Try Berserk history bonus formula

[eduherminio]

With max history 8192:

Score of Lynx-history-bonus-2068-win-x64 vs Lynx 2063 - main: 1793 - 1629 - 2158  [0.515] 5580
...      Lynx-history-bonus-2068-win-x64 playing White: 1226 - 521 - 1043  [0.626] 2790
...      Lynx-history-bonus-2068-win-x64 playing Black: 567 - 1108 - 1115  [0.403] 2790
...      White vs Black: 2334 - 1088 - 2158  [0.612] 5580
Elo difference: 10.2 +/- 7.1, LOS: 99.7 %, DrawRatio: 38.7 %
SPRT: llr 2.91 (100.6%), lbound -2.25, ubound 2.89 - H1 was accepted

With max history 16384 (let's remember that #521 failed, though):

Score of Lynx-history-bonus-2068-win-x64-increased vs Lynx-history-bonus-2068-win-x64: 2114 - 2162 - 2627  [0.497] 6903
...      Lynx-history-bonus-2068-win-x64-increased playing White: 1400 - 712 - 1340  [0.600] 3452
...      Lynx-history-bonus-2068-win-x64-increased playing Black: 714 - 1450 - 1287  [0.393] 3451
...      White vs Black: 2850 - 1426 - 2627  [0.603] 6903
Elo difference: -2.4 +/- 6.4, LOS: 23.1 %, DrawRatio: 38.1 %
SPRT: llr -2.27 (-78.5%), lbound -2.25, ubound 2.89 - H0 was accepted

Pre-calculation, quick 4+0.04 test

Score of Lynx-history-bonus-2075-win-x64 vs Lynx-history-bonus-2068-win-x64: 155 - 153 - 202  [0.502] 510
...      Lynx-history-bonus-2075-win-x64 playing White: 102 - 54 - 99  [0.594] 255
...      Lynx-history-bonus-2075-win-x64 playing Black: 53 - 99 - 103  [0.410] 255
...      White vs Black: 201 - 107 - 202  [0.592] 510
Elo difference: 1.4 +/- 23.4, LOS: 54.5 %, DrawRatio: 39.6 %
SPRT: llr -0.04 (-1.4%), lbound -2.25, ubound 2.89

Max raw bonus per move 948

Score of Lynx-history-bonus-2075-win-x64-mod vs Lynx-history-bonus-2075-win-x64: 1005 - 1079 - 1249  [0.489] 3333
...      Lynx-history-bonus-2075-win-x64-mod playing White: 692 - 346 - 628  [0.604] 1666
...      Lynx-history-bonus-2075-win-x64-mod playing Black: 313 - 733 - 621  [0.374] 1667
...      White vs Black: 1425 - 659 - 1249  [0.615] 3333
Elo difference: -7.7 +/- 9.3, LOS: 5.3 %, DrawRatio: 37.5 %
SPRT: llr -2.26 (-78.1%), lbound -2.25, ubound 2.89 - H0 was accepted

2075 vs main, 40+0.4

Score of Lynx-history-bonus-2075-win-x64 vs Lynx 2063 - main: 812 - 682 - 1231  [0.524] 2725
...      Lynx-history-bonus-2075-win-x64 playing White: 585 - 180 - 597  [0.649] 1362
...      Lynx-history-bonus-2075-win-x64 playing Black: 227 - 502 - 634  [0.399] 1363
...      White vs Black: 1087 - 407 - 1231  [0.625] 2725
Elo difference: 16.6 +/- 9.6, LOS: 100.0 %, DrawRatio: 45.2 %
SPRT: llr 2.9 (100.5%), lbound -2.25, ubound 2.89 - H1 was accepted

My original idea
Keep history bonus increasing with depth after the maximum,

8+0.08 👎🏽

Score of Lynx-history-bonus-2078-win-x64-mod vs Lynx-history-bonus-2075-win-x64: 830 - 906 - 1092  [0.487] 2828
...      Lynx-history-bonus-2078-win-x64-mod playing White: 554 - 298 - 562  [0.591] 1414
...      Lynx-history-bonus-2078-win-x64-mod playing Black: 276 - 608 - 530  [0.383] 1414
...      White vs Black: 1162 - 574 - 1092  [0.604] 2828
Elo difference: -9.3 +/- 10.0, LOS: 3.4 %, DrawRatio: 38.6 %
SPRT: llr -2.26 (-78.2%), lbound -2.25, ubound 2.89 - H0 was accepted

Score of Lynx-history-bonus-2078-win-x64 vs Lynx-history-bonus-2075-win-x64: 1432 - 1495 - 1827  [0.493] 4754
...      Lynx-history-bonus-2078-win-x64 playing White: 977 - 496 - 904  [0.601] 2377
...      Lynx-history-bonus-2078-win-x64 playing Black: 455 - 999 - 923  [0.386] 2377
...      White vs Black: 1976 - 951 - 1827  [0.608] 4754
Elo difference: -4.6 +/- 7.7, LOS: 12.2 %, DrawRatio: 38.4 %
SPRT: llr -2.27 (-78.6%), lbound -2.25, ubound 2.89 - H0 was accepted

40+0.4 ~~

Score of Lynx-history-bonus-2078-win-x64 vs Lynx-history-bonus-2075-win-x64: 1734 - 1682 - 2634  [0.504] 6050
...      Lynx-history-bonus-2078-win-x64 playing White: 1264 - 448 - 1313  [0.635] 3025
...      Lynx-history-bonus-2078-win-x64 playing Black: 470 - 1234 - 1321  [0.374] 3025
...      White vs Black: 2498 - 918 - 2634  [0.631] 6050
Elo difference: 3.0 +/- 6.6, LOS: 81.3 %, DrawRatio: 43.5 %
SPRT: llr 0.216 (7.5%), lbound -2.25, ubound 2.89

Original idea vs main, 40+0.4 👍🏽

Score of Lynx-history-bonus-2078-win-x64-mod vs Lynx 2063 - main: 891 - 753 - 1175  [0.524] 2819
...      Lynx-history-bonus-2078-win-x64-mod playing White: 654 - 187 - 569  [0.666] 1410
...      Lynx-history-bonus-2078-win-x64-mod playing Black: 237 - 566 - 606  [0.383] 1409
...      White vs Black: 1220 - 424 - 1175  [0.641] 2819
Elo difference: 17.0 +/- 9.8, LOS: 100.0 %, DrawRatio: 41.7 %
SPRT: llr 2.91 (100.7%), lbound -2.25, ubound 2.89 - H1 was accepted

With 1285, 40+0.4 👎🏽ish

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Back without the idea, try reducing rawbonus:

1481, 8+0.08 👎🏽

Score of Lynx-history-bonus-2095-win-x64-mod vs Lynx-history-bonus-2095-win-x64: 3567 - 3573 - 4420  [0.500] 11560
...      Lynx-history-bonus-2095-win-x64-mod playing White: 2415 - 1169 - 2196  [0.608] 5780
...      Lynx-history-bonus-2095-win-x64-mod playing Black: 1152 - 2404 - 2224  [0.392] 5780
...      White vs Black: 4819 - 2321 - 4420  [0.608] 11560
Elo difference: -0.2 +/- 5.0, LOS: 47.2 %, DrawRatio: 38.2 %
SPRT: llr -2.08 (-71.9%), lbound -2.25, ubound 2.89

1481, 40+0.4 👎🏽

Score of Lynx-history-bonus-2095-win-x64-mod vs Lynx-history-bonus-2095-win-x64: 1160 - 1216 - 1931  [0.493] 4307
...      Lynx-history-bonus-2095-win-x64-mod playing White: 829 - 346 - 979  [0.612] 2154
...      Lynx-history-bonus-2095-win-x64-mod playing Black: 331 - 870 - 952  [0.375] 2153
...      White vs Black: 1699 - 677 - 1931  [0.619] 4307
Elo difference: -4.5 +/- 7.7, LOS: 12.5 %, DrawRatio: 44.8 %
SPRT: llr -2.27 (-78.5%), lbound -2.25, ubound 2.89 - H0 was accepted

2350, 40+0.4 👎🏽

Score of Lynx-history-bonus-2078-win-x64-mod vs Lynx-history-bonus-2078-win-x64: 896 - 937 - 1487  [0.494] 3320
...      Lynx-history-bonus-2078-win-x64-mod playing White: 636 - 244 - 780  [0.618] 1660
...      Lynx-history-bonus-2078-win-x64-mod playing Black: 260 - 693 - 707  [0.370] 1660
...      White vs Black: 1329 - 504 - 1487  [0.624] 3320
Elo difference: -4.3 +/- 8.8, LOS: 16.9 %, DrawRatio: 44.8 %
SPRT: llr -1.69 (-58.5%), lbound -2.25, ubound 2.89