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H. G. Muller wrote on Thu, Sep 20, 2018 05:39 PM UTC:

There are only 98 positions (out of a total of 64*63*62 = 249984, counting also illegal positions) where King + Charging Knight is not won against a bare King, when the strong side is on move. With the bare King on move, he loses in 80.5% of the positions. In the other 20% of the positions he captures the enemy King or the (unprotected) Charging Knight on his first move, or is stalemated.

It takes at most 33 moves to force the checkmate:

        mated    mate
King captures 50168
mates      36         ( 0.00 sec)
in-1       30     126 ( 0.01 sec)
in-2       90     158 ( 0.01 sec)
in-3      138     446 ( 0.01 sec)
in-4      198     560 ( 0.01 sec)
in-5      334     772 ( 0.01 sec)
in-6      278    1122 ( 0.01 sec)
in-7      498     908 ( 0.01 sec)
in-8      770    1630 ( 0.01 sec)
in-9      808    2246 ( 0.02 sec)
in-10    1240    2274 ( 0.02 sec)
in-11    1720    3124 ( 0.02 sec)
in-12    2312    3978 ( 0.02 sec)
in-13    2606    4922 ( 0.03 sec)
in-14    2930    5294 ( 0.03 sec)
in-15    4002    5400 ( 0.03 sec)
in-16    4432    6778 ( 0.04 sec)
in-17    4966    6770 ( 0.04 sec)
in-18    5072    7006 ( 0.04 sec)
in-19    6334    6988 ( 0.04 sec)
in-20    7678    8402 ( 0.04 sec)
in-21    8512    9134 ( 0.05 sec)
in-22    9074    8836 ( 0.05 sec)
in-23   11468   10968 ( 0.05 sec)
in-24   15336   13132 ( 0.06 sec)
in-25   17800   16642 ( 0.06 sec)
in-26   20122   17610 ( 0.07 sec)
in-27   21332   18210 ( 0.07 sec)
in-28   20308   15816 ( 0.08 sec)
in-29   16108   11550 ( 0.08 sec)
in-30   10430    7332 ( 0.08 sec)
in-31    3470    1386 ( 0.08 sec)
in-32     666     174 ( 0.08 sec)
in-33     124      24 ( 0.09 sec)
in-34       0       0 ( 0.09 sec)
won:     249886 (100.0%)
lost:    201222 ( 80.5%)
avg:       23.7 moves
 

 


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