - 269.5 ( 46.100%): 0.8475% 9.5223% 90.4777%
231.0 - 269.0 ( 46.200%): 0.9196% 10.4419% 89.5581%
231.5 - 268.5 ( 46.300%): 0.9847% 11.4266% 88.5734%
232.0 - 268.0 ( 46.400%): 1.0347% 12.4613% 87.5387%
232.5 - 267.5 ( 46.500%): 1.1162% 13.5775% 86.4225%
233.0 - 267.0 ( 46.600%): 1.1762% 14.7537% 85.2463%
233.5 - 266.5 ( 46.700%): 1.2427% 15.9964% 84.0036%
234.0 - 266.0 ( 46.800%): 1.2924% 17.2888% 82.7112%
234.5 - 265.5 ( 46.900%): 1.3813% 18.6701% 81.3299%
235.0 - 265.0 ( 47.000%): 1.4433% 20.1134% 79.8866%
235.5 - 264.5 ( 47.100%): 1.5006% 21.6140% 78.3860%
236.0 - 264.0 ( 47.200%): 1.5414% 23.1554% 76.8446%
236.5 - 263.5 ( 47.300%): 1.6096% 24.7650% 75.2350%
237.0 - 263.0 ( 47.400%): 1.6862% 26.4512% 73.5488%
237.5 - 262.5 ( 47.500%): 1.7364% 28.1876% 71.8124%
238.0 - 262.0 ( 47.600%): 1.7884% 29.9760% 70.0240%
238.5 - 261.5 ( 47.700%): 1.8278% 31.8038% 68.1962%
239.0 - 261.0 ( 47.800%): 1.8770% 33.6808% 66.3192%
239.5 - 260.5 ( 47.900%): 1.9303% 35.6111% 64.3889%
240.0 - 260.0 ( 48.000%): 1.9394% 37.5505% 62.4495%
240.5 - 259.5 ( 48.100%): 2.0111% 39.5616% 60.4384%
241.0 - 259.0 ( 48.200%): 2.0302% 41.5918% 58.4082%
241.5 - 258.5 ( 48.300%): 2.0374% 43.6292% 56.3708%
242.0 - 258.0 ( 48.400%): 2.0690% 45.6982% 54.3018%
242.5 - 257.5 ( 48.500%): 2.0547% 47.7529% 52.2471%
243.0 - 257.0 ( 48.600%): 2.0818% 49.8347% 50.1653%
243.5 - 256.5 ( 48.700%): 2.0973% 51.9320% 48.0680%
244.0 - 256.0 ( 48.800%): 2.0533% 53.9853% 46.0147%
244.5 - 255.5 ( 48.900%): 2.0808% 56.0661% 43.9339%
245.0 - 255.0 ( 49.000%): 2.0540% 58.1201% 41.8799%
245.5 - 254.5 ( 49.100%): 2.0550% 60.1751% 39.8249%
246.0 - 254.0 ( 49.200%): 1.9859% 62.1610% 37.8390%
246.5 - 253.5 ( 49.300%): 1.9629% 64.1239% 35.8761%
247.0 - 253.0 ( 49.400%): 1.9293% 66.0532% 33.9468%
247.5 - 252.5 ( 49.500%): 1.8988% 67.9520% 32.0480%
248.0 - 252.0 ( 49.600%): 1.8490% 69.8010% 30.1990%
248.5 - 251.5 ( 49.700%): 1.8075% 71.6085% 28.3915%
249.0 - 251.0 ( 49.800%): 1.7326% 73.3411% 26.6589%
249.5 - 250.5 ( 49.900%): 1.6901% 75.0312% 24.9688%
250.0 - 250.0 ( 50.000%): 1.6448% 76.6760% 23.3240%
250.5 - 249.5 ( 50.100%): 1.5632% 78.2392% 21.7608%
251.0 - 249.0 ( 50.200%): 1.5087% 79.7479% 20.2521%
251.5 - 248.5 ( 50.300%): 1.4293% 81.1772% 18.8228%
252.0 - 248.0 ( 50.400%): 1.3832% 82.5604% 17.4396%
252.5 - 247.5 ( 50.500%): 1.3148% 83.8752% 16.1248%
253.0 - 247.0 ( 50.600%): 1.2545% 85.1297% 14.8703%
253.5 - 246.5 ( 50.700%): 1.1869% 86.3166% 13.6834%
254.0 - 246.0 ( 50.800%): 1.1023% 87.4189% 12.5811%
254.5 - 245.5 ( 50.900%): 1.0483% 88.4672% 11.5328%
255.0 - 245.0 ( 51.000%): 0.9606% 89.4278% 10.5722%
255.5 - 244.5 ( 51.100%): 0.9212% 90.3490% 9.6510%
256.0 - 244.0 ( 51.200%): 0.8629% 91.2119% 8.7881%
256.5 - 243.5 ( 51.300%): 0.8083% 92.0202% 7.9798%
257.0 - 243.0 ( 51.400%): 0.7457% 92.7659% 7.2341%
257.5 - 242.5 ( 51.500%): 0.6987% 93.4646% 6.5354%
258.0 - 242.0 ( 51.600%): 0.6367% 94.1013% 5.8987%
258.5 - 241.5 ( 51.700%): 0.5864% 94.6877% 5.3123%
259.0 - 241.0 ( 51.800%): 0.5303% 95.2180% 4.7820%
259.5 - 240.5 ( 51.900%): 0.4915% 95.7095% 4.2905%
260.0 - 240.0 ( 52.000%): 0.4565% 96.1660% 3.8340%
260.5 - 239.5 ( 52.100%): 0.4260% 96.5920% 3.4080%
261.0 - 239.0 ( 52.200%): 0.3681% 96.9601% 3.0399%
261.5 - 238.5 ( 52.300%): 0.3442% 97.3043% 2.6957%
262.0 - 238.0 ( 52.400%): 0.3110% 97.6153% 2.3847%
262.5 - 237.5 ( 52.500%): 0.2839% 97.8992% 2.1008%
263.0 - 237.0 ( 52.600%): 0.2511% 98.1503% 1.8497%
263.5 - 236.5 ( 52.700%): 0.2092% 98.3595% 1.6405%
264.0 - 236.0 ( 52.800%): 0.1953% 98.5548% 1.4452%
264.5 - 235.5 ( 52.900%): 0.1788% 98.7336% 1.2664%
265.0 - 235.0 ( 53.000%): 0.1595% 98.8931% 1.1069%
265.5 - 234.5 ( 53.100%): 0.1445% 99.0376% 0.9624%
266.0 - 234.0 ( 53.200%): 0.1261% 99.1637% 0.8363%
266.5 - 233.5 ( 53.300%): 0.1098% 99.2735% 0.7265%
267.0 - 233.0 ( 53.400%): 0.0955% 99.3690% 0.6310%
267.5 - 232.5 ( 53.500%): 0.0868% 99.4558% 0.5442%
268.0 - 232.0 ( 53.600%): 0.0729% 99.5287% 0.4713%
268.5 - 231.5 ( 53.700%): 0.0672% 99.5959% 0.4041%
269.0 - 231.0 ( 53.800%): 0.0573% 99.6532% 0.3468%
269.5 - 230.5 ( 53.900%): 0.0524% 99.7056% 0.2944%
270.0 - 230.0 ( 54.000%): 0.0452% 99.7508% 0.2492%
270.5 - 229.5 ( 54.100%): 0.0376% 99.7884% 0.2116%
271.0 - 229.0 ( 54.200%): 0.0344% 99.8228% 0.1772%
271.5 - 228.5 ( 54.300%): 0.0283% 99.8511% 0.1489%
272.0 - 228.0 ( 54.400%): 0.0216% 99.8727% 0.1273%
272.5 - 227.5 ( 54.500%): 0.0222% 99.8949% 0.1051%
273.0 - 227.0 ( 54.600%): 0.0163% 99.9112% 0.0888%
273.5 - 226.5 ( 54.700%): 0.0148% 99.9260% 0.0740%
274.0 - 226.0 ( 54.800%): 0.0118% 99.9378% 0.0622%
274.5 - 225.5 ( 54.900%): 0.0089% 99.9467% 0.0533%
275.0 - 225.0 ( 55.000%): 0.0083% 99.9550% 0.0450%
275.5 - 224.5 ( 55.100%): 0.0086% 99.9636% 0.0364%
276.0 - 224.0 ( 55.200%): 0.0063% 99.9699% 0.0301%
276.5 - 223.5 ( 55.300%): 0.0055% 99.9754% 0.0246%
277.0 - 223.0 ( 55.400%): 0.0048% 99.9802% 0.0198%
277.5 - 222.5 ( 55.500%): 0.0041% 99.9843% 0.0157%
278.0 - 222.0 ( 55.600%): 0.0031% 99.9874% 0.0126%
278.5 - 221.5 ( 55.700%): 0.0029% 99.9903% 0.0097%
279.0 - 221.0 ( 55.800%): 0.0012% 99.9915% 0.0085%
279.5 - 220.5 ( 55.900%): 0.0016% 99.9931% 0.0069%
280.0 - 220.0 ( 56.000%): 0.0009% 99.9940% 0.0060%
280.5 - 219.5 ( 56.100%): 0.0011% 99.9951% 0.0049%
281.0 - 219.0 ( 56.200%): 0.0007% 99.9958% 0.0042%
281.5 - 218.5 ( 56.300%): 0.0006% 99.9964% 0.0036%
282.0 - 218.0 ( 56.400%): 0.0004% 99.9968% 0.0032%
282.5 - 217.5 ( 56.500%): 0.0006% 99.9974% 0.0026%
283.0 - 217.0 ( 56.600%): 0.0004% 99.9978% 0.0022%
283.5 - 216.5 ( 56.700%): 0.0004% 99.9982% 0.0018%
284.0 - 216.0 ( 56.800%): 0.0004% 99.9986% 0.0014%
284.5 - 215.5 ( 56.900%): 0.0002% 99.9988% 0.0012%
285.0 - 215.0 ( 57.000%): 0.0004% 99.9992% 0.0008%
285.5 - 214.5 ( 57.100%): 0.0001% 99.9993% 0.0007%
286.0 - 214.0 ( 57.200%): 0.0002% 99.9995% 0.0005%
286.5 - 213.5 ( 57.300%): 0.0002% 99.9997% 0.0003%
287.0 - 213.0 ( 57.400%): 0.0001% 99.9998% 0.0002%
287.5 - 212.5 ( 57.500%): 0.0001% 99.9999% 0.0001%
289.0 - 211.0 ( 57.800%): 0.0001% 100.0000% 0.0000%
Average result of simulation 48.6568%
CPU-time 21.531 s, PRNG was called 5e+008 times, 0.04306 us/PRN
1000 games:
Result of chess matches
Player A as white wins 42.1%, draws 24.5% and loses 33.4%
Player A as black wins 29.9%, draws 26.1% and loses 44.0%
Expected result: 48.6593% (as white 54.3612%, as black 42.9573%)
A match of 1000 games was simulated 1000000 times by a Monte Carlo method
result probability p <= res. p > res.
411.0 - 589.0 ( 41.100%): 0.0001% 0.0001% 99.9999%
424.5 - 575.5 ( 42.450%): 0.0001% 0.0002% 99.9998%
425.5 - 574.5 ( 42.550%): 0.0002% 0.0004% 99.9996%
426.5 - 573.5 ( 42.650%): 0.0001% 0.0005% 99.9995%
427.0 - 573.0 ( 42.700%): 0.0001% 0.0006% 99.9994%
428.5 - 571.5 ( 42.850%): 0.0002% 0.0008% 99.9992%
429.0 - 571.0 ( 42.900%): 0.0003% 0.0011% 99.9989%
430.0 - 570.0 ( 43.000%): 0.0002% 0.0013% 99.9987%
430.5 - 569.5 ( 43.050%): 0.0003% 0.0016% 99.9984%
431.5 - 568.5 ( 43.150%): 0.0002% 0.0018% 99.9982%
432.0 - 568.0 ( 43.200%): 0.0005% 0.0023% 99.9977%
432.5 - 567.5 ( 43.250%): 0.0005% 0.0028% 99.9972%
433.0 - 567.0 ( 43.300%): 0.0001% 0.0029% 99.9971%
433.5 - 566.5 ( 43.350%): 0.0004% 0.0033% 99.9967%
434.0 - 566.0 ( 43.400%): 0.0004% 0.0037% 99.9963%
434.5 - 565.5 ( 43.450%): 0.0008% 0.0045% 99.9955%
435.0 - 565.0 ( 43.500%): 0.0008% 0.0053% 99.9947%
435.5 - 564.5 ( 43.550%): 0.0011% 0.0064% 99.9936%
436.0 - 564.0 ( 43.600%): 0.0018% 0.0082% 99.9918%
436.5 - 563.5 ( 43.650%): 0.0016% 0.0098% 99.9902%
437.0 - 563.0 ( 43.700%): 0.0013% 0.0111% 99.9889%
437.5 - 562.5 ( 43.750%): 0.0016% 0.0127% 99.9873%
438.0 - 562.0 ( 43.800%): 0.0028% 0.0155% 99.9845%
438.5 - 561.5 ( 43.850%): 0.0029% 0.0184% 99.9816%
439.0 - 561.0 ( 43.900%): 0.0037% 0.0221% 99.9779%
439.5 - 560.5 ( 43.950%): 0.0041% 0.0262% 99.9738%
440.0 - 560.0 ( 44.000%): 0.0053% 0.0315% 99.9685%
440.5 - 559.5 ( 44.050%): 0.0048% 0.0363% 99.9637%
441.0 - 559.0 ( 44.100%): 0.0042% 0.0405% 99.9595%
441.5 - 558.5 ( 44.150%): 0.0052% 0.0457% 99.9543%
442.0 - 558.0 ( 44.200%): 0.0061% 0.0518% 99.9482%
442.5 - 557.5 ( 44.250%): 0.0069% 0.0587% 99.9413%
443.0 - 557.0 ( 44.300%): 0.0075% 0.0662% 99.9338%
443.5 - 556.5 ( 44.350%): 0.0106% 0.0768% 99.9232%
444.0 - 556.0 ( 44.400%): 0.0101% 0.0869% 99.9131%
444.5 - 555.5 ( 44.450%): 0.0115% 0.0984% 99.9016%
445.0 - 555.0 ( 44.500%): 0.0122% 0.1106% 99.8894%
445.5 - 554.5 ( 44.550%): 0.0142% 0.1248% 99.8752%
446.0 - 554.0 ( 44.600%): 0.0171% 0.1419% 99.8581%
446.5 - 553.5 ( 44.650%): 0.0184% 0.1603% 99.8397%
447.0 - 553.0 ( 44.700%): 0.0193% 0.1796% 99.8204%
447.5 - 552.5 ( 44.750%): 0.0232% 0.2028% 99.7972%
448.0 - 552.0 ( 44.800%): 0.0261% 0.2289% 99.7711%
448.5 - 551.5 ( 44.850%): 0.0295% 0.2584% 99.7416%
449.0 - 551.0 ( 44.900%): 0.0302% 0.2886% 99.7114%
449.5 - 550.5 ( 44.950%): 0.0341% 0.3227% 99.6773%
450.0 - 550.0 ( 45.000%): 0.0385% 0.3612% 99.6388%
450.5 - 549.5 ( 45.050%): 0.0408% 0.4020% 99.5980%
451.0 - 549.0 ( 45.100%): 0.0452% 0.4472% 99.5528%
451.5 - 548.5 ( 45.150%): 0.0529% 0.5001% 99.4999%
452.0 - 548.0 ( 45.200%): 0.0583% 0.5584% 99.4416%
452.5 - 547.5 ( 45.250%): 0.0642% 0.6226% 99.3774%
453.0 - 547.0 ( 45.300%): 0.0611% 0.6837% 99.3163%
453.5 - 546.5 ( 45.350%): 0.0731% 0.7568% 99.2432%
454.0 - 546.0 ( 45.400%): 0.0811% 0.8379% 99.1621%
454.5 - 545.5 ( 45.450%): 0.0892% 0.9271% 99.0729%
455.0 - 545.0 ( 45.500%): 0.0979% 1.0250% 98.9750%
455.5 - 544.5 ( 45.550%): 0.1076% 1.1326% 98.8674%
456.0 - 544.0 ( 45.600%): 0.1154% 1.2480% 98.7520%
456.5 - 543.5 ( 45.650%): 0.1230% 1.3710% 98.6290%
457.0 - 543.0 ( 45.700%): 0.1366% 1.5076% 98.4924%
457.5 - 542.5 ( 45.750%): 0.1431% 1.6507% 98.3493%
458.0 - 542.0 ( 45.800%): 0.1602% 1.8109% 98.1891%
458.5 - 541.5 ( 45.850%): 0.1725% 1.9834% 98.0166%
459.0 - 541.0 ( 45.900%): 0.1784% 2.1618% 97.8382%
459.5 - 540.5 ( 45.950%): 0.1967% 2.3585% 97.6415%
460.0 - 540.0 ( 46.000%): 0.2223% 2.5808% 97.4192%
460.5 - 539.5 ( 46.050%): 0.2301% 2.8109% 97.1891%
461.0 - 539.0 ( 46.100%): 0.2507% 3.0616% 96.9384%
461.5 - 538.5 ( 46.150%): 0.2506% 3.3122% 96.6878%
462.0 - 538.0 ( 46.200%): 0.2845% 3.5967% 96.4033%
462.5 - 537.5 ( 46.250%): 0.3094% 3.9061% 96.0939%
463.0 - 537.0 ( 46.300%): 0.3234% 4.2295% 95.7705%
463.5 - 536.5 ( 46.350%): 0.3463% 4.5758% 95.4242%
464.0 - 536.0 ( 46.400%): 0.3678% 4.9436% 95.0564%
464.5 - 535.5 ( 46.450%): 0.3898% 5.3334% 94.6666%
465.0 - 535.0 ( 46.500%): 0.4138% 5.7472% 94.2528%
465.5 - 534.5 ( 46.550%): 0.4421% 6.1893% 93.8107%
466.0 - 534.0 ( 46.600%): 0.4765% 6.6658% 93.3342%
466.5 - 533.5 ( 46.650%): 0.4910% 7.1568% 92.8432%
467.0 - 533.0 ( 46.700%): 0.5315% 7.6883% 92.3117%
467.5 - 532.5 ( 46.750%): 0.5444% 8.2327% 91.7673%
468.0 - 532.0 ( 46.800%): 0.5844% 8.8171% 91.1829%
468.5 - 531.5 ( 46.850%): 0.5967% 9.4138% 90.5862%
469.0 - 531.0 ( 46.900%): 0.6289% 10.0427% 89.9573%
469.5 - 530.5 ( 46.950%): 0.6651% 10.7078% 89.2922%
470.0 - 530.0 ( 47.000%): 0.6998% 11.4076% 88.5924%
470.5 - 529.5 ( 47.050%): 0.7332% 12.1408% 87.8592%
471.0 - 529.0 ( 47.100%): 0.7613% 12.9021% 87.0979%
471.5 - 528.5 ( 47.150%): 0.8073% 13.7094% 86.2906%
472.0 - 528.0 ( 47.200%): 0.8272% 14.5366% 85.4634%
472.5 - 527.5 ( 47.250%): 0.8833% 15.4199% 84.5801%
473.0 - 527.0 ( 47.300%): 0.8758% 16.2957% 83.7043%
473.5 - 526.5 ( 47.350%): 0.9284% 17.2241% 82.7759%
474.0 - 526.0 ( 47.400%): 0.9605% 18.1846% 81.8154%
474.5 - 525.5 ( 47.450%): 0.9960% 19.1806% 80.8194%
475.0 - 525.0 ( 47.500%): 1.0294% 20.2100% 79.7900%
475.5 - 524.5 ( 47.550%): 1.0625% 21.2725% 78.7275%
476.0 - 524.0 ( 47.600%): 1.0622% 22.3347% 77.6653%
476.5 - 523.5 ( 47.650%): 1.1213% 23.4560% 76.5440%
477.0 - 523.0 ( 47.700%): 1.1428% 24.5988% 75.4012%
477.5 - 522.5 ( 47.750%): 1.1721% 25.7709% 74.2291%
478.0 - 522.0 ( 47.800%): 1.2060% 26.9769% 73.0231%
478.5 - 521.5 ( 47.850%): 1.2274% 28.2043% 71.7957%
479.0 - 521.0 ( 47.900%): 1.2768% 29.4811% 70.5189%
479.5 - 520.5 ( 47.950%): 1.2942% 30.7753% 69.2247%
480.0 - 520.0 ( 48.000%): 1.2895% 32.0648% 67.9352%
480.5 - 519.5 ( 48.050%): 1.3447% 33.4095% 66.5905%
481.0 - 519.0 ( 48.100%): 1.3604% 34.7699% 65.2301%
481.5 - 518.5 ( 48.150%): 1.3594% 36.1293% 63.8707%
482.0 - 518.0 ( 48.200%): 1.3945% 37.5238% 62.4762%
482.5 - 517.5 ( 48.250%): 1.4127% 38.9365% 61.0635%
483.0 - 517.0 ( 48.300%): 1.4268% 40.3633% 59.6367%
483.5 - 516.5 ( 48.350%): 1.4288% 41.7921% 58.2079%
484.0 - 516.0 ( 48.400%): 1.4502% 43.2423% 56.7577%
484.5 - 515.5 ( 48.450%): 1.4632% 44.7055% 55.2945%
485.0 - 515.0 ( 48.500%): 1.4298% 46.1353% 53.8647%
485.5 - 514.5 ( 48.550%): 1.4693% 47.6046% 52.3954%
486.0 - 514.0 ( 48.600%): 1.4786% 49.0832% 50.9168%
486.5 - 513.5 ( 48.650%): 1.4602% 50.5434% 49.4566%
487.0 - 513.0 ( 48.700%): 1.4625% 52.0059% 47.9941%
487.5 - 512.5 ( 48.750%): 1.4540% 53.4599% 46.5401%
488.0 - 512.0 ( 48.800%): 1.4795% 54.9394% 45.0606%
488.5 - 511.5 ( 48.850%): 1.4514% 56.3908% 43.6092%
489.0 - 511.0 ( 48.900%): 1.4446% 57.8354% 42.1646%
489.5 - 510.5 ( 48.950%): 1.4385% 59.2739% 40.7261%
490.0 - 510.0 ( 49.000%): 1.4061% 60.6800% 39.3200%
490.5 - 509.5 ( 49.050%): 1.4032% 62.0832% 37.9168%
491.0 - 509.0 ( 49.100%): 1.3812% 63.4644% 36.5356%
491.5 - 508.5 ( 49.150%): 1.3827% 64.8471% 35.1529%
492.0 - 508.0 ( 49.200%): 1.3555% 66.2026% 33.7974%
492.5 - 507.5 ( 49.250%): 1.3253% 67.5279% 32.4721%
493.0 - 507.0 ( 49.300%): 1.3118% 68.8397% 31.1603%
493.5 - 506.5 ( 49.350%): 1.2781% 70.1178% 29.8822%
494.0 - 506.0 ( 49.400%): 1.2501% 71.3679% 28.6321%
494.5 - 505.5 ( 49.450%): 1.2317% 72.5996% 27.4004%
495.0 - 505.0 ( 49.500%): 1.2154% 73.8150% 26.1850%
495.5 - 504.5 ( 49.550%): 1.1894% 75.0044% 24.9956%
496.0 - 504.0 ( 49.600%): 1.1408% 76.1452% 23.8548%
496.5 - 503.5 ( 49.650%): 1.1428% 77.2880% 22.7120%
497.0 - 503.0 ( 49.700%): 1.0835% 78.3715% 21.6285%
497.5 - 502.5 ( 49.750%): 1.0773% 79.4488% 20.5512%
498.0 - 502.0 ( 49.800%): 1.0382% 80.4870% 19.5130%
498.5 - 501.5 ( 49.850%): 0.9989% 81.4859% 18.5141%
499.0 - 501.0 ( 49.900%): 0.9664% 82.4523% 17.5477%
499.5 - 500.5 ( 49.950%): 0.9404% 83.3927% 16.6073%
500.0 - 500.0 ( 50.000%): 0.9123% 84.3050% 15.6950%
500.5 - 499.5 ( 50.050%): 0.8623% 85.1673% 14.8327%
501.0 - 499.0 ( 50.100%): 0.8270% 85.9943% 14.0057%
501.5 - 498.5 ( 50.150%): 0.8096% 86.8039% 13.1961%
502.0 - 498.0 ( 50.200%): 0.7661% 87.5700% 12.4300%
502.5 - 497.5 ( 50.250%): 0.7362% 88.3062% 11.6938%
503.0 - 497.0 ( 50.300%): 0.7104% 89.0166% 10.9834%
503.5 - 496.5 ( 50.350%): 0.6821% 89.6987% 10.3013%
504.0 - 496.0 ( 50.400%): 0.6518% 90.3505% 9.6495%
504.5 - 495.5 ( 50.450%): 0.6172% 90.9677% 9.0323%
505.0 - 495.0 ( 50.500%): 0.5793% 91.5470% 8.4530%
505.5 - 494.5 ( 50.550%): 0.5470% 92.0940% 7.9060%
506.0 - 494.0 ( 50.600%): 0.5345% 92.6285% 7.3715%
506.5 - 493.5 ( 50.650%): 0.5031% 93.1316% 6.8684%
507.0 - 493.0 ( 50.700%): 0.4714% 93.6030% 6.3970%
507.5 - 492.5 ( 50.750%): 0.4539% 94.0569% 5.9431%
508.0 - 492.0 ( 50.800%): 0.4178% 94.4747% 5.5253%
508.5 - 491.5 ( 50.850%): 0.3951% 94.8698% 5.1302%
509.0 - 491.0 ( 50.900%): 0.3834% 95.2532% 4.7468%
509.5 - 490.5 ( 50.950%): 0.3510% 95.6042% 4.3958%
510.0 - 490.0 ( 51.000%): 0.3308% 95.9350% 4.0650%
510.5 - 489.5 ( 51.050%): 0.3104% 96.2454% 3.7546%
511.0 - 489.0 ( 51.100%): 0.2812% 96.5266% 3.4734%
511.5 - 488.5 ( 51.150%): 0.2786% 96.8052% 3.1948%
512.0 - 488.0 ( 51.200%): 0.2549% 97.0601% 2.9399%
512.5 - 487.5 ( 51.250%): 0.2387% 97.2988% 2.7012%
513.0 - 487.0 ( 51.300%): 0.2160% 97.5148% 2.4852%
513.5 - 486.5 ( 51.350%): 0.2067% 97.7215% 2.2785%
514.0 - 486.0 ( 51.400%): 0.1948% 97.9163% 2.0837%
514.5 - 485.5 ( 51.450%): 0.1763% 98.0926% 1.9074%
515.0 - 485.0 ( 51.500%): 0.1660% 98.2586% 1.7414%
515.5 - 484.5 ( 51.550%): 0.1531% 98.4117% 1.5883%
516.0 - 484.0 ( 51.600%): 0.1431% 98.5548% 1.4452%
516.5 - 483.5 ( 51.650%): 0.1328% 98.6876% 1.3124%
517.0 - 483.0 ( 51.700%): 0.1227% 98.8103% 1.1897%
517.5 - 482.5 ( 51.750%): 0.1068% 98.9171% 1.0829%
518.0 - 482.0 ( 51.800%): 0.0974% 99.0145% 0.9855%
518.5 - 481.5 ( 51.850%): 0.0971% 99.1116% 0.8884%
519.0 - 481.0 ( 51.900%): 0.0849% 99.1965% 0.8035%
519.5 - 480.5 ( 51.950%): 0.0779% 99.2744% 0.7256%
520.0 - 480.0 ( 52.000%): 0.0647% 99.3391% 0.6609%
520.5 - 479.5 ( 52.050%): 0.0665% 99.4056% 0.5944%
521.0 - 479.0 ( 52.100%): 0.0544% 99.4600% 0.5400%
521.5 - 478.5 ( 52.150%): 0.0566% 99.5166% 0.4834%
522.0 - 478.0 ( 52.200%): 0.0511% 99.5677% 0.4323%
522.5 - 477.5 ( 52.250%): 0.0430% 99.6107% 0.3893%
523.0 - 477.0 ( 52.300%): 0.0425% 99.6532% 0.3468%
523.5 - 476.5 ( 52.350%): 0.0362% 99.6894% 0.3106%
524.0 - 476.0 ( 52.400%): 0.0340% 99.7234% 0.2766%
524.5 - 475.5 ( 52.450%): 0.0292% 99.7526% 0.2474%
525.0 - 475.0 ( 52.500%): 0.0296% 99.7822% 0.2178%
525.5 - 474.5 ( 52.550%): 0.0245% 99.8067% 0.1933%
526.0 - 474.0 ( 52.600%): 0.0230% 99.8297% 0.1703%
526.5 - 473.5 ( 52.650%): 0.0178% 99.8475% 0.1525%
527.0 - 473.0 ( 52.700%): 0.0163% 99.8638% 0.1362%
527.5 - 472.5 ( 52.750%): 0.0132% 99.8770% 0.1230%
528.0 - 472.0 ( 52.800%): 0.0134% 99.8904% 0.1096%
528.5 - 471.5 ( 52.850%): 0.0133% 99.9037% 0.0963%
529.0 - 471.0 ( 52.900%): 0.0122% 99.9159% 0.0841%
529.5 - 470.5 ( 52.950%): 0.0099% 99.9258% 0.0742%
530.0 - 470.0 ( 53.000%): 0.0077% 99.9335% 0.0665%
530.5 - 469.5 ( 53.050%): 0.0074% 99.9409% 0.0591%
531.0 - 469.0 ( 53.100%): 0.0079% 99.9488% 0.0512%
531.5 - 468.5 ( 53.150%): 0.0054% 99.9542% 0.0458%
532.0 - 468.0 ( 53.200%): 0.0051% 99.9593% 0.0407%
532.5 - 467.5 ( 53.250%): 0.0048% 99.9641% 0.0359%
533.0 - 467.0 ( 53.300%): 0.0043% 99.9684% 0.0316%
533.5 - 466.5 ( 53.350%): 0.0044% 99.9728% 0.0272%
534.0 - 466.0 ( 53.400%): 0.0044% 99.9772% 0.0228%
534.5 - 465.5 ( 53.450%): 0.0037% 99.9809% 0.0191%
535.0 - 465.0 ( 53.500%): 0.0027% 99.9836% 0.0164%
535.5 - 464.5 ( 53.550%): 0.0030% 99.9866% 0.0134%
536.0 - 464.0 ( 53.600%): 0.0019% 99.9885% 0.0115%
536.5 - 463.5 ( 53.650%): 0.0010% 99.9895% 0.0105%
537.0 - 463.0 ( 53.700%): 0.0015% 99.9910% 0.0090%
537.5 - 462.5 ( 53.750%): 0.0010% 99.9920% 0.0080%
538.0 - 462.0 ( 53.800%): 0.0007% 99.9927% 0.0073%
538.5 - 461.5 ( 53.850%): 0.0012% 99.9939% 0.0061%
539.0 - 461.0 ( 53.900%): 0.0007% 99.9946% 0.0054%
539.5 - 460.5 ( 53.950%): 0.0003% 99.9949% 0.0051%
540.0 - 460.0 ( 54.000%): 0.0007% 99.9956% 0.0044%
540.5 - 459.5 ( 54.050%): 0.0006% 99.9962% 0.0038%
541.0 - 459.0 ( 54.100%): 0.0008% 99.9970% 0.0030%
541.5 - 458.5 ( 54.150%): 0.0005% 99.9975% 0.0025%
542.0 - 458.0 ( 54.200%): 0.0002% 99.9977% 0.0023%
542.5 - 457.5 ( 54.250%): 0.0003% 99.9980% 0.0020%
543.0 - 457.0 ( 54.300%): 0.0003% 99.9983% 0.0017%
543.5 - 456.5 ( 54.350%): 0.0004% 99.9987% 0.0013%
544.0 - 456.0 ( 54.400%): 0.0002% 99.9989% 0.0011%
544.5 - 455.5 ( 54.450%): 0.0004% 99.9993% 0.0007%
545.5 - 454.5 ( 54.550%): 0.0001% 99.9994% 0.0006%
546.0 - 454.0 ( 54.600%): 0.0002% 99.9996% 0.0004%
548.0 - 452.0 ( 54.800%): 0.0002% 99.9998% 0.0002%
549.0 - 451.0 ( 54.900%): 0.0001% 99.9999% 0.0001%
550.0 - 450.0 ( 55.000%): 0.0001% 100.0000% 0.0000%
Average result of simulation 48.6587%
CPU-time 43.984 s, PRNG was called 1e+009 times, 0.04398 us/PRN
2000 games:
Result of chess matches
Player A as white wins 42.1%, draws 24.5% and loses 33.4%
Player A as black wins 29.9%, draws 26.1% and loses 44.0%
Expected result: 48.6593% (as white 54.3612%, as black 42.9573%)
A match of 2000 games was simulated 1000000 times by a Monte Carlo method
result probability p <= res. p > res.
884.0 - 1116.0 ( 44.200%): 0.0001% 0.0001% 99.9999%
885.0 - 1115.0 ( 44.250%): 0.0001% 0.0002% 99.9998%
887.5 - 1112.5 ( 44.375%): 0.0001% 0.0003% 99.9997%
888.0 - 1112.0 ( 44.400%): 0.0001% 0.0004% 99.9996%
889.0 - 1111.0 ( 44.450%): 0.0001% 0.0005% 99.9995%
891.5 - 1108.5 ( 44.575%): 0.0002% 0.0007% 99.9993%
892.0 - 1108.0 ( 44.600%): 0.0001% 0.0008% 99.9992%
892.5 - 1107.5 ( 44.625%): 0.0001% 0.0009% 99.9991%
893.0 - 1107.0 ( 44.650%): 0.0006% 0.0015% 99.9985%
893.5 - 1106.5 ( 44.675%): 0.0002% 0.0017% 99.9983%
894.0 - 1106.0 ( 44.700%): 0.0004% 0.0021% 99.9979%
894.5 - 1105.5 ( 44.725%): 0.0003% 0.0024% 99.9976%
895.0 - 1105.0 ( 44.750%): 0.0001% 0.0025% 99.9975%
895.5 - 1104.5 ( 44.775%): 0.0001% 0.0026% 99.9974%
896.0 - 1104.0 ( 44.800%): 0.0001% 0.0027% 99.9973%
896.5 - 1103.5 ( 44.825%): 0.0005% 0.0032% 99.9968%
897.0 - 1103.0 ( 44.850%): 0.0002% 0.0034% 99.9966%
897.5 - 1102.5 ( 44.875%): 0.0003% 0.0037% 99.9963%
898.0 - 1102.0 ( 44.900%): 0.0002% 0.0039% 99.9961%
898.5 - 1101.5 ( 44.925%): 0.0004% 0.0043% 99.9957%
899.0 - 1101.0 ( 44.950%): 0.0003% 0.0046% 99.9954%
899.5 - 1100.5 ( 44.975%): 0.0005% 0.0051% 99.9949%
900.0 - 1100.0 ( 45.000%): 0.0003% 0.0054% 99.9946%
900.5 - 1099.5 ( 45.025%): 0.0009% 0.0063% 99.9937%
901.0 - 1099.0 ( 45.050%): 0.0009% 0.0072% 99.9928%
901.5 - 1098.5 ( 45.075%): 0.0015% 0.0087% 99.9913%
902.0 - 1098.0 ( 45.100%): 0.0005% 0.0092% 99.9908%
902.5 - 1097.5 ( 45.125%): 0.0009% 0.0101% 99.9899%
903.0 - 1097.0 ( 45.150%): 0.0005% 0.0106% 99.9894%
903.5 - 1096.5 ( 45.175%): 0.0016% 0.0122% 99.9878%
904.0 - 1096.0 ( 45.200%): 0.0022% 0.0144% 99.9856%
904.5 - 1095.5 ( 45.225%): 0.0015% 0.0159% 99.9841%
905.0 - 1095.0 ( 45.250%): 0.0016% 0.0175% 99.9825%
905.5 - 1094.5 ( 45.275%): 0.0025% 0.0200% 99.9800%
906.0 - 1094.0 ( 45.300%): 0.0021% 0.0221% 99.9779%
906.5 - 1093.5 ( 45.325%): 0.0026% 0.0247% 99.9753%
907.0 - 1093.0 ( 45.350%): 0.0028% 0.0275% 99.9725%
907.5 - 1092.5 ( 45.375%): 0.0037% 0.0312% 99.9688%
908.0 - 1092.0 ( 45.400%): 0.0039% 0.0351% 99.9649%
908.5 - 1091.5 ( 45.425%): 0.0038% 0.0389% 99.9611%
909.0 - 1091.0 ( 45.450%): 0.0041% 0.0430% 99.9570%
909.5 - 1090.5 ( 45.475%): 0.0039% 0.0469% 99.9531%
910.0 - 1090.0 ( 45.500%): 0.0055% 0.0524% 99.9476%
910.5 - 1089.5 ( 45.525%): 0.0037% 0.0561% 99.9439%
911.0 - 1089.0 ( 45.550%): 0.0050% 0.0611% 99.9389%
911.5 - 1088.5 ( 45.575%): 0.0062% 0.0673% 99.9327%
912.0 - 1088.0 ( 45.600%): 0.0063% 0.0736% 99.9264%
912.5 - 1087.5 ( 45.625%): 0.0085% 0.0821% 99.9179%
913.0 - 1087.0 ( 45.650%): 0.0073% 0.0894% 99.9106%
913.5 - 1086.5 ( 45.675%): 0.0077% 0.0971% 99.9029%
914.0 - 1086.0 ( 45.700%): 0.0092% 0.1063% 99.8937%
914.5 - 1085.5 ( 45.725%): 0.0092% 0.1155% 99.8845%
915.0 - 1085.0 ( 45.750%): 0.0115% 0.1270% 99.8730%
915.5 - 1084.5 ( 45.775%): 0.0108% 0.1378% 99.8622%
916.0 - 1084.0 ( 45.800%): 0.0134% 0.1512% 99.8488%
916.5 - 1083.5 ( 45.825%): 0.0137% 0.1649% 99.8351%
917.0 - 1083.0 ( 45.850%): 0.0135% 0.1784% 99.8216%
917.5 - 1082.5 ( 45.875%): 0.0133% 0.1917% 99.8083%
918.0 - 1082.0 ( 45.900%): 0.0166% 0.2083% 99.7917%
918.5 - 1081.5 ( 45.925%): 0.0179% 0.2262% 99.7738%
919.0 - 1081.0 ( 45.950%): 0.0202% 0.2464% 99.7536%
919.5 - 1080.5 ( 45.975%): 0.0184% 0.2648% 99.7352%
920.0 - 1080.0 ( 46.000%): 0.0252% 0.2900% 99.7100%
920.5 - 1079.5 ( 46.025%): 0.0221% 0.3121% 99.6879%
921.0 - 1079.0 ( 46.050%): 0.0263% 0.3384% 99.6616%
921.5 - 1078.5 ( 46.075%): 0.0282% 0.3666% 99.6334%
922.0 - 1078.0 ( 46.100%): 0.0279% 0.3945% 99.6055%
922.5 - 1077.5 ( 46.125%): 0.0303% 0.4248% 99.5752%
923.0 - 1077.0 ( 46.150%): 0.0328% 0.4576% 99.5424%
923.5 - 1076.5 ( 46.175%): 0.0355% 0.4931% 99.5069%
924.0 - 1076.0 ( 46.200%): 0.0365% 0.5296% 99.4704%
924.5 - 1075.5 ( 46.225%): 0.0431% 0.5727% 99.4273%
925.0 - 1075.0 ( 46.250%): 0.0420% 0.6147% 99.3853%
925.5 - 1074.5 ( 46.275%): 0.0431% 0.6578% 99.3422%
926.0 - 1074.0 ( 46.300%): 0.0473% 0.7051% 99.2949%
926.5 - 1073.5 ( 46.325%): 0.0551% 0.7602% 99.2398%
927.0 - 1073.0 ( 46.350%): 0.0546% 0.8148% 99.1852%
927.5 - 1072.5 ( 46.375%): 0.0590% 0.8738% 99.1262%
928.0 - 1072.0 ( 46.400%): 0.0609% 0.9347% 99.0653%
928.5 - 1071.5 ( 46.425%): 0.0662% 1.0009% 98.9991%
929.0 - 1071.0 ( 46.450%): 0.0711% 1.0720% 98.9280%
929.5 - 1070.5 ( 46.475%): 0.0769% 1.1489% 98.8511%
930.0 - 1070.0 ( 46.500%): 0.0862% 1.2351% 98.7649%
930.5 - 1069.5 ( 46.525%): 0.0911% 1.3262% 98.6738%
931.0 - 1069.0 ( 46.550%): 0.0909% 1.4171% 98.5829%
931.5 - 1068.5 ( 46.575%): 0.1013% 1.5184% 98.4816%
932.0 - 1068.0 ( 46.600%): 0.1026% 1.6210% 98.3790%
932.5 - 1067.5 ( 46.625%): 0.1125% 1.7335% 98.2665%
933.0 - 1067.0 ( 46.650%): 0.1178% 1.8513% 98.1487%
933.5 - 1066.5 ( 46.675%): 0.1197% 1.9710% 98.0290%
934.0 - 1066.0 ( 46.700%): 0.1276% 2.0986% 97.9014%
934.5 - 1065.5 ( 46.725%): 0.1331% 2.2317% 97.7683%
935.0 - 1065.0 ( 46.750%): 0.1393% 2.3710% 97.6290%
935.5 - 1064.5 ( 46.775%): 0.1493% 2.5203% 97.4797%
936.0 - 1064.0 ( 46.800%): 0.1528% 2.6731% 97.3269%
936.5 - 1063.5 ( 46.825%): 0.1696% 2.8427% 97.1573%
937.0 - 1063.0 ( 46.850%): 0.1752% 3.0179% 96.9821%
937.5 - 1062.5 ( 46.875%): 0.1824% 3.2003% 96.7997%
938.0 - 1062.0 ( 46.900%): 0.1959% 3.3962% 96.6038%
938.5 - 1061.5 ( 46.925%): 0.2019% 3.5981% 96.4019%
939.0 - 1061.0 ( 46.950%): 0.2084% 3.8065% 96.1935%
939.5 - 1060.5 ( 46.975%): 0.2230% 4.0295% 95.9705%
940.0 - 1060.0 ( 47.000%): 0.2379% 4.2674% 95.7326%
940.5 - 1059.5 ( 47.025%): 0.2368% 4.5042% 95.4958%
941.0 - 1059.0 ( 47.050%): 0.2498% 4.7540% 95.2460%
941.5 - 1058.5 ( 47.075%): 0.2692% 5.0232% 94.9768%
942.0 - 1058.0 ( 47.100%): 0.2660% 5.2892% 94.7108%
942.5 - 1057.5 ( 47.125%): 0.2870% 5.5762% 94.4238%
943.0 - 1057.0 ( 47.150%): 0.2963% 5.8725% 94.1275%
943.5 - 1056.5 ( 47.175%): 0.3126% 6.1851% 93.8149%
944.0 - 1056.0 ( 47.200%): 0.3147% 6.4998% 93.5002%
944.5 - 1055.5 ( 47.225%): 0.3339% 6.8337% 93.1663%
945.0 - 1055.0 ( 47.250%): 0.3550% 7.1887% 92.8113%
945.5 - 1054.5 ( 47.275%): 0.3615% 7.5502% 92.4498%
946.0 - 1054.0 ( 47.300%): 0.3868% 7.9370% 92.0630%
946.5 - 1053.5 ( 47.325%): 0.3852% 8.3222% 91.6778%
947.0 - 1053.0 ( 47.350%): 0.4054% 8.7276% 91.2724%
947.5 - 1052.5 ( 47.375%): 0.4345% 9.1621% 90.8379%
948.0 - 1052.0 ( 47.400%): 0.4324% 9.5945% 90.4055%
948.5 - 1051.5 ( 47.425%): 0.4620% 10.0565% 89.9435%
949.0 - 1051.0 ( 47.450%): 0.4805% 10.5370% 89.4630%
949.5 - 1050.5 ( 47.475%): 0.4875% 11.0245% 88.9755%
950.0 - 1050.0 ( 47.500%): 0.5088% 11.5333% 88.4667%
950.5 - 1049.5 ( 47.525%): 0.5204% 12.0537% 87.9463%
951.0 - 1049.0 ( 47.550%): 0.5400% 12.5937% 87.4063%
951.5 - 1048.5 ( 47.575%): 0.5534% 13.1471% 86.8529%
952.0 - 1048.0 ( 47.600%): 0.5517% 13.6988% 86.3012%
952.5 - 1047.5 ( 47.625%): 0.5832% 14.2820% 85.7180%
953.0 - 1047.0 ( 47.650%): 0.5899% 14.8719% 85.1281%
953.5 - 1046.5 ( 47.675%): 0.6067% 15.4786% 84.5214%
954.0 - 1046.0 ( 47.700%): 0.6163% 16.0949% 83.9051%
954.5 - 1045.5 ( 47.725%): 0.6487% 16.7436% 83.2564%
955.0 - 1045.0 ( 47.750%): 0.6616% 17.4052% 82.5948%
955.5 - 1044.5 ( 47.775%): 0.6755% 18.0807% 81.9193%
956.0 - 1044.0 ( 47.800%): 0.6891% 18.7698% 81.2302%
956.5 - 1043.5 ( 47.825%): 0.7016% 19.4714% 80.5286%
957.0 - 1043.0 ( 47.850%): 0.7130% 20.1844% 79.8156%
957.5 - 1042.5 ( 47.875%): 0.7546% 20.9390% 79.0610%
958.0 - 1042.0 ( 47.900%): 0.7510% 21.6900% 78.3100%
958.5 - 1041.5 ( 47.925%): 0.7893% 22.4793% 77.5207%
959.0 - 1041.0 ( 47.950%): 0.7955% 23.2748% 76.7252%
959.5 - 1040.5 ( 47.975%): 0.8005% 24.0753% 75.9247%
960.0 - 1040.0 ( 48.000%): 0.8300% 24.9053% 75.0947%
960.5 - 1039.5 ( 48.025%): 0.8430% 25.7483% 74.2517%
961.0 - 1039.0 ( 48.050%): 0.8637% 26.6120% 73.3880%
961.5 - 1038.5 ( 48.075%): 0.8615% 27.4735% 72.5265%
962.0 - 1038.0 ( 48.100%): 0.8985% 28.3720% 71.6280%
962.5 - 1037.5 ( 48.125%): 0.8809% 29.2529% 70.7471%
963.0 - 1037.0 ( 48.150%): 0.9076% 30.1605% 69.8395%
963.5 - 1036.5 ( 48.175%): 0.9266% 31.0871% 68.9129%
964.0 - 1036.0 ( 48.200%): 0.9225% 32.0096% 67.9904%
964.5 - 1035.5 ( 48.225%): 0.9481% 32.9577% 67.0423%
965.0 - 1035.0 ( 48.250%): 0.9557% 33.9134% 66.0866%
965.5 - 1034.5 ( 48.275%): 0.9488% 34.8622% 65.1378%
966.0 - 1034.0 ( 48.300%): 0.9731% 35.8353% 64.1647%
966.5 - 1033.5 ( 48.325%): 0.9736% 36.8089% 63.1911%
967.0 - 1033.0 ( 48.350%): 0.9918% 37.8007% 62.1993%
967.5 - 1032.5 ( 48.375%): 0.9931% 38.7938% 61.2062%
968.0 - 1032.0 ( 48.400%): 1.0135% 39.8073% 60.1927%
968.5 - 1031.5 ( 48.425%): 1.0020% 40.8093% 59.1907%
969.0 - 1031.0 ( 48.450%): 1.0211% 41.8304% 58.1696%
969.5 - 1030.5 ( 48.475%): 1.0298% 42.8602% 57.1398%
970.0 - 1030.0 ( 48.500%): 1.0250% 43.8852% 56.1148%
970.5 - 1029.5 ( 48.525%): 1.0387% 44.9239% 55.0761%
971.0 - 1029.0 ( 48.550%): 1.0423% 45.9662% 54.0338%
971.5 - 1028.5 ( 48.575%): 1.0430% 47.0092% 52.9908%
972.0 - 1028.0 ( 48.600%): 1.0223% 48.0315% 51.9685%
972.5 - 1027.5 ( 48.625%): 1.0549% 49.0864% 50.9136%
973.0 - 1027.0 ( 48.650%): 1.0426% 50.1290% 49.8710%
973.5 - 1026.5 ( 48.675%): 1.0600% 51.1890% 48.8110%
974.0 - 1026.0 ( 48.700%): 1.0444% 52.2334% 47.7666%
974.5 - 1025.5 ( 48.725%): 1.0317% 53.2651% 46.7349%
975.0 - 1025.0 ( 48.750%): 1.0269% 54.2920% 45.7080%
975.5 - 1024.5 ( 48.775%): 1.0409% 55.3329% 44.6671%
976.0 - 1024.0 ( 48.800%): 1.0305% 56.3634% 43.6366%
976.5 - 1023.5 ( 48.825%): 1.0217% 57.3851% 42.6149%
977.0 - 1023.0 ( 48.850%): 1.0309% 58.4160% 41.5840%
977.5 - 1022.5 ( 48.875%): 0.9936% 59.4096% 40.5904%
978.0 - 1022.0 ( 48.900%): 1.0003% 60.4099% 39.5901%
978.5 - 1021.5 ( 48.925%): 1.0090% 61.4189% 38.5811%
979.0 - 1021.0 ( 48.950%): 0.9782% 62.3971% 37.6029%
979.5 - 1020.5 ( 48.975%): 0.9888% 63.3859% 36.6141%
980.0 - 1020.0 ( 49.000%): 0.9792% 64.3651% 35.6349%
980.5 - 1019.5 ( 49.025%): 0.9860% 65.3511% 34.6489%
981.0 - 1019.0 ( 49.050%): 0.9687% 66.3198% 33.6802%
981.5 - 1018.5 ( 49.075%): 0.9562% 67.2760% 32.7240%
982.0 - 1018.0 ( 49.100%): 0.9233% 68.1993% 31.8007%
982.5 - 1017.5 ( 49.125%): 0.9340% 69.1333% 30.8667%
983.0 - 1017.0 ( 49.150%): 0.9038% 70.0371% 29.9629%
983.5 - 1016.5 ( 49.175%): 0.9006% 70.9377% 29.0623%
984.0 - 1016.0 ( 49.200%): 0.9144% 71.8521% 28.1479%
984.5 - 1015.5 ( 49.225%): 0.8686% 72.7207% 27.2793%
985.0 - 1015.0 ( 49.250%): 0.8679% 73.5886% 26.4114%
985.5 - 1014.5 ( 49.275%): 0.8482% 74.4368% 25.5632%
986.0 - 1014.0 ( 49.300%): 0.8350% 75.2718% 24.7282%
986.5 - 1013.5 ( 49.325%): 0.8108% 76.0826% 23.9174%
987.0 - 1013.0 ( 49.350%): 0.7973% 76.8799% 23.1201%
987.5 - 1012.5 ( 49.375%): 0.7879% 77.6678% 22.3322%
988.0 - 1012.0 ( 49.400%): 0.7717% 78.4395% 21.5605%
988.5 - 1011.5 ( 49.425%): 0.7541% 79.1936% 20.8064%
989.0 - 1011.0 ( 49.450%): 0.7386% 79.9322% 20.0678%
989.5 - 1010.5 ( 49.475%): 0.7253% 80.6575% 19.3425%
990.0 - 1010.0 ( 49.500%): 0.7216% 81.3791% 18.6209%
990.5 - 1009.5 ( 49.525%): 0.6836% 82.0627% 17.9373%
991.0 - 1009.0 ( 49.550%): 0.6820% 82.7447% 17.2553%
991.5 - 1008.5 ( 49.575%): 0.6636% 83.4083% 16.5917%
992.0 - 1008.0 ( 49.600%): 0.6536% 84.0619% 15.9381%
992.5 - 1007.5 ( 49.625%): 0.6237% 84.6856% 15.3144%
993.0 - 1007.0 ( 49.650%): 0.6097% 85.2953% 14.7047%
993.5 - 1006.5 ( 49.675%): 0.5963% 85.8916% 14.1084%
994.0 - 1006.0 ( 49.700%): 0.5716% 86.4632% 13.5368%
994.5 - 1005.5 ( 49.725%): 0.5453% 87.0085% 12.9915%
995.0 - 1005.0 ( 49.750%): 0.5362% 87.5447% 12.4553%
995.5 - 1004.5 ( 49.775%): 0.5283% 88.0730% 11.9270%
996.0 - 1004.0 ( 49.800%): 0.5102% 88.5832% 11.4168%
996.5 - 1003.5 ( 49.825%): 0.4933% 89.0765% 10.9235%
997.0 - 1003.0 ( 49.850%): 0.4802% 89.5567% 10.4433%
997.5 - 1002.5 ( 49.875%): 0.4645% 90.0212% 9.9788%
998.0 - 1002.0 ( 49.900%): 0.4533% 90.4745% 9.5255%
998.5 - 1001.5 ( 49.925%): 0.4343% 90.9088% 9.0912%
999.0 - 1001.0 ( 49.950%): 0.4236% 91.3324% 8.6676%
999.5 - 1000.5 ( 49.975%): 0.4079% 91.7403% 8.2597%
1000.0 - 1000.0 ( 50.000%): 0.3844% 92.1247% 7.8753%
1000.5 - 999.5 ( 50.025%): 0.3726% 92.4973% 7.5027%
1001.0 - 999.0 ( 50.050%): 0.3611% 92.8584% 7.1416%
1001.5 - 998.5 ( 50.075%): 0.3489% 93.2073% 6.7927%
1002.0 - 998.0 ( 50.100%): 0.3387% 93.5460% 6.4540%
1002.5 - 997.5 ( 50.125%): 0.3216% 93.8676% 6.1324%
1003.0 - 997.0 ( 50.150%): 0.3113% 94.1789% 5.8211%
1003.5 - 996.5 ( 50.175%): 0.3030% 94.4819% 5.5181%
1004.0 - 996.0 ( 50.200%): 0.2839% 94.7658% 5.2342%
1004.5 - 995.5 ( 50.225%): 0.2722% 95.0380% 4.9620%
1005.0 - 995.0 ( 50.250%): 0.2591% 95.2971% 4.7029%
1005.5 - 994.5 ( 50.275%): 0.2496% 95.5467% 4.4533%
1006.0 - 994.0 ( 50.300%): 0.2417% 95.7884% 4.2116%
1006.5 - 993.5 ( 50.325%): 0.2317% 96.0201% 3.9799%
1007.0 - 993.0 ( 50.350%): 0.2132% 96.2333% 3.7667%
1007.5 - 992.5 ( 50.375%): 0.2150% 96.4483% 3.5517%
1008.0 - 992.0 ( 50.400%): 0.1976% 96.6459% 3.3541%
1008.5 - 991.5 ( 50.425%): 0.1895% 96.8354% 3.1646%
1009.0 - 991.0 ( 50.450%): 0.1837% 97.0191% 2.9809%
1009.5 - 990.5 ( 50.475%): 0.1761% 97.1952% 2.8048%
1010.0 - 990.0 ( 50.500%): 0.1665% 97.3617% 2.6383%
1010.5 - 989.5 ( 50.525%): 0.1624% 97.5241% 2.4759%
1011.0 - 989.0 ( 50.550%): 0.1475% 97.6716% 2.3284%
1011.5 - 988.5 ( 50.575%): 0.1382% 97.8098% 2.1902%
1012.0 - 988.0 ( 50.600%): 0.1340% 97.9438% 2.0562%
1012.5 - 987.5 ( 50.625%): 0.1270% 98.0708% 1.9292%
1013.0 - 987.0 ( 50.650%): 0.1136% 98.1844% 1.8156%
1013.5 - 986.5 ( 50.675%): 0.1180% 98.3024% 1.6976%
1014.0 - 986.0 ( 50.700%): 0.1109% 98.4133% 1.5867%
1014.5 - 985.5 ( 50.725%): 0.1055% 98.5188% 1.4812%
1015.0 - 985.0 ( 50.750%): 0.0969% 98.6157% 1.3843%
1015.5 - 984.5 ( 50.775%): 0.0825% 98.6982% 1.3018%
1016.0 - 984.0 ( 50.800%): 0.0859% 98.7841% 1.2159%
1016.5 - 983.5 ( 50.825%): 0.0782% 98.8623% 1.1377%
1017.0 - 983.0 ( 50.850%): 0.0739% 98.9362% 1.0638%
1017.5 - 982.5 ( 50.875%): 0.0745% 99.0107% 0.9893%
1018.0 - 982.0 ( 50.900%): 0.0654% 99.0761% 0.9239%
1018.5 - 981.5 ( 50.925%): 0.0616% 99.1377% 0.8623%
1019.0 - 981.0 ( 50.950%): 0.0549% 99.1926% 0.8074%
1019.5 - 980.5 ( 50.975%): 0.0558% 99.2484% 0.7516%
1020.0 - 980.0 ( 51.000%): 0.0510% 99.2994% 0.7006%
1020.5 - 979.5 ( 51.025%): 0.0481% 99.3475% 0.6525%
1021.0 - 979.0 ( 51.050%): 0.0462% 99.3937% 0.6063%
1021.5 - 978.5 ( 51.075%): 0.0454% 99.4391% 0.5609%
1022.0 - 978.0 ( 51.100%): 0.0405% 99.4796% 0.5204%
1022.5 - 977.5 ( 51.125%): 0.0398% 99.5194% 0.4806%
1023.0 - 977.0 ( 51.150%): 0.0335% 99.5529% 0.4471%
1023.5 - 976.5 ( 51.175%): 0.0358% 99.5887% 0.4113%
1024.0 - 976.0 ( 51.200%): 0.0303% 99.6190% 0.3810%
1024.5 - 975.5 ( 51.225%): 0.0304% 99.6494% 0.3506%
1025.0 - 975.0 ( 51.250%): 0.0263% 99.6757% 0.3243%
1025.5 - 974.5 ( 51.275%): 0.0256% 99.7013% 0.2987%
1026.0 - 974.0 ( 51.300%): 0.0240% 99.7253% 0.2747%
1026.5 - 973.5 ( 51.325%): 0.0210% 99.7463% 0.2537%
1027.0 - 973.0 ( 51.350%): 0.0199% 99.7662% 0.2338%
1027.5 - 972.5 ( 51.375%): 0.0188% 99.7850% 0.2150%
1028.0 - 972.0 ( 51.400%): 0.0162% 99.8012% 0.1988%
1028.5 - 971.5 ( 51.425%): 0.0143% 99.8155% 0.1845%
1029.0 - 971.0 ( 51.450%): 0.0158% 99.8313% 0.1687%
1029.5 - 970.5 ( 51.475%): 0.0130% 99.8443% 0.1557%
1030.0 - 970.0 ( 51.500%): 0.0130% 99.8573% 0.1427%
1030.5 - 969.5 ( 51.525%): 0.0120% 99.8693% 0.1307%
1031.0 - 969.0 ( 51.550%): 0.0110% 99.8803% 0.1197%
1031.5 - 968.5 ( 51.575%): 0.0103% 99.8906% 0.1094%
1032.0 - 968.0 ( 51.600%): 0.0104% 99.9010% 0.0990%
1032.5 - 967.5 ( 51.625%): 0.0094% 99.9104% 0.0896%
1033.0 - 967.0 ( 51.650%): 0.0078% 99.9182% 0.0818%
1033.5 - 966.5 ( 51.675%): 0.0082% 99.9264% 0.0736%
1034.0 - 966.0 ( 51.700%): 0.0062% 99.9326% 0.0674%
1034.5 - 965.5 ( 51.725%): 0.0056% 99.9382% 0.0618%
1035.0 - 965.0 ( 51.750%): 0.0050% 99.9432% 0.0568%
1035.5 - 964.5 ( 51.775%): 0.0052% 99.9484% 0.0516%
1036.0 - 964.0 ( 51.800%): 0.0047% 99.9531% 0.0469%
1036.5 - 963.5 ( 51.825%): 0.0046% 99.9577% 0.0423%
1037.0 - 963.0 ( 51.850%): 0.0039% 99.9616% 0.0384%
1037.5 - 962.5 ( 51.875%): 0.0040% 99.9656% 0.0344%
1038.0 - 962.0 ( 51.900%): 0.0025% 99.9681% 0.0319%
1038.5 - 961.5 ( 51.925%): 0.0025% 99.9706% 0.0294%
1039.0 - 961.0 ( 51.950%): 0.0024% 99.9730% 0.0270%
1039.5 - 960.5 ( 51.975%): 0.0018% 99.9748% 0.0252%
1040.0 - 960.0 ( 52.000%): 0.0022% 99.9770% 0.0230%
1040.5 - 959.5 ( 52.025%): 0.0019% 99.9789% 0.0211%
1041.0 - 959.0 ( 52.050%): 0.0014% 99.9803% 0.0197%
1041.5 - 958.5 ( 52.075%): 0.0018% 99.9821% 0.0179%
1042.0 - 958.0 ( 52.100%): 0.0013% 99.9834% 0.0166%
1042.5 - 957.5 ( 52.125%): 0.0028% 99.9862% 0.0138%
1043.0 - 957.0 ( 52.150%): 0.0012% 99.9874% 0.0126%
1043.5 - 956.5 ( 52.175%): 0.0016% 99.9890% 0.0110%
1044.0 - 956.0 ( 52.200%): 0.0007% 99.9897% 0.0103%
1044.5 - 955.5 ( 52.225%): 0.0009% 99.9906% 0.0094%
1045.0 - 955.0 ( 52.250%): 0.0005% 99.9911% 0.0089%
1045.5 - 954.5 ( 52.275%): 0.0004% 99.9915% 0.0085%
1046.0 - 954.0 ( 52.300%): 0.0003% 99.9918% 0.0082%
1046.5 - 953.5 ( 52.325%): 0.0008% 99.9926% 0.0074%
1047.0 - 953.0 ( 52.350%): 0.0008% 99.9934% 0.0066%
1047.5 - 952.5 ( 52.375%): 0.0008% 99.9942% 0.0058%
1048.0 - 952.0 ( 52.400%): 0.0003% 99.9945% 0.0055%
1048.5 - 951.5 ( 52.425%): 0.0002% 99.9947% 0.0053%
1049.0 - 951.0 ( 52.450%): 0.0005% 99.9952% 0.0048%
1049.5 - 950.5 ( 52.475%): 0.0005% 99.9957% 0.0043%
1050.0 - 950.0 ( 52.500%): 0.0001% 99.9958% 0.0042%
1050.5 - 949.5 ( 52.525%): 0.0003% 99.9961% 0.0039%
1051.0 - 949.0 ( 52.550%): 0.0006% 99.9967% 0.0033%
1051.5 - 948.5 ( 52.575%): 0.0007% 99.9974% 0.0026%
1052.0 - 948.0 ( 52.600%): 0.0003% 99.9977% 0.0023%
1052.5 - 947.5 ( 52.625%): 0.0003% 99.9980% 0.0020%
1053.0 - 947.0 ( 52.650%): 0.0004% 99.9984% 0.0016%
1053.5 - 946.5 ( 52.675%): 0.0001% 99.9985% 0.0015%
1054.0 - 946.0 ( 52.700%): 0.0003% 99.9988% 0.0012%
1054.5 - 945.5 ( 52.725%): 0.0003% 99.9991% 0.0009%
1056.0 - 944.0 ( 52.800%): 0.0002% 99.9993% 0.0007%
1058.0 - 942.0 ( 52.900%): 0.0002% 99.9995% 0.0005%
1060.0 - 940.0 ( 53.000%): 0.0001% 99.9996% 0.0004%
1062.0 - 938.0 ( 53.100%): 0.0002% 99.9998% 0.0002%
1062.5 - 937.5 ( 53.125%): 0.0001% 99.9999% 0.0001%
1064.5 - 935.5 ( 53.225%): 0.0001% 100.0000% 0.0000%
Average result of simulation 48.6597%
CPU-time 86.421 s, PRNG was called 2e+009 times, 0.04321 us/PRN
5000 games
Result of chess matches
Player A as white wins 42.1%, draws 24.5% and loses 33.4%
Player A as black wins 29.9%, draws 26.1% and loses 44.0%
Expected result: 48.6593% (as white 54.3612%, as black 42.9573%)
A match of 5000 games was simulated 100000 times by a Monte Carlo method
result probability p <= res. p > res.
2313.5 - 2686.5 ( 46.270%): 0.0010% 0.0010% 99.9990%
2315.5 - 2684.5 ( 46.310%): 0.0010% 0.0020% 99.9980%
2316.5 - 2683.5 ( 46.330%): 0.0010% 0.0030% 99.9970%
2318.5 - 2681.5 ( 46.370%): 0.0020% 0.0050% 99.9950%
2323.5 - 2676.5 ( 46.470%): 0.0010% 0.0060% 99.9940%
2324.0 - 2676.0 ( 46.480%): 0.0010% 0.0070% 99.9930%
2325.0 - 2675.0 ( 46.500%): 0.0030% 0.0100% 99.9900%
2325.5 - 2674.5 ( 46.510%): 0.0010% 0.0110% 99.9890%
2326.0 - 2674.0 ( 46.520%): 0.0010% 0.0120% 99.9880%
2326.5 - 2673.5 ( 46.530%): 0.0040% 0.0160% 99.9840%
2327.0 - 2673.0 ( 46.540%): 0.0010% 0.0170% 99.9830%
2327.5 - 2672.5 ( 46.550%): 0.0020% 0.0190% 99.9810%
2329.5 - 2670.5 ( 46.590%): 0.0030% 0.0220% 99.9780%
2330.0 - 2670.0 ( 46.600%): 0.0030% 0.0250% 99.9750%
2330.5 - 2669.5 ( 46.610%): 0.0010% 0.0260% 99.9740%
2331.0 - 2669.0 ( 46.620%): 0.0030% 0.0290% 99.9710%
2331.5 - 2668.5 ( 46.630%): 0.0010% 0.0300% 99.9700%
2332.0 - 2668.0 ( 46.640%): 0.0030% 0.0330% 99.9670%
2332.5 - 2667.5 ( 46.650%): 0.0040% 0.0370% 99.9630%
2333.0 - 2667.0 ( 46.660%): 0.0040% 0.0410% 99.9590%
2333.5 - 2666.5 ( 46.670%): 0.0040% 0.0450% 99.9550%
2334.0 - 2666.0 ( 46.680%): 0.0020% 0.0470% 99.9530%
2334.5 - 2665.5 ( 46.690%): 0.0030% 0.0500% 99.9500%
2335.0 - 2665.0 ( 46.700%): 0.0030% 0.0530% 99.9470%
2335.5 - 2664.5 ( 46.710%): 0.0050% 0.0580% 99.9420%
2336.0 - 2664.0 ( 46.720%): 0.0060% 0.0640% 99.9360%
2336.5 - 2663.5 ( 46.730%): 0.0040% 0.0680% 99.9320%
2337.0 - 2663.0 ( 46.740%): 0.0030% 0.0710% 99.9290%
2337.5 - 2662.5 ( 46.750%): 0.0060% 0.0770% 99.9230%
2338.0 - 2662.0 ( 46.760%): 0.0040% 0.0810% 99.9190%
2338.5 - 2661.5 ( 46.770%): 0.0080% 0.0890% 99.9110%
2339.0 - 2661.0 ( 46.780%): 0.0010% 0.0900% 99.9100%
2339.5 - 2660.5 ( 46.790%): 0.0060% 0.0960% 99.9040%
2340.0 - 2660.0 ( 46.800%): 0.0060% 0.1020% 99.8980%
2340.5 - 2659.5 ( 46.810%): 0.0080% 0.1100% 99.8900%
2341.0 - 2659.0 ( 46.820%): 0.0050% 0.1150% 99.8850%
2341.5 - 2658.5 ( 46.830%): 0.0070% 0.1220% 99.8780%
2342.0 - 2658.0 ( 46.840%): 0.0020% 0.1240% 99.8760%
2342.5 - 2657.5 ( 46.850%): 0.0080% 0.1320% 99.8680%
2343.0 - 2657.0 ( 46.860%): 0.0120% 0.1440% 99.8560%
2343.5 - 2656.5 ( 46.870%): 0.0120% 0.1560% 99.8440%
2344.0 - 2656.0 ( 46.880%): 0.0040% 0.1600% 99.8400%
2344.5 - 2655.5 ( 46.890%): 0.0070% 0.1670% 99.8330%
2345.0 - 2655.0 ( 46.900%): 0.0090% 0.1760% 99.8240%
2345.5 - 2654.5 ( 46.910%): 0.0110% 0.1870% 99.8130%
2346.0 - 2654.0 ( 46.920%): 0.0050% 0.1920% 99.8080%
2346.5 - 2653.5 ( 46.930%): 0.0110% 0.2030% 99.7970%
2347.0 - 2653.0 ( 46.940%): 0.0110% 0.2140% 99.7860%
2347.5 - 2652.5 ( 46.950%): 0.0080% 0.2220% 99.7780%
2348.0 - 2652.0 ( 46.960%): 0.0140% 0.2360% 99.7640%
2348.5 - 2651.5 ( 46.970%): 0.0200% 0.2560% 99.7440%
2349.0 - 2651.0 ( 46.980%): 0.0060% 0.2620% 99.7380%
2349.5 - 2650.5 ( 46.990%): 0.0170% 0.2790% 99.7210%
2350.0 - 2650.0 ( 47.000%): 0.0220% 0.3010% 99.6990%
2350.5 - 2649.5 ( 47.010%): 0.0140% 0.3150% 99.6850%
2351.0 - 2649.0 ( 47.020%): 0.0180% 0.3330% 99.6670%
2351.5 - 2648.5 ( 47.030%): 0.0220% 0.3550% 99.6450%
2352.0 - 2648.0 ( 47.040%): 0.0240% 0.3790% 99.6210%
2352.5 - 2647.5 ( 47.050%): 0.0220% 0.4010% 99.5990%
2353.0 - 2647.0 ( 47.060%): 0.0240% 0.4250% 99.5750%
2353.5 - 2646.5 ( 47.070%): 0.0240% 0.4490% 99.5510%
2354.0 - 2646.0 ( 47.080%): 0.0150% 0.4640% 99.5360%
2354.5 - 2645.5 ( 47.090%): 0.0180% 0.4820% 99.5180%
2355.0 - 2645.0 ( 47.100%): 0.0260% 0.5080% 99.4920%
2355.5 - 2644.5 ( 47.110%): 0.0250% 0.5330% 99.4670%
2356.0 - 2644.0 ( 47.120%): 0.0260% 0.5590% 99.4410%
2356.5 - 2643.5 ( 47.130%): 0.0230% 0.5820% 99.4180%
2357.0 - 2643.0 ( 47.140%): 0.0280% 0.6100% 99.3900%
2357.5 - 2642.5 ( 47.150%): 0.0270% 0.6370% 99.3630%
2358.0 - 2642.0 ( 47.160%): 0.0310% 0.6680% 99.3320%
2358.5 - 2641.5 ( 47.170%): 0.0350% 0.7030% 99.2970%
2359.0 - 2641.0 ( 47.180%): 0.0340% 0.7370% 99.2630%
2359.5 - 2640.5 ( 47.190%): 0.0350% 0.7720% 99.2280%
2360.0 - 2640.0 ( 47.200%): 0.0380% 0.8100% 99.1900%
2360.5 - 2639.5 ( 47.210%): 0.0450% 0.8550% 99.1450%
2361.0 - 2639.0 ( 47.220%): 0.0340% 0.8890% 99.1110%
2361.5 - 2638.5 ( 47.230%): 0.0370% 0.9260% 99.0740%
2362.0 - 2638.0 ( 47.240%): 0.0350% 0.9610% 99.0390%
2362.5 - 2637.5 ( 47.250%): 0.0510% 1.0120% 98.9880%
2363.0 - 2637.0 ( 47.260%): 0.0490% 1.0610% 98.9390%
2363.5 - 2636.5 ( 47.270%): 0.0430% 1.1040% 98.8960%
2364.0 - 2636.0 ( 47.280%): 0.0500% 1.1540% 98.8460%
2364.5 - 2635.5 ( 47.290%): 0.0610% 1.2150% 98.7850%
2365.0 - 2635.0 ( 47.300%): 0.0550% 1.2700% 98.7300%
2365.5 - 2634.5 ( 47.310%): 0.0560% 1.3260% 98.6740%
2366.0 - 2634.0 ( 47.320%): 0.0540% 1.3800% 98.6200%
2366.5 - 2633.5 ( 47.330%): 0.0510% 1.4310% 98.5690%
2367.0 - 2633.0 ( 47.340%): 0.0640% 1.4950% 98.5050%
2367.5 - 2632.5 ( 47.350%): 0.0730% 1.5680% 98.4320%
2368.0 - 2632.0 ( 47.360%): 0.0580% 1.6260% 98.3740%
2368.5 - 2631.5 ( 47.370%): 0.0540% 1.6800% 98.3200%
2369.0 - 2631.0 ( 47.380%): 0.0840% 1.7640% 98.2360%
2369.5 - 2630.5 ( 47.390%): 0.0720% 1.8360% 98.1640%
2370.0 - 2630.0 ( 47.400%): 0.0670% 1.9030% 98.0970%
2370.5 - 2629.5 ( 47.410%): 0.0610% 1.9640% 98.0360%
2371.0 - 2629.0 ( 47.420%): 0.0810% 2.0450% 97.9550%
2371.5 - 2628.5 ( 47.430%): 0.0790% 2.1240% 97.8760%
2372.0 - 2628.0 ( 47.440%): 0.0850% 2.2090% 97.7910%
2372.5 - 2627.5 ( 47.450%): 0.0880% 2.2970% 97.7030%
2373.0 - 2627.0 ( 47.460%): 0.1190% 2.4160% 97.5840%
2373.5 - 2626.5 ( 47.470%): 0.1070% 2.5230% 97.4770%
2374.0 - 2626.0 ( 47.480%): 0.1010% 2.6240% 97.3760%
2374.5 - 2625.5 ( 47.490%): 0.0960% 2.7200% 97.2800%
2375.0 - 2625.0 ( 47.500%): 0.0980% 2.8180% 97.1820%
2375.5 - 2624.5 ( 47.510%): 0.1110% 2.9290% 97.0710%
2376.0 - 2624.0 ( 47.520%): 0.1090% 3.0380% 96.9620%
2376.5 - 2623.5 ( 47.530%): 0.1100% 3.1480% 96.8520%
2377.0 - 2623.0 ( 47.540%): 0.1070% 3.2550% 96.7450%
2377.5 - 2622.5 ( 47.550%): 0.1370% 3.3920% 96.6080%
2378.0 - 2622.0 ( 47.560%): 0.1420% 3.5340% 96.4660%
2378.5 - 2621.5 ( 47.570%): 0.1200% 3.6540% 96.3460%
2379.0 - 2621.0 ( 47.580%): 0.1280% 3.7820% 96.2180%
2379.5 - 2620.5 ( 47.590%): 0.1480% 3.9300% 96.0700%
2380.0 - 2620.0 ( 47.600%): 0.1300% 4.0600% 95.9400%
2380.5 - 2619.5 ( 47.610%): 0.1590% 4.2190% 95.7810%
2381.0 - 2619.0 ( 47.620%): 0.1680% 4.3870% 95.6130%
2381.5 - 2618.5 ( 47.630%): 0.1360% 4.5230% 95.4770%
2382.0 - 2618.0 ( 47.640%): 0.1680% 4.6910% 95.3090%
2382.5 - 2617.5 ( 47.650%): 0.1650% 4.8560% 95.1440%
2383.0 - 2617.0 ( 47.660%): 0.1760% 5.0320% 94.9680%
2383.5 - 2616.5 ( 47.670%): 0.1610% 5.1930% 94.8070%
2384.0 - 2616.0 ( 47.680%): 0.1950% 5.3880% 94.6120%
2384.5 - 2615.5 ( 47.690%): 0.1980% 5.5860% 94.4140%
2385.0 - 2615.0 ( 47.700%): 0.1850% 5.7710% 94.2290%
2385.5 - 2614.5 ( 47.710%): 0.1970% 5.9680% 94.0320%
2386.0 - 2614.0 ( 47.720%): 0.1930% 6.1610% 93.8390%
2386.5 - 2613.5 ( 47.730%): 0.1920% 6.3530% 93.6470%
2387.0 - 2613.0 ( 47.740%): 0.2050% 6.5580% 93.4420%
2387.5 - 2612.5 ( 47.750%): 0.2060% 6.7640% 93.2360%
2388.0 - 2612.0 ( 47.760%): 0.2320% 6.9960% 93.0040%
2388.5 - 2611.5 ( 47.770%): 0.2140% 7.2100% 92.7900%
2389.0 - 2611.0 ( 47.780%): 0.2220% 7.4320% 92.5680%
2389.5 - 2610.5 ( 47.790%): 0.2240% 7.6560% 92.3440%
2390.0 - 2610.0 ( 47.800%): 0.2450% 7.9010% 92.0990%
2390.5 - 2609.5 ( 47.810%): 0.2870% 8.1880% 91.8120%
2391.0 - 2609.0 ( 47.820%): 0.2750% 8.4630% 91.5370%
2391.5 - 2608.5 ( 47.830%): 0.2660% 8.7290% 91.2710%
2392.0 - 2608.0 ( 47.840%): 0.2730% 9.0020% 90.9980%
2392.5 - 2607.5 ( 47.850%): 0.2500% 9.2520% 90.7480%
2393.0 - 2607.0 ( 47.860%): 0.2710% 9.5230% 90.4770%
2393.5 - 2606.5 ( 47.870%): 0.2630% 9.7860% 90.2140%
2394.0 - 2606.0 ( 47.880%): 0.2910% 10.0770% 89.9230%
2394.5 - 2605.5 ( 47.890%): 0.2960% 10.3730% 89.6270%
2395.0 - 2605.0 ( 47.900%): 0.2970% 10.6700% 89.3300%
2395.5 - 2604.5 ( 47.910%): 0.2950% 10.9650% 89.0350%
2396.0 - 2604.0 ( 47.920%): 0.3110% 11.2760% 88.7240%
2396.5 - 2603.5 ( 47.930%): 0.3210% 11.5970% 88.4030%
2397.0 - 2603.0 ( 47.940%): 0.3320% 11.9290% 88.0710%
2397.5 - 2602.5 ( 47.950%): 0.3460% 12.2750% 87.7250%
2398.0 - 2602.0 ( 47.960%): 0.3380% 12.6130% 87.3870%
2398.5 - 2601.5 ( 47.970%): 0.3230% 12.9360% 87.0640%
2399.0 - 2601.0 ( 47.980%): 0.3230% 13.2590% 86.7410%
2399.5 - 2600.5 ( 47.990%): 0.3770% 13.6360% 86.3640%
2400.0 - 2600.0 ( 48.000%): 0.3880% 14.0240% 85.9760%
2400.5 - 2599.5 ( 48.010%): 0.3720% 14.3960% 85.6040%
2401.0 - 2599.0 ( 48.020%): 0.3750% 14.7710% 85.2290%
2401.5 - 2598.5 ( 48.030%): 0.4230% 15.1940% 84.8060%
2402.0 - 2598.0 ( 48.040%): 0.3950% 15.5890% 84.4110%
2402.5 - 2597.5 ( 48.050%): 0.3480% 15.9370% 84.0630%
2403.0 - 2597.0 ( 48.060%): 0.4320% 16.3690% 83.6310%
2403.5 - 2596.5 ( 48.070%): 0.4440% 16.8130% 83.1870%
2404.0 - 2596.0 ( 48.080%): 0.4200% 17.2330% 82.7670%
2404.5 - 2595.5 ( 48.090%): 0.3800% 17.6130% 82.3870%
2405.0 - 2595.0 ( 48.100%): 0.4130% 18.0260% 81.9740%
2405.5 - 2594.5 ( 48.110%): 0.4490% 18.4750% 81.5250%
2406.0 - 2594.0 ( 48.120%): 0.4380% 18.9130% 81.0870%
2406.5 - 2593.5 ( 48.130%): 0.4470% 19.3600% 80.6400%
2407.0 - 2593.0 ( 48.140%): 0.4590% 19.8190% 80.1810%
2407.5 - 2592.5 ( 48.150%): 0.5100% 20.3290% 79.6710%
2408.0 - 2592.0 ( 48.160%): 0.5000% 20.8290% 79.1710%
2408.5 - 2591.5 ( 48.170%): 0.4720% 21.3010% 78.6990%
2409.0 - 2591.0 ( 48.180%): 0.4680% 21.7690% 78.2310%
2409.5 - 2590.5 ( 48.190%): 0.4840% 22.2530% 77.7470%
2410.0 - 2590.0 ( 48.200%): 0.4970% 22.7500% 77.2500%
2410.5 - 2589.5 ( 48.210%): 0.4920% 23.2420% 76.7580%
2411.0 - 2589.0 ( 48.220%): 0.4900% 23.7320% 76.2680%
2411.5 - 2588.5 ( 48.230%): 0.5010% 24.2330% 75.7670%
2412.0 - 2588.0 ( 48.240%): 0.5140% 24.7470% 75.2530%
2412.5 - 2587.5 ( 48.250%): 0.4990% 25.2460% 74.7540%
2413.0 - 2587.0 ( 48.260%): 0.5330% 25.7790% 74.2210%
2413.5 - 2586.5 ( 48.270%): 0.5520% 26.3310% 73.6690%
2414.0 - 2586.0 ( 48.280%): 0.5050% 26.8360% 73.1640%
2414.5 - 2585.5 ( 48.290%): 0.4980% 27.3340% 72.6660%
2415.0 - 2585.0 ( 48.300%): 0.5600% 27.8940% 72.1060%
2415.5 - 2584.5 ( 48.310%): 0.5810% 28.4750% 71.5250%
2416.0 - 2584.0 ( 48.320%): 0.6060% 29.0810% 70.9190%
2416.5 - 2583.5 ( 48.330%): 0.5810% 29.6620% 70.3380%
2417.0 - 2583.0 ( 48.340%): 0.5580% 30.2200% 69.7800%
2417.5 - 2582.5 ( 48.350%): 0.5720% 30.7920% 69.2080%
2418.0 - 2582.0 ( 48.360%): 0.5720% 31.3640% 68.6360%
2418.5 - 2581.5 ( 48.370%): 0.6090% 31.9730% 68.0270%
2419.0 - 2581.0 ( 48.380%): 0.6050% 32.5780% 67.4220%
2419.5 - 2580.5 ( 48.390%): 0.5810% 33.1590% 66.8410%
2420.0 - 2580.0 ( 48.400%): 0.6140% 33.7730% 66.2270%
2420.5 - 2579.5 ( 48.410%): 0.5930% 34.3660% 65.6340%
2421.0 - 2579.0 ( 48.420%): 0.6590% 35.0250% 64.9750%
2421.5 - 2578.5 ( 48.430%): 0.6150% 35.6400% 64.3600%
2422.0 - 2578.0 ( 48.440%): 0.5870% 36.2270% 63.7730%
2422.5 - 2577.5 ( 48.450%): 0.5980% 36.8250% 63.1750%
2423.0 - 2577.0 ( 48.460%): 0.6000% 37.4250% 62.5750%
2423.5 - 2576.5 ( 48.470%): 0.6550% 38.0800% 61.9200%
2424.0 - 2576.0 ( 48.480%): 0.6560% 38.7360% 61.2640%
2424.5 - 2575.5 ( 48.490%): 0.6300% 39.3660% 60.6340%
2425.0 - 2575.0 ( 48.500%): 0.6580% 40.0240% 59.9760%
2425.5 - 2574.5 ( 48.510%): 0.6420% 40.6660% 59.3340%
2426.0 - 2574.0 ( 48.520%): 0.6510% 41.3170% 58.6830%
2426.5 - 2573.5 ( 48.530%): 0.6780% 41.9950% 58.0050%
2427.0 - 2573.0 ( 48.540%): 0.6300% 42.6250% 57.3750%
2427.5 - 2572.5 ( 48.550%): 0.6650% 43.2900% 56.7100%
2428.0 - 2572.0 ( 48.560%): 0.6660% 43.9560% 56.0440%
2428.5 - 2571.5 ( 48.570%): 0.6390% 44.5950% 55.4050%
2429.0 - 2571.0 ( 48.580%): 0.6620% 45.2570% 54.7430%
2429.5 - 2570.5 ( 48.590%): 0.6290% 45.8860% 54.1140%
2430.0 - 2570.0 ( 48.600%): 0.6680% 46.5540% 53.4460%
2430.5 - 2569.5 ( 48.610%): 0.6510% 47.2050% 52.7950%
2431.0 - 2569.0 ( 48.620%): 0.6590% 47.8640% 52.1360%
2431.5 - 2568.5 ( 48.630%): 0.6730% 48.5370% 51.4630%
2432.0 - 2568.0 ( 48.640%): 0.6550% 49.1920% 50.8080%
2432.5 - 2567.5 ( 48.650%): 0.6640% 49.8560% 50.1440%
2433.0 - 2567.0 ( 48.660%): 0.6750% 50.5310% 49.4690%
2433.5 - 2566.5 ( 48.670%): 0.6200% 51.1510% 48.8490%
2434.0 - 2566.0 ( 48.680%): 0.6560% 51.8070% 48.1930%
2434.5 - 2565.5 ( 48.690%): 0.6520% 52.4590% 47.5410%
2435.0 - 2565.0 ( 48.700%): 0.6320% 53.0910% 46.9090%
2435.5 - 2564.5 ( 48.710%): 0.6890% 53.7800% 46.2200%
2436.0 - 2564.0 ( 48.720%): 0.6760% 54.4560% 45.5440%
2436.5 - 2563.5 ( 48.730%): 0.6530% 55.1090% 44.8910%
2437.0 - 2563.0 ( 48.740%): 0.6450% 55.7540% 44.2460%
2437.5 - 2562.5 ( 48.750%): 0.5880% 56.3420% 43.6580%
2438.0 - 2562.0 ( 48.760%): 0.6190% 56.9610% 43.0390%
2438.5 - 2561.5 ( 48.770%): 0.6400% 57.6010% 42.3990%
2439.0 - 2561.0 ( 48.780%): 0.6410% 58.2420% 41.7580%
2439.5 - 2560.5 ( 48.790%): 0.6410% 58.8830% 41.1170%
2440.0 - 2560.0 ( 48.800%): 0.6830% 59.5660% 40.4340%
2440.5 - 2559.5 ( 48.810%): 0.6420% 60.2080% 39.7920%
2441.0 - 2559.0 ( 48.820%): 0.5920% 60.8000% 39.2000%
2441.5 - 2558.5 ( 48.830%): 0.6830% 61.4830% 38.5170%
2442.0 - 2558.0 ( 48.840%): 0.6120% 62.0950% 37.9050%
2442.5 - 2557.5 ( 48.850%): 0.6290% 62.7240% 37.2760%
2443.0 - 2557.0 ( 48.860%): 0.6170% 63.3410% 36.6590%
2443.5 - 2556.5 ( 48.870%): 0.6190% 63.9600% 36.0400%
2444.0 - 2556.0 ( 48.880%): 0.5980% 64.5580% 35.4420%
2444.5 - 2555.5 ( 48.890%): 0.6190% 65.1770% 34.8230%
2445.0 - 2555.0 ( 48.900%): 0.6010% 65.7780% 34.2220%
2445.5 - 2554.5 ( 48.910%): 0.6020% 66.3800% 33.6200%
2446.0 - 2554.0 ( 48.920%): 0.5910% 66.9710% 33.0290%
2446.5 - 2553.5 ( 48.930%): 0.5990% 67.5700% 32.4300%
2447.0 - 2553.0 ( 48.940%): 0.6080% 68.1780% 31.8220%
2447.5 - 2552.5 ( 48.950%): 0.6060% 68.7840% 31.2160%
2448.0 - 2552.0 ( 48.960%): 0.5880% 69.3720% 30.6280%
2448.5 - 2551.5 ( 48.970%): 0.5490% 69.9210% 30.0790%
2449.0 - 2551.0 ( 48.980%): 0.5370% 70.4580% 29.5420%
2449.5 - 2550.5 ( 48.990%): 0.5750% 71.0330% 28.9670%
2450.0 - 2550.0 ( 49.000%): 0.5730% 71.6060% 28.3940%
2450.5 - 2549.5 ( 49.010%): 0.5570% 72.1630% 27.8370%
2451.0 - 2549.0 ( 49.020%): 0.5540% 72.7170% 27.2830%
2451.5 - 2548.5 ( 49.030%): 0.5550% 73.2720% 26.7280%
2452.0 - 2548.0 ( 49.040%): 0.4980% 73.7700% 26.2300%
2452.5 - 2547.5 ( 49.050%): 0.5690% 74.3390% 25.6610%
2453.0 - 2547.0 ( 49.060%): 0.5540% 74.8930% 25.1070%
2453.5 - 2546.5 ( 49.070%): 0.5010% 75.3940% 24.6060%
2454.0 - 2546.0 ( 49.080%): 0.5540% 75.9480% 24.0520%
2454.5 - 2545.5 ( 49.090%): 0.5080% 76.4560% 23.5440%
2455.0 - 2545.0 ( 49.100%): 0.5280% 76.9840% 23.0160%
2455.5 - 2544.5 ( 49.110%): 0.5230% 77.5070% 22.4930%
2456.0 - 2544.0 ( 49.120%): 0.5240% 78.0310% 21.9690%
2456.5 - 2543.5 ( 49.130%): 0.5040% 78.5350% 21.4650%
2457.0 - 2543.0 ( 49.140%): 0.4750% 79.0100% 20.9900%
2457.5 - 2542.5 ( 49.150%): 0.4830% 79.4930% 20.5070%
2458.0 - 2542.0 ( 49.160%): 0.4630% 79.9560% 20.0440%
2458.5 - 2541.5 ( 49.170%): 0.4490% 80.4050% 19.5950%
2459.0 - 2541.0 ( 49.180%): 0.4550% 80.8600% 19.1400%
2459.5 - 2540.5 ( 49.190%): 0.4250% 81.2850% 18.7150%
2460.0 - 2540.0 ( 49.200%): 0.4250% 81.7100% 18.2900%
2460.5 - 2539.5 ( 49.210%): 0.4410% 82.1510% 17.8490%
2461.0 - 2539.0 ( 49.220%): 0.4400% 82.5910% 17.4090%
2461.5 - 2538.5 ( 49.230%): 0.4350% 83.0260% 16.9740%
2462.0 - 2538.0 ( 49.240%): 0.4280% 83.4540% 16.5460%
2462.5 - 2537.5 ( 49.250%): 0.4140% 83.8680% 16.1320%
2463.0 - 2537.0 ( 49.260%): 0.4430% 84.3110% 15.6890%
2463.5 - 2536.5 ( 49.270%): 0.4020% 84.7130% 15.2870%
2464.0 - 2536.0 ( 49.280%): 0.3910% 85.1040% 14.8960%
2464.5 - 2535.5 ( 49.290%): 0.3710% 85.4750% 14.5250%
2465.0 - 2535.0 ( 49.300%): 0.3850% 85.8600% 14.1400%
2465.5 - 2534.5 ( 49.310%): 0.3690% 86.2290% 13.7710%
2466.0 - 2534.0 ( 49.320%): 0.3780% 86.6070% 13.3930%
2466.5 - 2533.5 ( 49.330%): 0.3870% 86.9940% 13.0060%
2467.0 - 2533.0 ( 49.340%): 0.3560% 87.3500% 12.6500%
2467.5 - 2532.5 ( 49.350%): 0.3670% 87.7170% 12.2830%
2468.0 - 2532.0 ( 49.360%): 0.3280% 88.0450% 11.9550%
2468.5 - 2531.5 ( 49.370%): 0.3220% 88.3670% 11.6330%
2469.0 - 2531.0 ( 49.380%): 0.3190% 88.6860% 11.3140%
2469.5 - 2530.5 ( 49.390%): 0.3180% 89.0040% 10.9960%
2470.0 - 2530.0 ( 49.400%): 0.3130% 89.3170% 10.6830%
2470.5 - 2529.5 ( 49.410%): 0.2960% 89.6130% 10.3870%
2471.0 - 2529.0 ( 49.420%): 0.3010% 89.9140% 10.0860%
2471.5 - 2528.5 ( 49.430%): 0.3260% 90.2400% 9.7600%
2472.0 - 2528.0 ( 49.440%): 0.2760% 90.5160% 9.4840%
2472.5 - 2527.5 ( 49.450%): 0.2690% 90.7850% 9.2150%
2473.0 - 2527.0 ( 49.460%): 0.2780% 91.0630% 8.9370%
2473.5 - 2526.5 ( 49.470%): 0.2500% 91.3130% 8.6870%
2474.0 - 2526.0 ( 49.480%): 0.2160% 91.5290% 8.4710%
2474.5 - 2525.5 ( 49.490%): 0.2390% 91.7680% 8.2320%
2475.0 - 2525.0 ( 49.500%): 0.2420% 92.0100% 7.9900%
2475.5 - 2524.5 ( 49.510%): 0.2400% 92.2500% 7.7500%
2476.0 - 2524.0 ( 49.520%): 0.2390% 92.4890% 7.5110%
2476.5 - 2523.5 ( 49.530%): 0.2450% 92.7340% 7.2660%
2477.0 - 2523.0 ( 49.540%): 0.2500% 92.9840% 7.0160%
2477.5 - 2522.5 ( 49.550%): 0.2080% 93.1920% 6.8080%
2478.0 - 2522.0 ( 49.560%): 0.2140% 93.4060% 6.5940%
2478.5 - 2521.5 ( 49.570%): 0.1920% 93.5980% 6.4020%
2479.0 - 2521.0 ( 49.580%): 0.2340% 93.8320% 6.1680%
2479.5 - 2520.5 ( 49.590%): 0.1970% 94.0290% 5.9710%
2480.0 - 2520.0 ( 49.600%): 0.1910% 94.2200% 5.7800%
2480.5 - 2519.5 ( 49.610%): 0.1900% 94.4100% 5.5900%
2481.0 - 2519.0 ( 49.620%): 0.1790% 94.5890% 5.4110%
2481.5 - 2518.5 ( 49.630%): 0.2040% 94.7930% 5.2070%
2482.0 - 2518.0 ( 49.640%): 0.1950% 94.9880% 5.0120%
2482.5 - 2517.5 ( 49.650%): 0.1740% 95.1620% 4.8380%
2483.0 - 2517.0 ( 49.660%): 0.1490% 95.3110% 4.6890%
2483.5 - 2516.5 ( 49.670%): 0.1380% 95.4490% 4.5510%
2484.0 - 2516.0 ( 49.680%): 0.1420% 95.5910% 4.4090%
2484.5 - 2515.5 ( 49.690%): 0.1500% 95.7410% 4.2590%
2485.0 - 2515.0 ( 49.700%): 0.1520% 95.8930% 4.1070%
2485.5 - 2514.5 ( 49.710%): 0.1430% 96.0360% 3.9640%
2486.0 - 2514.0 ( 49.720%): 0.1410% 96.1770% 3.8230%
2486.5 - 2513.5 ( 49.730%): 0.1270% 96.3040% 3.6960%
2487.0 - 2513.0 ( 49.740%): 0.1170% 96.4210% 3.5790%
2487.5 - 2512.5 ( 49.750%): 0.1130% 96.5340% 3.4660%
2488.0 - 2512.0 ( 49.760%): 0.1150% 96.6490% 3.3510%
2488.5 - 2511.5 ( 49.770%): 0.1260% 96.7750% 3.2250%
2489.0 - 2511.0 ( 49.780%): 0.0930% 96.8680% 3.1320%
2489.5 - 2510.5 ( 49.790%): 0.1230% 96.9910% 3.0090%
2490.0 - 2510.0 ( 49.800%): 0.1100% 97.1010% 2.8990%
2490.5 - 2509.5 ( 49.810%): 0.1080% 97.2090% 2.7910%
2491.0 - 2509.0 ( 49.820%): 0.1030% 97.3120% 2.6880%
2491.5 - 2508.5 ( 49.830%): 0.0890% 97.4010% 2.5990%
2492.0 - 2508.0 ( 49.840%): 0.0990% 97.5000% 2.5000%
2492.5 - 2507.5 ( 49.850%): 0.0780% 97.5780% 2.4220%
2493.0 - 2507.0 ( 49.860%): 0.0970% 97.6750% 2.3250%
2493.5 - 2506.5 ( 49.870%): 0.0850% 97.7600% 2.2400%
2494.0 - 2506.0 ( 49.880%): 0.0940% 97.8540% 2.1460%
2494.5 - 2505.5 ( 49.890%): 0.0780% 97.9320% 2.0680%
2495.0 - 2505.0 ( 49.900%): 0.0770% 98.0090% 1.9910%
2495.5 - 2504.5 ( 49.910%): 0.0830% 98.0920% 1.9080%
2496.0 - 2504.0 ( 49.920%): 0.0750% 98.1670% 1.8330%
2496.5 - 2503.5 ( 49.930%): 0.0870% 98.2540% 1.7460%
2497.0 - 2503.0 ( 49.940%): 0.0630% 98.3170% 1.6830%
2497.5 - 2502.5 ( 49.950%): 0.0570% 98.3740% 1.6260%
2498.0 - 2502.0 ( 49.960%): 0.0580% 98.4320% 1.5680%
2498.5 - 2501.5 ( 49.970%): 0.0570% 98.4890% 1.5110%
2499.0 - 2501.0 ( 49.980%): 0.0630% 98.5520% 1.4480%
2499.5 - 2500.5 ( 49.990%): 0.0450% 98.5970% 1.4030%
2500.0 - 2500.0 ( 50.000%): 0.0520% 98.6490% 1.3510%
2500.5 - 2499.5 ( 50.010%): 0.0540% 98.7030% 1.2970%
2501.0 - 2499.0 ( 50.020%): 0.0610% 98.7640% 1.2360%
2501.5 - 2498.5 ( 50.030%): 0.0600% 98.8240% 1.1760%
2502.0 - 2498.0 ( 50.040%): 0.0490% 98.8730% 1.1270%
2502.5 - 2497.5 ( 50.050%): 0.0450% 98.9180% 1.0820%
2503.0 - 2497.0 ( 50.060%): 0.0510% 98.9690% 1.0310%
2503.5 - 2496.5 ( 50.070%): 0.0380% 99.0070% 0.9930%
2504.0 - 2496.0 ( 50.080%): 0.0430% 99.0500% 0.9500%
2504.5 - 2495.5 ( 50.090%): 0.0360% 99.0860% 0.9140%
2505.0 - 2495.0 ( 50.100%): 0.0430% 99.1290% 0.8710%
2505.5 - 2494.5 ( 50.110%): 0.0230% 99.1520% 0.8480%
2506.0 - 2494.0 ( 50.120%): 0.0420% 99.1940% 0.8060%
2506.5 - 2493.5 ( 50.130%): 0.0340% 99.2280% 0.7720%
2507.0 - 2493.0 ( 50.140%): 0.0340% 99.2620% 0.7380%
2507.5 - 2492.5 ( 50.150%): 0.0410% 99.3030% 0.6970%
2508.0 - 2492.0 ( 50.160%): 0.0340% 99.3370% 0.6630%
2508.5 - 2491.5 ( 50.170%): 0.0330% 99.3700% 0.6300%
2509.0 - 2491.0 ( 50.180%): 0.0220% 99.3920% 0.6080%
2509.5 - 2490.5 ( 50.190%): 0.0270% 99.4190% 0.5810%
2510.0 - 2490.0 ( 50.200%): 0.0330% 99.4520% 0.5480%
2510.5 - 2489.5 ( 50.210%): 0.0250% 99.4770% 0.5230%
2511.0 - 2489.0 ( 50.220%): 0.0200% 99.4970% 0.5030%
2511.5 - 2488.5 ( 50.230%): 0.0260% 99.5230% 0.4770%
2512.0 - 2488.0 ( 50.240%): 0.0220% 99.5450% 0.4550%
2512.5 - 2487.5 ( 50.250%): 0.0200% 99.5650% 0.4350%
2513.0 - 2487.0 ( 50.260%): 0.0190% 99.5840% 0.4160%
2513.5 - 2486.5 ( 50.270%): 0.0160% 99.6000% 0.4000%
2514.0 - 2486.0 ( 50.280%): 0.0150% 99.6150% 0.3850%
2514.5 - 2485.5 ( 50.290%): 0.0180% 99.6330% 0.3670%
2515.0 - 2485.0 ( 50.300%): 0.0200% 99.6530% 0.3470%
2515.5 - 2484.5 ( 50.310%): 0.0110% 99.6640% 0.3360%
2516.0 - 2484.0 ( 50.320%): 0.0240% 99.6880% 0.3120%
2516.5 - 2483.5 ( 50.330%): 0.0220% 99.7100% 0.2900%
2517.0 - 2483.0 ( 50.340%): 0.0120% 99.7220% 0.2780%
2517.5 - 2482.5 ( 50.350%): 0.0150% 99.7370% 0.2630%
2518.0 - 2482.0 ( 50.360%): 0.0130% 99.7500% 0.2500%
2518.5 - 2481.5 ( 50.370%): 0.0130% 99.7630% 0.2370%
2519.0 - 2481.0 ( 50.380%): 0.0140% 99.7770% 0.2230%
2519.5 - 2480.5 ( 50.390%): 0.0150% 99.7920% 0.2080%
2520.0 - 2480.0 ( 50.400%): 0.0090% 99.8010% 0.1990%
2520.5 - 2479.5 ( 50.410%): 0.0120% 99.8130% 0.1870%
2521.0 - 2479.0 ( 50.420%): 0.0100% 99.8230% 0.1770%
2521.5 - 2478.5 ( 50.430%): 0.0070% 99.8300% 0.1700%
2522.0 - 2478.0 ( 50.440%): 0.0100% 99.8400% 0.1600%
2522.5 - 2477.5 ( 50.450%): 0.0070% 99.8470% 0.1530%
2523.0 - 2477.0 ( 50.460%): 0.0060% 99.8530% 0.1470%
2523.5 - 2476.5 ( 50.470%): 0.0100% 99.8630% 0.1370%
2524.0 - 2476.0 ( 50.480%): 0.0100% 99.8730% 0.1270%
2524.5 - 2475.5 ( 50.490%): 0.0070% 99.8800% 0.1200%
2525.0 - 2475.0 ( 50.500%): 0.0060% 99.8860% 0.1140%
2525.5 - 2474.5 ( 50.510%): 0.0040% 99.8900% 0.1100%
2526.0 - 2474.0 ( 50.520%): 0.0080% 99.8980% 0.1020%
2526.5 - 2473.5 ( 50.530%): 0.0030% 99.9010% 0.0990%
2527.0 - 2473.0 ( 50.540%): 0.0040% 99.9050% 0.0950%
2527.5 - 2472.5 ( 50.550%): 0.0030% 99.9080% 0.0920%
2528.0 - 2472.0 ( 50.560%): 0.0040% 99.9120% 0.0880%
2528.5 - 2471.5 ( 50.570%): 0.0070% 99.9190% 0.0810%
2529.0 - 2471.0 ( 50.580%): 0.0110% 99.9300% 0.0700%
2529.5 - 2470.5 ( 50.590%): 0.0010% 99.9310% 0.0690%
2530.0 - 2470.0 ( 50.600%): 0.0040% 99.9350% 0.0650%
2530.5 - 2469.5 ( 50.610%): 0.0030% 99.9380% 0.0620%
2531.5 - 2468.5 ( 50.630%): 0.0050% 99.9430% 0.0570%
2532.0 - 2468.0 ( 50.640%): 0.0030% 99.9460% 0.0540%
2532.5 - 2467.5 ( 50.650%): 0.0020% 99.9480% 0.0520%
2533.0 - 2467.0 ( 50.660%): 0.0020% 99.9500% 0.0500%
2534.0 - 2466.0 ( 50.680%): 0.0010% 99.9510% 0.0490%
2534.5 - 2465.5 ( 50.690%): 0.0050% 99.9560% 0.0440%
2535.0 - 2465.0 ( 50.700%): 0.0020% 99.9580% 0.0420%
2535.5 - 2464.5 ( 50.710%): 0.0020% 99.9600% 0.0400%
2536.0 - 2464.0 ( 50.720%): 0.0030% 99.9630% 0.0370%
2536.5 - 2463.5 ( 50.730%): 0.0020% 99.9650% 0.0350%
2537.5 - 2462.5 ( 50.750%): 0.0020% 99.9670% 0.0330%
2538.0 - 2462.0 ( 50.760%): 0.0010% 99.9680% 0.0320%
2538.5 - 2461.5 ( 50.770%): 0.0030% 99.9710% 0.0290%
2539.5 - 2460.5 ( 50.790%): 0.0050% 99.9760% 0.0240%
2540.0 - 2460.0 ( 50.800%): 0.0020% 99.9780% 0.0220%
2541.0 - 2459.0 ( 50.820%): 0.0010% 99.9790% 0.0210%
2541.5 - 2458.5 ( 50.830%): 0.0010% 99.9800% 0.0200%
2542.0 - 2458.0 ( 50.840%): 0.0010% 99.9810% 0.0190%
2542.5 - 2457.5 ( 50.850%): 0.0020% 99.9830% 0.0170%
2543.0 - 2457.0 ( 50.860%): 0.0020% 99.9850% 0.0150%
2543.5 - 2456.5 ( 50.870%): 0.0020% 99.9870% 0.0130%
2544.0 - 2456.0 ( 50.880%): 0.0020% 99.9890% 0.0110%
2545.0 - 2455.0 ( 50.900%): 0.0010% 99.9900% 0.0100%
2545.5 - 2454.5 ( 50.910%): 0.0020% 99.9920% 0.0080%
2546.0 - 2454.0 ( 50.920%): 0.0020% 99.9940% 0.0060%
2546.5 - 2453.5 ( 50.930%): 0.0020% 99.9960% 0.0040%
2549.5 - 2450.5 ( 50.990%): 0.0010% 99.9970% 0.0030%
2555.0 - 2445.0 ( 51.100%): 0.0010% 99.9980% 0.0020%
2561.0 - 2439.0 ( 51.220%): 0.0010% 99.9990% 0.0010%
2562.5 - 2437.5 ( 51.250%): 0.0010% 100.0000% 0.0000%
Average result of simulation 48.6578%
CPU-time 21.546 s, PRNG was called 5e+008 times, 0.04309 us/PRN
This page took 0.01 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.