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Here, it is shown 90 of 960 positions involve having to move a rook on 1 side in order to castle on the other side (unless the rook is somehow captured or something). These 90 positions come from 18 rearrangements/permutations/combinations/whatever from each of 5 groups of starting positions (SPs)

  1. RKRXXXXX
  2. RKXRXXXX
  3. XRKRXXXX
  4. XXXXXRKR
  5. RXKRXXXX

Based on the Sesse evals for the 960 SPs (see here also) or based on other similar sources (such as practical instead of theoretical statistics like win rate eg this (computer chess) [again see here]), what is white's increased advantage in chess90 compared to chess870?

Note 1: This can't be vacuous. If white actually has a bigger advantage in chess870 compared to chess90, then the answer is simply negative.

Note 2: I'm answering below for the sesse evals. I have yet to answer or receive an answer for the computer chess statistics.

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Group of SPs and then average evaluation (rounded to 4 decimal places):

  1. RKRXXXXX - 0,1900
  2. RKXRXXXX - 0,1906
  3. XRKRXXXX - 0,1878
  4. XXXXXRKR - 0,2017
  5. RXKRXXXX - 0,1867
  6. Whole of Chess960 - 0.1801
  7. Whole of Chess90 - 0.1913
  8. Whole of Chess870 - 0.1790

Therefore,

(0.1913-0.1790)/0.1790 = 0.06871508379 ~ 6.87%, almost 7%.

Remarks:

  1. Chess960 has a higher evaluation than chess870, but only by (0.1801-0.1790)/(0.1790) = 0.00614525139 ~ 0.6%.

  2. Chess90 and each of its 5 SP groups have an average evaluation higher than the average evaluation of both chess960 and chess870.

  3. SP 518 is 0.22, which is higher than each of the 8 evaluations.

In case you want to verify for yourself, here are my google sheet codes for the 5 SP groups of chess90:

  1. RKRXXXXX - =IF(LEFT(B2;3)="RKR";1;0)
  2. RKXRXXXX - =IF(AND(LEFT(B2;2)="RK";MID(B2;4;1)="R");1;0)
  3. XRKRXXXX - =IF(MID(B2;2;3)="RKR";1;0)
  4. XXXXXRKR - =IF(RIGHT(B2;3)="RKR";1;0)
  5. RXKRXXXX - =IF(AND(LEFT(B2;1)="R";MID(B2;3;2)="KR");1;0)
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  • 2
    Are those differences meaningful though? What's the difference between a +0.18 position and a +0.20 one?
    – David
    Jan 20, 2022 at 19:55
  • 3
    @BCLC This percentage doesn't tell the whole picture or even close: there's a 200% difference between +0.01 and +0.03 but they're hardly distinguishable as chess engine evaluations. A better way would be to hypothesis test. (That said, it's an interesting question you ask and have started analysing.)
    – Mobeus Zoom
    Jan 20, 2022 at 20:32
  • @MobeusZoom oh lol you're right. thanks
    – BCLC
    Jan 21, 2022 at 9:07
  • @David anyway where did you get 0.18 and 0.20 ? i computed/calculated a 7% difference '(0.1913-0.1790)/0.1790 = 0.06871508379 ~ 6.87%, almost 7%' i.e. a chess90 SP is 7% more powerful for white compared to a chess870 SP Edit: Ah you mean XXXXXRKR and chess870 ?
    – BCLC
    Jan 21, 2022 at 9:08
  • 1
    Alright, call it 0.1913 and 0.1790 then. Same point applies
    – David
    Jan 23, 2022 at 0:49

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