The Chess Variant Pages



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H. G. Muller wrote on 2020-05-26 UTC

Are you sure about those numbers? I cannot do the Omega Chess board, but my EGT generator for a plain 10x10 board says KBNK maximally takes 47 moves (average 39.4), and Knight + Wizard maximally 48 moves (average 40.1). I can imagine that having the Wizard squares could take 2 or 3 moves extra, but not nearly as much as what you mention. The hard part is usually to get the bare King in the desired corner. For Bishop + Knight it might not take any extra moves, as in the standard mating patterns the Bishop would automatically attack the Wizard square as well.

I agree that 50 moves does not leave much room for errors, and in general it can take longer to make progress in large games.

[Edit] Oh, I now also see your previous comment. And no, Kevin did not misunderstand me; for maximum DTM with a WD on 10x10 I get 52 moves, while 95.7% of the positions with the strong side to move are forced wins (see table below). On the Omega board this is of course no longer true; not even a Rook can force mate there. The WAD probably doesn't fare any better.

$ ./3men10x10 KwK
allocate 1010064 at 6d0040
        mated    mate
King captures 129224
mates      16         ( 0.01 sec)
in-1       40      64 ( 0.01 sec)
in-2      208     248 ( 0.01 sec)
in-3       88     916 ( 0.01 sec)
in-4      300     624 ( 0.01 sec)
in-5      224    1428 ( 0.02 sec)
in-6      468     768 ( 0.02 sec)
in-7      528    1696 ( 0.02 sec)
in-8      468    1728 ( 0.02 sec)
in-9      400    1836 ( 0.02 sec)
in-10     480    1080 ( 0.03 sec)
in-11     396    1328 ( 0.03 sec)
in-12     312    1416 ( 0.03 sec)
in-13     512    1192 ( 0.03 sec)
in-14     304    1656 ( 0.03 sec)
in-15      72     812 ( 0.04 sec)
in-16      56     304 ( 0.04 sec)
in-17      80     280 ( 0.04 sec)
in-18     168     392 ( 0.04 sec)
in-19     468     712 ( 0.04 sec)
in-20     768    1408 ( 0.04 sec)
in-21     768    2096 ( 0.04 sec)
in-22     708    2152 ( 0.05 sec)
in-23    1056    2080 ( 0.05 sec)
in-24     908    2812 ( 0.05 sec)
in-25    1640    2620 ( 0.05 sec)
in-26    1376    4128 ( 0.06 sec)
in-27    1516    3720 ( 0.06 sec)
in-28    3944    4524 ( 0.06 sec)
in-29    4536   10044 ( 0.06 sec)
in-30    6588   11060 ( 0.07 sec)
in-31    9456   15224 ( 0.07 sec)
in-32   15880   20516 ( 0.08 sec)
in-33   27248   32184 ( 0.09 sec)
in-34   33956   48452 ( 0.10 sec)
in-35   45448   56908 ( 0.12 sec)
in-36   60972   71044 ( 0.13 sec)
in-37   77556   89008 ( 0.15 sec)
in-38   88852  100212 ( 0.17 sec)
in-39   86540   90180 ( 0.19 sec)
in-40   81708   71664 ( 0.21 sec)
in-41   57772   46460 ( 0.22 sec)
in-42   40900   31352 ( 0.23 sec)
in-43   25296   20336 ( 0.24 sec)
in-44   19160   15656 ( 0.25 sec)
in-45   12944   11152 ( 0.25 sec)
in-46    8928    6976 ( 0.25 sec)
in-47    5456    4136 ( 0.26 sec)
in-48    2520    1968 ( 0.26 sec)
in-49     912     696 ( 0.26 sec)
in-50     224     200 ( 0.26 sec)
in-51      72      56 ( 0.26 sec)
in-52      32      16 ( 0.26 sec)
in-53       0       0 ( 0.27 sec)
won:     928744 ( 95.7%)
lost:    731228 ( 75.4%)
avg:       37.9 moves

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