# [Retros] More than 100 positions leading to the foolish mate. Yefim 10/09/2004

TregerYefim at aol.com TregerYefim at aol.com
Sat Oct 9 12:49:38 EDT 2004

Hello, from Yefim.
My position with only one e.p. move is:
6b1/ppp1p2p/3pPk1P/3PpPpK/6P1/8/8/8 w - - 0 1
Interesting observations: mathematically a requirement about last Black
move to be a pawn move is not necessary as long we have the main condition: only
one move is e.p. The given position in a graph has only one inward edge and
one outward edge. Further, this e.p. move does not lead to final position as in
two previous examples. Let me popularly explain a difference between final
positions and not final ones.
The key idea is a local degree for a position in a graph what is a sum of
all indegree positions (leading to the given one) and outdegree (leading from
the given one) positions.
Examples of two other wonderful moves. If you have castle (in this moment)
you have minimum 4 outward edges (4 moves). If you have a promotion move the
minimal local outdegree for the position is also 4.
It is a pity that computer programs do not recognize some simple
properties for
positions. But there is a deep reason for that: e.p. properties, castle
properties (if castle is possible only in future) and some others are mostly game
properties.
The funny example: a foolish mate: 1.f3 e6 2.g4 Qh4# Computer (WinBoard)
gives final position as:
rnb1kbnr/pppp1ppp/4p3/8/6Pq/5P2/PPPPP2P/RNBQKBNR w KQkq - 0 3
with all possible castles!?
For all of us: No final position contains any castle rights! Local
Outdegree for them is 0.
Now, my question about last mate position: what is local degree for it? Or:
how many positions lead to this final one? (final position does not need any
number in a game, mate or stalemate is always superior). My answer is 112.
Why: wait for the next teaching lesson...
Yefim (still writing a book about Math and Chess) 10/09/2004.
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