Piece Values - CAST

## Command Area Speed Targets

CAST is a method for valuing chess piece types used in a given CV.

### Introduction

CAST arose out of my frustration with using the SMIRF approach combined with my liking for playing with numbers. Whereas SMIRF uses per square figures CAST uses per board numbers and is therefore easier to apply with less room for error.

It is still a work-in-progress, with the latest addition being the Command element; and soon there may be a Range element - when I shall have to change the acronym! (C-STAR?)

### Examples

Before getting into the detail here are 3 examples of valuing Pawn, Knight, Bishop, Rook, Archbishop, Chancellor, Queen and King on various sized boards.

Note: Over the 3 tables the 19 comparisons (CAST*100/SMIRF) have a mean of 99.95 with a s.d. of 4.84

### The Calculation

A piece's total points value (TPV) is given by

TPV = AP - B + (TP + SP) x C

where

• AP represents the Area Points
• B the Blocking Value
• TP the Target Points
• SP the Speed Points
• C the Coverage Factor

taking each parameter in turn

#### Area Points (AP)

This is a measure of the total target area covered by a piece. Any enemy piece within the target area is potentially in danger of being captured. The final value is derived by determining its maximum and minimum and then applying appropriate weights.

AP = (Wmax x APmax) + (Wmin x APmin)

The maximum target area is derived by placing the piece in the center of an empty board and counting the squares attacked. The minimum target area repeats the process but with the piece placed on a corner square.

The weights allow for the pattern of per-square AP values across the whole board as they diminish from the center outwards.

#### Target Points (TP)

This measures the number of enemy pieces within the target area that can be threatened with capture at the same time. For standard pieces where moves finish with the first capture, this equates to the number of directions in which a piece may move. The calculation follows that of the Area Points, thus

TP = (Wmax x TPmax) + (Wmin x TPmin)