[Retros] My estimate: 10 in power 20 dead positions. Yefim T 09/03/2004

[TregerYefim at aol.com]

 As I understand, you (Ryan McCracken) admit a possibility to end a chess 
game by side judgment.
"Sorry to disappoint, but even a game so logical as chess must sometimes be 
decided by a judgment call".
1. I think judgment call is allowed only for terrorist attack, fire, 
earthquake and something like this (extraordinary situations; unlimited match K-K, not 
a single game).
2. Remember my idea about eternally winning position? If you admit that some 
heuristic logic is allowed to prevent futility, then you have to admit that 
such a position is won instantly (so easy to prove it, FEN below).
8/b1p5/1pP5/1P6/3p1p1p/2pP1P1k/2P1BP1p/7K w - -
3. What about position necessarily leading to mate independently on play of 
sides?
K1k5/P1Pp4/1p1P4/8/p7/P2P4/8/8 w - -
4. Judgment decision denies a right of player to resign (denies a right of 
one player
to wait for other to resign:); denies a hope:((. 
5. You think that "dead position is rare occurrence". Almost any position 
after
30-th move is rare occurrence (it rare happens in two different games). The 
question is how many dead position do exist. Simple calculations shows:
a) Position WK against BK+BQ:
FEN: 
8/8/8/4k3/8/8/q7/K7 w - - 58 positions (if BK on other squares);
b) Shifting WK and BK to the right (left) and up (down) we got 58*30=1740 
(all approximately).
c) Adding a BK or BB  we got 1740*50*50=4350000;
d) Adding two, three, ...nine one color BB we got: 
4350000*50*49*48*47*46*45*44*42=40000000000000000 (16 zeroes)
e) actually, we do not need BQ we got the same amount additionally;
400000000000000000;
f) Instead of BB let it be WB (or several bishops: WB+BB); so multiplying:
400000000000000000*9*8*7*6*5*4*3*2 (alternating color for the given amount of 
bishops); We need Stirling formula replacing factorial by power... It would 
be 
like 10 in power 20.
e) Plus examples (you say) of A.Buchanan. By the way, could you please give 
me some.
Sincerely, Yefim 09/03/2004
  
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