SPRT and narrowing of (elo1 - elo0) difference.
Posted: Sat Oct 05, 2013 5:43 pm
Hello:
I toyed a little with elo0 (bayeselo_0) and elo1 (bayeselo_1) parameters of SPRT with my own SPRT simulator. I choosed the special case of elo0 = -elo1 and the worst case inside it: elo (bayeselo) = (elo0 + elo1)/2 = 0.
I find slight similarities in the number (bayeselo_1 - bayeselo_0)*sqrt(<Games>/simulation) for each group of simulations with a fixed drawelo parameter. A rough approximation could be that reducing elo1 - elo0 by 2 means multiplying by 4 the average number of games before stop by LLR criteria. What do you think?
It is needless to say that my simulator is far from perfect (I wrote the shortest and longest runs of each simulation with the aim of let people decide the accuracy of my simulator) and other people should verify my simulated numbers.
Regards from Spain.
Ajedrecista.
I toyed a little with elo0 (bayeselo_0) and elo1 (bayeselo_1) parameters of SPRT with my own SPRT simulator. I choosed the special case of elo0 = -elo1 and the worst case inside it: elo (bayeselo) = (elo0 + elo1)/2 = 0.
Code: Select all
alpha = beta = 0.05; 2000 simulations each time; bayeselo_fixed = 0.
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drawelo_fixed = 240:
bayeselo_0 bayeselo_1 <Games>/simulation Shortest run Longest run
-5 5 10452 619 (+98 -163 =358) 65633 (+13227 -13162 =39244)
-4.75 4.75 11250 781 (+197 -129 =455) 74788 (+15043 -14975 =44770)
-4.5 4.5 12746 978 (+166 -238 =574) 88990 (+17776 -17848 =53366)
-4.25 4.25 13916 1031 (+240 -165 =626) 83352 (+16836 -16912 =49604)
-4 4 15932 1364 (+316 -236 =812) 88576 (+17830 -17911 =52835)
-3.75 3.75 18161 1510 (+342 -257 =911) 110664 (+22325 -22239 =66100)
-3.5 3.5 21176 1566 (+269 -361 =936) 162743 (+32579 -32671 =97493)
-3.25 3.25 23754 1961 (+447 -348 =1166) 147703 (+29700 -29601 =88402)
-3 3 28256 1870 (+404 -299 =1167) 189855 (+38018 -38125 =113712)
-2.75 2.75 34418 2331 (+415 -532 =1384) 240724 (+48381 -48498 =143845)
-2.5 2.5 40938 3020 (+676 -547 =1797) 235075 (+47393 -47264 =140418)
-2.25 2.25 51968 4133 (+897 -755 =2481) 315599 (+63554 -63697 =188348)
-2 2 65912 5002 (+1108 -947 =2947) 348841 (+70042 -69882 =208917)
-1.75 1.75 84304 6395 (+1184 -1367 =3844) 571957 (+114802 -114985 =342170)
-1.5 1.5 116123 10039 (+2095 -1882 =6062) 859506 (+171890 -172104 =515512)
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drawelo_fixed = 270:
bayeselo_0 bayeselo_1 <Games>/simulation Shortest run Longest run
-5 5 10981 851 (+179 -117 =555) 71265 (+12609 -12546 =46110)
-4.75 4.75 12456 922 (+184 -119 =619) 69056 (+12084 -12018 =44954)
-4.5 4.5 13897 831 (+113 -182 =536) 71696 (+12627 -12558 =46511)
-4.25 4.25 14979 1093 (+170 -245 =678) 79323 (+13787 -13714 =51822)
-4 4 17130 1218 (+239 -162 =817) 109297 (+18996 -19074 =71227)
-3.75 3.75 19609 1284 (+181 -264 =839) 190861 (+33502 -33419 =123940)
-3.5 3.5 21761 1754 (+267 -356 =1131) 134556 (+23532 -23621 =87403)
-3.25 3.25 25943 2043 (+408 -312 =1323) 191905 (+33695 -33599 =124611)
-3 3 30329 1611 (+235 -339 =1037) 172176 (+30231 -30127 =111818)
-2.75 2.75 35943 2321 (+351 -464 =1506) 225119 (+39352 -39239 =146528)
-2.5 2.5 43468 3835 (+592 -716 =2527) 302031 (+52796 -52921 =196314)
-2.25 2.25 54740 2535 (+379 -517 =1639) 304272 (+53063 -52925 =198284)
-2 2 70596 4213 (+811 -656 =2746) 465446 (+81160 -81005 =303281)
-1.75 1.75 91756 6607 (+1246 -1068 =4293) 767735 (+134078 -134256 =499401)
-1.5 1.5 125512 9500 (+1562 -1769 =6169) 778865 (+136041 -136248 =506576)
It is needless to say that my simulator is far from perfect (I wrote the shortest and longest runs of each simulation with the aim of let people decide the accuracy of my simulator) and other people should verify my simulated numbers.
Regards from Spain.
Ajedrecista.