Re: How to learn to count during midgame
Posted: Fri Nov 23, 2012 3:49 am
I promised an example for prisoners, so here it is. For the sake of simplicity, I let it look like an endgame position. Just imagine the local shape to be part of a middle game position.
INITIAL POSITION
POSITIONAL JUDGEMENT I - MISTAKE
Black's territory including the prisoners is
8 + 100 = 108 points.
Including the prisoners, White's territory is
8 + 100 = 108 points.
The territory count is Black's minus White's value:
108 - 108 = 0 points.
POSITIONAL JUDGEMENT II - CORRECT
Black's territory including the sequence's prisoners is
8 + 0 = 8 points.
Including the prisoners, White's territory is
8 - 0 = 8 points.
The territory count is Black's minus White's value and includes the initial prisoner difference:
8 - 8 + 100 = 0 + 100 = 100 points in Black's favour.
NAIVE PRINCIPLE
Count each prisoner only once.
BETTER PRINCIPLE
Count each prisoner only once, even if it occurs in different sequences that are not alternative variations.
REMARKS
Initial prisoners must be considered for each alternative variation. The sequences for determining either Black's or White's territory are not alternative to each other, but they coexist. We would be considering alternative variations if we continued the game from the initial position with different sequences and then make judgements of the black and white territories for the resulting game positions.
More principles for prisoners and positional judgement are needed but not discussed here at the moment.
Without knowing or thinking how and when to add or subtract prisoners during positional judgement, one can easily make mistakes and get wrong counts as a consequence of confusing addition and subtraction or counting prisoners several times that must be counted only once.
I have chosen the initial prisoner difference 100 to make it obvious why considering it twice is a mistake. If, however, the initial prisoner difference is small (a value such as 1) and more prisoners are made during one or both sequences, then it is easy to make wrong calculations because mistakes are not so obvious.
EDITS: corrections, early versions were wrong. More remarks.
INITIAL POSITION
POSITIONAL JUDGEMENT I - MISTAKE
Black's territory including the prisoners is
8 + 100 = 108 points.
Including the prisoners, White's territory is
8 + 100 = 108 points.
The territory count is Black's minus White's value:
108 - 108 = 0 points.
POSITIONAL JUDGEMENT II - CORRECT
Black's territory including the sequence's prisoners is
8 + 0 = 8 points.
Including the prisoners, White's territory is
8 - 0 = 8 points.
The territory count is Black's minus White's value and includes the initial prisoner difference:
8 - 8 + 100 = 0 + 100 = 100 points in Black's favour.
NAIVE PRINCIPLE
Count each prisoner only once.
BETTER PRINCIPLE
Count each prisoner only once, even if it occurs in different sequences that are not alternative variations.
REMARKS
Initial prisoners must be considered for each alternative variation. The sequences for determining either Black's or White's territory are not alternative to each other, but they coexist. We would be considering alternative variations if we continued the game from the initial position with different sequences and then make judgements of the black and white territories for the resulting game positions.
More principles for prisoners and positional judgement are needed but not discussed here at the moment.
Without knowing or thinking how and when to add or subtract prisoners during positional judgement, one can easily make mistakes and get wrong counts as a consequence of confusing addition and subtraction or counting prisoners several times that must be counted only once.
I have chosen the initial prisoner difference 100 to make it obvious why considering it twice is a mistake. If, however, the initial prisoner difference is small (a value such as 1) and more prisoners are made during one or both sequences, then it is easy to make wrong calculations because mistakes are not so obvious.
EDITS: corrections, early versions were wrong. More remarks.
