Tuesday, October 30, 2007

A system for counting

After 5 days stumbling in the dark finally the lightswitch turned on. I worked out all possible captures with different attackers, defenders and victims. What put me on the wrong foot is that the position of the previous post is an exception. Only when there is a queen involved, the order of access can play a role. Since a queen can stand in front of her rooks or her bishop. The other pieces cannot stand in each others way and at the same time play a role in capturing. In the following treatment I leave the situation out of a queen standing in front of her rooks or her bishop. Then a fairly simple system remains.

The most logical way of capture and recapture is to use the light pieces first before the heavier ones. To know if a sequence of capturing will give you wood:

n = #attackers
m = #defenders
A= Sum value of m attackers (take the lowest)
B= Sum value of n enemy pieces that are involved in the trade (take the lowest)
Gmax= maximum gain = value of the victim
Gtheor=theoretical gain if all pieces are traded= B - A
Geff= effective actual gain= MINIMUM (Gmax, Gtheor)

A few examples.

In all examples white is the attacker and to move.
Example 1

n = 4
m = 4
A= 14
B= 10
Gmax= 1
Gtheor= -4
Geff= -4 thus no wood

Example 2

n = 4
m = 4
A= 14
B= 12
Gmax= 1
Gtheor= -2
Geff= -2 thus no wood

Example 3

n = 4
m = 2
A= 6
B= 11
Gmax= 1
Gtheor= 5
Geff= 1 thus you win the victim

Tomorrow I will try to formulate a narrative to say it in clear language. Time for a little celebration: there is no need to go through the actual sequence!

1. Comments last post: thank you Polly.

We are all lucky she comes to visit and read some of the stuff in our circle, for instead of just starting to do it, or wants to do it, or wants to want to do it, she has already done it, evidenced by her results, and sustained ones.

its good to know an elder in results, as tempo is too, but fully established takes an interest and can look on.

thank you tempo, too. you do so much, and embody so much. dk

ps, my bullet phase is ending, and now i have 3,200 games to look at, including several hundred rapids or blitz, and can study endings and openings 'by hand'.

just as BDK was trying for SO long to finish his unit on, CTB was it, so here, this is my big unit, i feel... but, alas, im not quite done but pushing super hard to closure in definite result and shared results.

2. Thansformation: Thanks for your kind words. I'm really enjoying following all these different blogs. They're giving me a fresh perspective on ways to study. This old dog is ready to learn some new tricks.