[Retros] Retro Result Criterion 05/08/2012

[tregeryefim at aol.com]

Friends!

I am collecting material for the book about Math and Chess.
Here I want to discuss an idea of "RRC", "Retro Result Criterion" (a preliminary name).

Example 1.
Duras. White wins.

8/6p1/7k/8/1K6/8/1P6/8 w - - 0 1

This a useful study except for the following.
There are 24 previous positions (for the initial one), from 
each of them Black had made a loosing move! It leads to the 
idea of RRC-criterion.

Definition 1. "RRC-win" criterion.

For any given winning White (Black) position there must be at 
least one loosing Black (White) position previous to the given 
one. 

Or, in other words (for studies):
If all previous positions for the initial position of the study 
"White wins" are drawn (for Black) then the study is not "good" 
since it does not satisfy RR-criterion. 

Clearly, Duras' study does NOT satisfy "RRC-win" criterion. All 
Black positions leading to it are drawn. One of the reasons to call this study as "not a good one" is 
that: If a study has to have a unique solution, it did not have 
it in its past (Black did not make good moves). Of course, it 
does mean that this study is bad, it is just "not good"...

Example 2.
The given positions is:

k6r/2p5/1pP5/KP6/8/8/8/8 w - - 0 1

White draws.

Here all Black positions leading to this example are won (if 
the last move was a capture Black should better capture by c-
pawn). 

Definition of "RCC-draw" criterion.

For any given drawn (White or Black) position there must be at 
least one drawn, previous to it position (Black or White).
 
In other words:
If all previous positions for the initial position of the study 
"White draws" are won (for Black) then the study is not "good" 
since it does not satisfy RR-criterion.

Example 2 does not satisfy RRC-draw criterion. Actually, this 
is a not a study (I made it up), but I think there are some 
studies which do not satisfy RRC-draw too...

Can you find them or create some interesting examples 
(thoughts) for this topic? 

Yefim Treger.
05/08/2012


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