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

[Ryan M.]

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-----Original Message-----
From: retros-admin at janko.at [mailto:retros-admin at janko.at] On Behalf Of
TregerYefim at aol.com
Sent: Thursday, September 02, 2004 10:35 PM
To: retros at janko.at
Subject: [Retros] My estimate: 10 in power 20 dead positions. Yefim T
09/03/2004
 
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).
 
Why for the K-K match, if judgment calls are so offensive? Hey, they
signed up to play for 6 wins, so let it continue until one of them dies
from dehydration. And make the other guy run an hour off the dead guy's
clock to claim the forfeit.
 

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 - - 0 1
 
Really? What if white just plays Bd1-e2 over and over? You see, there
are still two possible outcomes to the game, so the arbiter must not
interfere! If white's flag falls, the arbiter would properly rule that
he does not lose the game, since there is obviously no possible
checkmate for black; the game is drawn.
 

3. What about position necessarily leading to mate independently on play
of sides?
K1k5/P1Pp4/1p1P4/8/p7/P2P4/8/8 w - - 0 1
 
Again, two possibilities; white could yield a draw by running out of
time. The arbiter can't rule when there are two possible outcomes.
 

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:((. 
 
In the example you gave (locked pawns on their own 4th ranks), there is
no hope for either side to checkmate the other. Nothing is being taken
away from the players except the right to gain a cheap victory by
running the opponent's clock down in a position they could never win
over-the-board. And somehow I can't see players protesting their loss of
right to resign drawn positions :-P.
 

5. You think that "dead position is rare occurrence".
 
Not quite - I said that dead positions that are 'deep' (requiring some
analysis to tell that they are dead) - are rare. Obvious dead positions
such as K+B v. K happen quite often. Therefore, the examples below are
moot, for they are obviously dead positions. Any seasoned player could
tell at a glance that they are dead. The calculations are meaningless,
because math isn't the best approach to evaluate these positions. The
math is becoming more important than the game it was meant to model.
 
 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
  
R0089 - Andrew Buchanan
StrateGems 16, 2001
[1Nk3K1/P1PN1B2/RBP1P3/2P1R1PQ/8/8/8/8]
14+1. (Dead Reckoning
<http://www.janko.at/Retros/Glossary/DeadReckonig.htm> ) Last
<http://www.janko.at/Retros/Glossary/LastMove.htm>  move? (White to
move.)
[1Nk3K1/P1PN1B2/RBP1P3/2P1R1PQ/8/8/8/8]
The last move was -1...Kd8-c8 (reaching a live position: 1...Ke7
2.c8N#), preceded by -2.d6x~c7+ Ke7-d8 -3.d5-d6+.  Try: -1...Kb7-c8?? is
still dead, as the alternative 1.Ka8 also leads to stalemate.
 
 
R0093 - Andrew Buchanan
StrateGems 18, 2002
[Bb1k1b2/bKp1p1p1/1pP1P1P1/1P6/p5P1/P7/8/8]
8+9. (Dead Reckoning
<http://www.janko.at/Retros/Glossary/DeadReckonig.htm> ) Last move
<http://www.janko.at/Retros/Glossary/LastMove.htm> ? White to move. 3
black Bishops.
[Bb1k1b2/bKp1p1p1/1pP1P1P1/1P6/p5P1/P7/8/8]
Last move was 0...a5-a4! (not 0...Ke8(x)d8??, which is already dead
before the diagram).  The possibility 1...Ke8 2.Ka6 Kd8 3.Bb7 Ke8 4.Bc8
Kd8 5.Kb7 Ke8 6.Ka8 Kd8 7.Ba6 Ke8 8.Bb7 Kd8 9.Bc8 Ke8 10.Bd7+ Kd8 11.Be8
Kc8 12.Bf7 Kd8 13.Bg8 Ke8 14.Kb7 Kd8 15.g5 Ke8 16.Kc8 a4 17.Bf7# shows
that the position is alive.
 
-Ryan McCracken
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