Kevin Pacey wrote on Wed, Jul 19, 2017 11:59 PM UTC:
FYI, here's how I crudely estimated the value of the Cat:
Initial value (without multi-capture ability bonus estimate):
Just as Q=R+B+P in chess, similarly a Cat has a guard-movement component (worth 1.75 Pawns - see my previous post) plus more or less a knight-movement component, which is worth 3 Pawns IMO (max. 8 leaps that are 2 cells orthogonally or diagonally away, noting that though these all go to the same coloured cells, there's no concern about a Cat being colourbound since it moves as a Guard, too), plus a Pawn's value for being a compound piece like a queen, and so Cat's initial value =5.75.
Multi-capture bonus estimate (a really crude piece of guesswork here!):
First, estimate the Average value of an enemy piece at the start of a game, i.e. A=(Estimated Sum of Enemy Army's Piece Values [must be inexact since values of Cats, or Star-Cats, only initial ones, without multi-capture bonus]) divided by 24=approximately 3.5.
Next, estimate Limiting factor of a Cat's range, i.e. L=(max. number legal Cat moves) divided by 144=16/144=1/9 or 0.11.
Then, assume for now the chance of a Cat making a capturing move on any cell it can reach one or two cells away is 1/2 per cell (as if only in 1 direction). The value of zero captures available (x0) =1/4x0=0. The value of one capture available (x1)=1/2x1=1/2. The value of two captures available (x2) =1/4x2=1/2. The sum of these values is 0+1/2+1/2=1. We now take this sum and multiply it by A and by L to get our desired estimate:
Cat's multi-capture bonus estimate =1xAxL=approximately 0.39, or 0.5 Pawns (rounding to the nearest 0.25).
This estimate plus the Cat's initial value calculated gives final value of Cat=6.25 Pawns approx.
I used similar calculations to get the final approximate value of a Star-Cat as well.
FYI, here's how I crudely estimated the value of the Cat:
Initial value (without multi-capture ability bonus estimate):
Just as Q=R+B+P in chess, similarly a Cat has a guard-movement component (worth 1.75 Pawns - see my previous post) plus more or less a knight-movement component, which is worth 3 Pawns IMO (max. 8 leaps that are 2 cells orthogonally or diagonally away, noting that though these all go to the same coloured cells, there's no concern about a Cat being colourbound since it moves as a Guard, too), plus a Pawn's value for being a compound piece like a queen, and so Cat's initial value =5.75.
Multi-capture bonus estimate (a really crude piece of guesswork here!):
First, estimate the Average value of an enemy piece at the start of a game, i.e. A=(Estimated Sum of Enemy Army's Piece Values [must be inexact since values of Cats, or Star-Cats, only initial ones, without multi-capture bonus]) divided by 24=approximately 3.5.
Next, estimate Limiting factor of a Cat's range, i.e. L=(max. number legal Cat moves) divided by 144=16/144=1/9 or 0.11.
Then, assume for now the chance of a Cat making a capturing move on any cell it can reach one or two cells away is 1/2 per cell (as if only in 1 direction). The value of zero captures available (x0) =1/4x0=0. The value of one capture available (x1)=1/2x1=1/2. The value of two captures available (x2) =1/4x2=1/2. The sum of these values is 0+1/2+1/2=1. We now take this sum and multiply it by A and by L to get our desired estimate:
Cat's multi-capture bonus estimate =1xAxL=approximately 0.39, or 0.5 Pawns (rounding to the nearest 0.25).
This estimate plus the Cat's initial value calculated gives final value of Cat=6.25 Pawns approx.
I used similar calculations to get the final approximate value of a Star-Cat as well.