BrainKing - 讨论板 (Chess variants (10x8))

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Chess variants (10x8)

Sam has closed his piano and gone to bed ... now we can talk about the real stuff of life ... love, liberty and games such as
Janus, Capablanca Random, Embassy Chess & the odd mention of other 10x8 variants is welcome too

For posting:
- invitations to games (you can also use the New Game menu or for particular games: Janus; Capablanca Random; or Embassy)
- information about upcoming tournaments
- disussion of games (please limit this to completed games or discussion on how a game has arrived at a certain position
... speculation on who has an advantage or the benefits of potential moves is not permitted while that particular game is in progress)
- links to interesting related sites (non-promotional)

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31. 三月 2003, 19:25:12

Grim Reaper

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题目: A thought about the B + N data...

I looked at my numbers again from the database run:

Mate in 1 move: 2400 positions
Mate in 2 moves: 1324 positions
Mate in 3 moves: 3247 positions

I thought that was strange that the mate in 2 numbers went down from the mate in 1 counts. I would have thought that this number should steadily climb until reaching a saturation point, then it should taper down as fewer positions are resolveable near the end.

But, on second examination, this make sense.

The mate in 1 count is artificially high since it includes all of the mates in 1 executed by a Knight. Recall this mate cannot be forced, but clearly the weak side can walk into it. Fewer of these Knight mates can be forced in 2 moves, much fewer than the additional number of Bishop mates that can occur by move two.

Then the count rises again, etc.

FYI.