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 楼主| 发表于 2018-5-18 05:56:16 | 显示全部楼层
本帖最后由 小铃铛 于 2018-5-18 09:16 编辑

13Y9:  分组  1,234,5678,9abc,d    (修正版)
A在后12轮中共有4096种选择,其中高3位相同的有1024种,可以达成3+9Y6,所以还剩3072种
其中高3位2:1,接着4位相同的有384种,可以达成2+4+5Y3,所以还剩2688种
其中高3位2:1,接着4位是3:1,后5位是3:1+1的有768种,可以达成2+3+3+1,所以还剩1920种
其中高3位2:1,接着4位是3:1,后5位是4:0+1的有192种,可以达成2+3+4,所以还剩1728种

1728种中只包含了下面三种类型:
一.高3位2:1,接着4位是3:1,后5位是2:2+1的有576种
二.高3位2:1,接着4位是2:2,后5位是3:1+1的或是4:0+1有720种
三.高3位2:1,接着4位是2:2,后5位是2:2+1的有432种

2:2的形式可分3种:eeff,efef,effe(ef=10或01)

在一.中即:高3位2:1,接着4位是3:1,后5位是2:2+1.
对后5位是eeff+d这种类型,C只需在第9轮和第10轮减赢1轮,以表示后5轮=eeff+d,用减赢轮次的不同来提示不同的d就可以了,2+3+3+1=9,即可再排除192种

在二.中即:高3位2:1,接着4位是2:2,后5位是3:1+1或是4:0+1
这种类型C只需在5678=eeff时在第5,6轮减赢1轮,指示A5678=eeff,前后减赢,指示出9abc,从而拿定5678中3轮+9abc中4轮或9abc中(3轮+d)的4轮,即 2+3+4=9
        C只需在5678=efef时在第234轮减赢1轮,指示A5678=efef,错轮指示e,前后减赢,指示出9abc,从而拿定5678,再加上9abc中4轮或9abc中(3轮+d)的4轮,  即 1+4+4=9
        C只需在5678=effe时在第234轮利用反信息来减赢1轮,前错轮提示5678中的e,从而拿定5678的4轮。后错轮提示出9abc,就能赢取9abc中4轮或9abc中(3轮+d)的4轮,即 1+4+4=9

在三.中即:高3位2:1,接着4位是2:2,后5位是2:2+1
这种类型C只需在9abc=eeff时,5678的2:2通过56轮的1种减赢和234轮的2种不同的减赢手法,指示A5678的不同的2:2组合,最终拿定前8轮中的5轮并提供出一个信息,这个信息用来指向        
9abc=eeff中的e,这个策略会和二.中的9abc=3:1或是4:0时重合,其区别就在第9,a轮,在三.中它会需要减赢一轮,前后减赢,指示d轮,从而拿定9abc=eeff中的3轮加d轮,即5+3+1=9,可再排除144种

小计:还可以排除144+192+720=1056种,还剩下672种,其中包括下面几种类型:

1.  高3位2:1,接着4位是3:1,后5位是efef+d或后5位是effe+d的有384种
2.  高3位2:1,接着4位是2:2,后5位是efef+d或后5位是effe+d的有288种

接着就是13赢9的关键,策略上是可以有重合,只需要C有不同的变化就可以。其实,A也是可以加以利用的。

在所有策略中,5678轮都没有出现过不使用减赢手法的2:2,下面到了使用它的时候:
分组  1,234,5678,9abc,d
2.  高3位2:1,接着4位是2:2,后5位是efef+d或后5位是effe+d
  234的错轮指向第9位的e。这对接下来的5678轮都没影响,都会产生2赢2输的结果。前输轮指向第b轮,后输轮指向d。
  B能发现在5678轮中没有减赢动作,即表示9abc=efef或effe,第9轮的e和第b轮的指示都有了,还有了d,就确定了后5轮。即2+2+5=9

现在还剩下唯一的一种类型:
1.高3位2:1,接着4位是3:1,后5位是efef+d或后5位是effe+d的有384种
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2018-5-18 09:24:35 | 显示全部楼层
最后的这种类型留待感兴趣的坛友自己去挖掘,兴许会有完全不同的思路和解法。
13Y9只是热身,为推出第二问作铺垫:
问二:怎样的策略,才能确保 B 和 C 在 18 轮游戏中赢取 13 轮?
这相当于2个9Y6组合上再多赢1轮!

点评

你这问我暂时没空搞哦~我也不知道我什么时候才有空。要不你自己先搞起来试试?  发表于 2019-3-4 07:36
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-7-27 15:33:59 | 显示全部楼层
KeyTo9_Fans 发表于 2018-5-2 16:23
对于$13$局赢$9$局的问题,我的猜想是无解。

证明无解的大致思路如下:


KetTo9_Fans的证明和an等计算是此问题理论研究的开创性结果
可能带来求解策略全新思路,解决n较大时的难题,例如: (25 赢 18),等
希望重新整理证明,去掉推理中的错误数据,
提供an的计算代码,谢谢
实际原题有附加题,难度比18赢13 难得多,尚未见解答
As a bonus question: when n goes to infinity, can they do better?
What is the maximal probability they can guarantee in the worst case?
KetTo9_Fans的证明和an等计算也许有助于回答此问题


为了学习,我做了3项验算工作,
1 利用KetTo9_Fans 前20项列表扩展到996项 记为maxwin
  得到许多新的难题
(1 赢 0),
(2 赢 1),
(3 赢 1),
(4 赢 2),
(5 赢 3),
(6 赢 3),
(7 赢 4),
(8 赢 5),
(9 赢 6),
(10 赢 6),
(11 赢 7),
(12 赢 8),
(13 赢 9),
(14 赢 9),
(15 赢 10),
(16 赢 11),
(17 赢 12),
(18 赢 13),
(19 赢 13),以下为新难题
(20 赢 14),
(21 赢 15),
(22 赢 16),
(23 赢 17),
(24 赢 17),
(25 赢 18),
(26 赢 19),
(27 赢 20),
(28 赢 21),
(29 赢 21),
(30 赢 22),
(31 赢 23),
(32 赢 24),
(33 赢 25),
(34 赢 25),

2 比较A213854和maxwin (100项中,前33项相同,通项神奇的相似)
3 an 192项 和 知乎白无妨31项 互相印证,理论证明和计算an的公式可信

下面列出几个重要的数据列表
1 an列输出 ,192项
an k  n   m   m/n
{1,1,(2 赢 1),0.5}
{2,2,(5 赢 3),0.6}
{3,3,(9 赢 6),0.666667}
{4,4,(13 赢 9),0.692308}
{5,5,(18 赢 13),0.722222}
{6,6,(23 赢 17),0.73913}
{7,7,(28 赢 21),0.75}
{8,8,(33 赢 25),0.757576}
{9,9,(38 赢 29),0.763158}
{10,10,(43 赢 33),0.767442}
{11,11,(48 赢 37),0.770833}
{12,12,(53 赢 41),0.773585}
{13,13,(58 赢 45),0.775862}
{14,14,(63 赢 49),0.777778}
{15,15,(68 赢 53),0.779412}
{16,16,(73 赢 57),0.780822}
{17,17,(78 赢 61),0.782051}
{18,18,(83 赢 65),0.783133}
{19,19,(88 赢 69),0.784091}
{20,20,(94 赢 74),0.787234}
{21,21,(99 赢 78),0.787879}
{22,22,(104 赢 82),0.788462}
{23,23,(109 赢 86),0.788991}
{24,24,(114 赢 90),0.789474}
{25,25,(119 赢 94),0.789916}
{26,26,(125 赢 99),0.792}
{27,27,(130 赢 103),0.792308}
{28,28,(135 赢 107),0.792593}
{29,29,(140 赢 111),0.792857}
{30,30,(145 赢 115),0.793103}
{31,31,(150 赢 119),0.793333}
{32,32,(156 赢 124),0.794872}
{33,33,(161 赢 128),0.795031}
{34,34,(166 赢 132),0.795181}
{35,35,(171 赢 136),0.795322}
{36,36,(176 赢 140),0.795455}
{37,37,(182 赢 145),0.796703}
{38,38,(187 赢 149),0.796791}
{39,39,(192 赢 153),0.796875}
{40,40,(197 赢 157),0.796954}
{41,41,(203 赢 162),0.79803}
{42,42,(208 赢 166),0.798077}
{43,43,(213 赢 170),0.798122}
{44,44,(218 赢 174),0.798165}
{45,45,(223 赢 178),0.798206}
{46,46,(229 赢 183),0.799127}
{47,47,(234 赢 187),0.799145}
{48,48,(239 赢 191),0.799163}
{49,49,(244 赢 195),0.79918}
{50,50,(250 赢 200),0.8}
{51,51,(255 赢 204),0.8}
{52,52,(260 赢 208),0.8}
{53,53,(265 赢 212),0.8}
{54,54,(270 赢 216),0.8}
{55,55,(276 赢 221),0.800725}
{56,56,(281 赢 225),0.800712}
{57,57,(286 赢 229),0.800699}
{58,58,(291 赢 233),0.800687}
{59,59,(297 赢 238),0.801347}
{60,60,(302 赢 242),0.801325}
{61,61,(307 赢 246),0.801303}
{62,62,(312 赢 250),0.801282}
{63,63,(318 赢 255),0.801887}
{64,64,(323 赢 259),0.801858}
{65,65,(328 赢 263),0.801829}
{66,66,(333 赢 267),0.801802}
{67,67,(339 赢 272),0.80236}
{68,68,(344 赢 276),0.802326}
{69,69,(349 赢 280),0.802292}
{70,70,(354 赢 284),0.80226}
{71,71,(359 赢 288),0.802228}
{72,72,(365 赢 293),0.80274}
{73,73,(370 赢 297),0.802703}
{74,74,(375 赢 301),0.802667}
{75,75,(380 赢 305),0.802632}
{76,76,(386 赢 310),0.803109}
{77,77,(391 赢 314),0.803069}
{78,78,(396 赢 318),0.80303}
{79,79,(401 赢 322),0.802993}
{80,80,(407 赢 327),0.80344}
{81,81,(412 赢 331),0.803398}
{82,82,(417 赢 335),0.803357}
{83,83,(422 赢 339),0.803318}
{84,84,(428 赢 344),0.803738}
{85,85,(433 赢 348),0.803695}
{86,86,(438 赢 352),0.803653}
{87,87,(443 赢 356),0.803612}
{88,88,(449 赢 361),0.804009}
{89,89,(454 赢 365),0.803965}
{90,90,(459 赢 369),0.803922}
{91,91,(464 赢 373),0.803879}
{92,92,(470 赢 378),0.804255}
{93,93,(475 赢 382),0.804211}
{94,94,(480 赢 386),0.804167}
{95,95,(485 赢 390),0.804124}
{96,96,(491 赢 395),0.804481}
{97,97,(496 赢 399),0.804435}
{98,98,(501 赢 403),0.804391}
{99,99,(506 赢 407),0.804348}
{100,100,(512 赢 412),0.804688}
{101,101,(517 赢 416),0.804642}
{102,102,(522 赢 420),0.804598}
{103,103,(527 赢 424),0.804554}
{104,104,(533 赢 429),0.804878}
{105,105,(538 赢 433),0.804833}
{106,106,(543 赢 437),0.804788}
{107,107,(548 赢 441),0.804745}
{108,108,(554 赢 446),0.805054}
{109,109,(559 赢 450),0.805009}
{110,110,(564 赢 454),0.804965}
{111,111,(570 赢 459),0.805263}
{112,112,(575 赢 463),0.805217}
{113,113,(580 赢 467),0.805172}
{114,114,(585 赢 471),0.805128}
{115,115,(591 赢 476),0.805415}
{116,116,(596 赢 480),0.805369}
{117,117,(601 赢 484),0.805324}
{118,118,(606 赢 488),0.805281}
{119,119,(612 赢 493),0.805556}
{120,120,(617 赢 497),0.805511}
{121,121,(622 赢 501),0.805466}
{122,122,(627 赢 505),0.805423}
{123,123,(633 赢 510),0.805687}
{124,124,(638 赢 514),0.805643}
{125,125,(643 赢 518),0.805599}
{126,126,(648 赢 522),0.805556}
{127,127,(654 赢 527),0.80581}
{128,128,(659 赢 531),0.805766}
{129,129,(664 赢 535),0.805723}
{130,130,(669 赢 539),0.80568}
{131,131,(675 赢 544),0.805926}
{132,132,(680 赢 548),0.805882}
{133,133,(685 赢 552),0.805839}
{134,134,(690 赢 556),0.805797}
{135,135,(696 赢 561),0.806034}
{136,136,(701 赢 565),0.805991}
{137,137,(706 赢 569),0.805949}
{138,138,(712 赢 574),0.80618}
{139,139,(717 赢 578),0.806137}
{140,140,(722 赢 582),0.806094}
{141,141,(727 赢 586),0.806052}
{142,142,(733 赢 591),0.806276}
{143,143,(738 赢 595),0.806233}
{144,144,(743 赢 599),0.806191}
{145,145,(748 赢 603),0.80615}
{146,146,(754 赢 608),0.806366}
{147,147,(759 赢 612),0.806324}
{148,148,(764 赢 616),0.806283}
{149,149,(769 赢 620),0.806242}
{150,150,(775 赢 625),0.806452}
{151,151,(780 赢 629),0.80641}
{152,152,(785 赢 633),0.806369}
{153,153,(790 赢 637),0.806329}
{154,154,(796 赢 642),0.806533}
{155,155,(801 赢 646),0.806492}
{156,156,(806 赢 650),0.806452}
{157,157,(812 赢 655),0.80665}
{158,158,(817 赢 659),0.80661}
{159,159,(822 赢 663),0.806569}
{160,160,(827 赢 667),0.80653}
{161,161,(833 赢 672),0.806723}
{162,162,(838 赢 676),0.806683}
{163,163,(843 赢 680),0.806643}
{164,164,(848 赢 684),0.806604}
{165,165,(854 赢 689),0.806792}
{166,166,(859 赢 693),0.806752}
{167,167,(864 赢 697),0.806713}
{168,168,(869 赢 701),0.806674}
{169,169,(875 赢 706),0.806857}
{170,170,(880 赢 710),0.806818}
{171,171,(885 赢 714),0.80678}
{172,172,(890 赢 718),0.806742}
{173,173,(896 赢 723),0.80692}
{174,174,(901 赢 727),0.806881}
{175,175,(906 赢 731),0.806843}
{176,176,(912 赢 736),0.807018}
{177,177,(917 赢 740),0.806979}
{178,178,(922 赢 744),0.806941}
{179,179,(927 赢 748),0.806904}
{180,180,(933 赢 753),0.807074}
{181,181,(938 赢 757),0.807036}
{182,182,(943 赢 761),0.806999}
{183,183,(948 赢 765),0.806962}
{184,184,(954 赢 770),0.807128}
{185,185,(959 赢 774),0.807091}
{186,186,(964 赢 778),0.807054}
{187,187,(969 赢 782),0.807018}
{188,188,(975 赢 787),0.807179}
{189,189,(980 赢 791),0.807143}
{190,190,(985 赢 795),0.807107}
{191,191,(991 赢 800),0.807265}
{192,192,(996 赢 804),0.807229}
-----------------------------------
2 maxwin(扩展到996项)=
{0,1,1,2,3,3,4,5,6,6,7,8,9,9,10,11,12,13,13,14,
15,16,17,17,18,19,20,21,21,22,23,24,25,25,26,27,
28,29,29,30,31,32,33,33,34,35,36,37,37,38,39,40,
41,41,42,43,44,45,45,46,47,48,49,49,50,51,52,53,
53,54,55,56,57,57,58,59,60,61,61,62,63,64,65,65,
66,67,68,69,69,70,71,72,73,74,74,75,76,77,78,78,
79,80,81,82,82,83,84,85,86,86,87,88,89,90,90,91,
92,93,94,94,95,96,97,98,99,99,100,101,102,103,
103,104,105,106,107,107,108,109,110,111,111,112,
113,114,115,115,116,117,118,119,119,120,121,122,
123,124,124,125,126,127,128,128,129,130,131,132,
132,133,134,135,136,136,137,138,139,140,140,141,
142,143,144,145,145,146,147,148,149,149,150,151,
152,153,153,154,155,156,157,157,158,159,160,161,
162,162,163,164,165,166,166,167,168,169,170,170,
171,172,173,174,174,175,176,177,178,178,179,180,
181,182,183,183,184,185,186,187,187,188,189,190,
191,191,192,193,194,195,195,196,197,198,199,200,
200,201,202,203,204,204,205,206,207,208,208,209,
210,211,212,212,213,214,215,216,216,217,218,219,
220,221,221,222,223,224,225,225,226,227,228,229,
229,230,231,232,233,233,234,235,236,237,238,238,
239,240,241,242,242,243,244,245,246,246,247,248,
249,250,250,251,252,253,254,255,255,256,257,258,
259,259,260,261,262,263,263,264,265,266,267,267,
268,269,270,271,272,272,273,274,275,276,276,277,
278,279,280,280,281,282,283,284,284,285,286,287,
288,288,289,290,291,292,293,293,294,295,296,297,
297,298,299,300,301,301,302,303,304,305,305,306,
307,308,309,310,310,311,312,313,314,314,315,316,
317,318,318,319,320,321,322,322,323,324,325,326,
327,327,328,329,330,331,331,332,333,334,335,335,
336,337,338,339,339,340,341,342,343,344,344,345,
346,347,348,348,349,350,351,352,352,353,354,355,
356,356,357,358,359,360,361,361,362,363,364,365,
365,366,367,368,369,369,370,371,372,373,373,374,
375,376,377,378,378,379,380,381,382,382,383,384,
385,386,386,387,388,389,390,390,391,392,393,394,
395,395,396,397,398,399,399,400,401,402,403,403,
404,405,406,407,407,408,409,410,411,412,412,413,
414,415,416,416,417,418,419,420,420,421,422,423,
424,424,425,426,427,428,429,429,430,431,432,433,
433,434,435,436,437,437,438,439,440,441,441,442,
---
795,795,796,797,798,799,800,800,801,802,803,804}

3 maxwin直观列输出(n m loss,(n应m) m/n)=(共996项,摘录前101项)
{1,0,1,(1 赢 0),0.}
{2,1,1,(2 赢 1),0.5}
{3,1,2,(3 赢 1),0.333333}
{4,2,2,(4 赢 2),0.5}
{5,3,2,(5 赢 3),0.6}
{6,3,3,(6 赢 3),0.5}
{7,4,3,(7 赢 4),0.571429}
{8,5,3,(8 赢 5),0.625}
{9,6,3,(9 赢 6),0.666667}
{10,6,4,(10 赢 6),0.6}
{11,7,4,(11 赢 7),0.636364}
{12,8,4,(12 赢 8),0.666667}
{13,9,4,(13 赢 9),0.692308}
{14,9,5,(14 赢 9),0.642857}
{15,10,5,(15 赢 10),0.666667}
{16,11,5,(16 赢 11),0.6875}
{17,12,5,(17 赢 12),0.705882}
{18,13,5,(18 赢 13),0.722222}
{19,13,6,(19 赢 13),0.684211}
{20,14,6,(20 赢 14),0.7}
{21,15,6,(21 赢 15),0.714286}
{22,16,6,(22 赢 16),0.727273}
{23,17,6,(23 赢 17),0.73913}
{24,17,7,(24 赢 17),0.708333}
{25,18,7,(25 赢 18),0.72}
{26,19,7,(26 赢 19),0.730769}
{27,20,7,(27 赢 20),0.740741}
{28,21,7,(28 赢 21),0.75}
{29,21,8,(29 赢 21),0.724138}
{30,22,8,(30 赢 22),0.733333}
{31,23,8,(31 赢 23),0.741935}
{32,24,8,(32 赢 24),0.75}
{33,25,8,(33 赢 25),0.757576}
{34,25,9,(34 赢 25),0.735294}
{35,26,9,(35 赢 26),0.742857}
{36,27,9,(36 赢 27),0.75}
{37,28,9,(37 赢 28),0.756757}
{38,29,9,(38 赢 29),0.763158}
{39,29,10,(39 赢 29),0.74359}
{40,30,10,(40 赢 30),0.75}
{41,31,10,(41 赢 31),0.756098}
{42,32,10,(42 赢 32),0.761905}
{43,33,10,(43 赢 33),0.767442}
{44,33,11,(44 赢 33),0.75}
{45,34,11,(45 赢 34),0.755556}
{46,35,11,(46 赢 35),0.76087}
{47,36,11,(47 赢 36),0.765957}
{48,37,11,(48 赢 37),0.770833}
{49,37,12,(49 赢 37),0.755102}
{50,38,12,(50 赢 38),0.76}
{51,39,12,(51 赢 39),0.764706}
{52,40,12,(52 赢 40),0.769231}
{53,41,12,(53 赢 41),0.773585}
{54,41,13,(54 赢 41),0.759259}
{55,42,13,(55 赢 42),0.763636}
{56,43,13,(56 赢 43),0.767857}
{57,44,13,(57 赢 44),0.77193}
{58,45,13,(58 赢 45),0.775862}
{59,45,14,(59 赢 45),0.762712}
{60,46,14,(60 赢 46),0.766667}
{61,47,14,(61 赢 47),0.770492}
{62,48,14,(62 赢 48),0.774194}
{63,49,14,(63 赢 49),0.777778}
{64,49,15,(64 赢 49),0.765625}
{65,50,15,(65 赢 50),0.769231}
{66,51,15,(66 赢 51),0.772727}
{67,52,15,(67 赢 52),0.776119}
{68,53,15,(68 赢 53),0.779412}
{69,53,16,(69 赢 53),0.768116}
{70,54,16,(70 赢 54),0.771429}
{71,55,16,(71 赢 55),0.774648}
{72,56,16,(72 赢 56),0.777778}
{73,57,16,(73 赢 57),0.780822}
{74,57,17,(74 赢 57),0.77027}
{75,58,17,(75 赢 58),0.773333}
{76,59,17,(76 赢 59),0.776316}
{77,60,17,(77 赢 60),0.779221}
{78,61,17,(78 赢 61),0.782051}
{79,61,18,(79 赢 61),0.772152}
{80,62,18,(80 赢 62),0.775}
{81,63,18,(81 赢 63),0.777778}
{82,64,18,(82 赢 64),0.780488}
{83,65,18,(83 赢 65),0.783133}
{84,65,19,(84 赢 65),0.77381}
{85,66,19,(85 赢 66),0.776471}
{86,67,19,(86 赢 67),0.77907}
{87,68,19,(87 赢 68),0.781609}
{88,69,19,(88 赢 69),0.784091}
{89,69,20,(89 赢 69),0.775281}
{90,70,20,(90 赢 70),0.777778}
{91,71,20,(91 赢 71),0.78022}
{92,72,20,(92 赢 72),0.782609}
{93,73,20,(93 赢 73),0.784946}
{94,74,20,(94 赢 74),0.787234}
{95,74,21,(95 赢 74),0.778947}
{96,75,21,(96 赢 75),0.78125}
{97,76,21,(97 赢 76),0.783505}
{98,77,21,(98 赢 77),0.785714}
{99,78,21,(99 赢 78),0.787879}
{100,78,22,(100 赢 78),0.78}
{101,79,22,(101 赢 79),0.782178}
--------------------------------
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-7-30 18:40:02 | 显示全部楼层
这个 0.807(还在增加中):

{192,192,(996 赢 804),0.807229}

和这个问题二里面的 C(1/2)≈0.811 很接近:

https://www.cnblogs.com/v-July-v/archive/2011/02/26/1983673.html

problem.png

这两个数会不会相等呢?

如果能证实相等,就是一个重大发现了,可以发表学术论文的。

点评

0/1串是最简单的串了,计算最长公共子列的程序的复杂度能到O(n)以下吗?  发表于 2020-7-31 09:29
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-8-3 21:06:41 | 显示全部楼层
本帖最后由 dlpg070 于 2020-8-3 21:45 编辑

KeyTo9_Fans 发表于 2020-7-30 18:40
这个 0.807(还在增加中):

{192,192,(996 赢 804),0.807229}


一个连接:               
J. D. Dixon, Longest common subsequences in binary sequences,
[math.GR], 2013.
https://arxiv.org/abs/1307.2796
给出 L(n,n)/n 9个估值
我仿照Dixon的方法计算12个点 n最大=65536 , 耗时10000秒
猜想 C1/2=gamma_2>0.8113 ,不等于 0.811

序号 n    均值     均方差      (    估值区间     ) 耗时 秒
{1, 32,   0.751875,0.032025,   (0.71985, 0.7839  ),0.0020002}
{2, 64,   0.777188,0.020825,   (0.756363,0.798013),0.0040002}
{3, 128,  0.788281,0.012875,   (0.775406,0.801156),0.0150008}
{4, 256,  0.796406,0.0116,     (0.784806,0.808006),0.0590034}
{5, 512,  0.800938,0.00539688, (0.795541,0.806335),0.260015}
{6, 1024, 0.805234,0.00443125, (0.800803,0.809665),1.18707}
{7, 2048, 0.806836,0.00277734, (0.804059,0.809613),5.52532}
{8, 4096, 0.809087,0.00147012, (0.807617,0.810557),25.1524}
{9, 8192, 0.81002, 0.0011166,  (0.808903,0.811137),113.417}
{10,16384,0.810876,0.000735352,(0.810141,0.811611),499.713}
{11,32768,0.811442,0.00050293, (0.810939,0.811945),2168.1}
{12,65536,0.811679,0.000346851,(0.811332,0.812026),9737.26}
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-8-4 11:23:32 | 显示全部楼层
本帖最后由 dlpg070 于 2020-8-4 11:30 编辑
dlpg070 发表于 2020-8-3 21:06
一个连接:               
J. D. Dixon, Longest common subsequences in binary sequences,
[math ...



KeyTo9_Fans的精确数据an太好了,遗憾n还不够大
通常用统计方法给出估值
下面比较KeyTo9_Fans的精确数据和我的统计结果
结果表明 :全部9项的精确值均在我的估值的 1 均方差之内!!!,统计结果正确
,足见这些精确值的重要 ,Dixon的统计方法是个好方法
说明:这里的KeyTo9_Fans的精确数据,由an计算maxwin数列,再提取给定条件的项得到
   n    nean   meandev  Fans   mean-Fans  

{1,2,  0.5,     0.18,      0.5,      0.,       (2 赢 1)}
{2,4,  0.64,    0.1632,    0.5,      0.14,     (4 赢 2)}
{3,8,  0.72,    0.0908,    0.625,    0.095,    (8 赢 5)}
{4,16, 0.71875, 0.055,     0.6875,   0.03125,  (16 赢 11)}
{5,32, 0.751875,0.032025,  0.75,     0.001875, (32 赢 24)}
{6,64, 0.777188,0.020825,  0.765625, 0.011563, (64 赢 49)}
{7,128,0.788281,0.012875,  0.789063,-0.0007815,(128 赢 101)}
{8,256,0.796406,0.0116,    0.796875,-0.000469, (256 赢 204)}
{9,512,0.800938,0.00539688,0.804688,-0.0037495,(512 赢 412)}
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-8-8 12:34:38 | 显示全部楼层
本帖最后由 dlpg070 于 2020-8-8 12:38 编辑
dlpg070 发表于 2020-8-4 11:23
KeyTo9_Fans的精确数据an太好了,遗憾n还不够大
通常用统计方法给出估值
下面比较KeyTo9_Fans的精确 ...


根据最近我的统计计算的结果和KeyTo9_Fans'的计算结果得到的Maxwin数列
画图观察渐进过程,明显逼近极限值 = 约0.811

maxwin/n

maxwin/n
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-8-8 17:32:06 | 显示全部楼层
dlpg070 发表于 2020-8-8 12:34
根据最近我的统计计算的结果和KeyTo9_Fans'的计算结果得到的Maxwin数列
画图观察渐进过程,明显逼近极 ...

一个外行的猜想,一个认真的笑话
对我的统计计算数据做曲线拟合,求极限,估计误差
拟合函数类似:
   f(x)= a + b * ArcTan[x^c]
得到C1/2=gamma_2估值如下:
   
   极限= 0.81230 ,标准差= 0.00052
   0.81177 <= gamma_2 <= 0.81283
也许有点靠谱!!!请专家们论证吧
我将继续研究游戏策略
参考图:

拟合

拟合
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
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