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Kevin Pacey wrote on 2018-12-29 UTC

I don't quite understand the bit about my apparently sometimes arbitrarily ignoring colourbinding, at least (the math parts of your last post are a little bit over my groggy head, tonight anyway, except I'd suggest my method for calculating at the least the first component of the compound left some margin for error, as in hindsight I clearly should have got 3.5 in a perfect world, rather than 3.625, on 8x8, and there was a similar sort of slight error for the 10x10 case - it too should have produced a final answer of 3.5, all in line with what you point out [else I'm unclear at the moment where "3.75" comes from]). First, note I never removed the implicit (i.e. built-in) colourbinding penalty (whatever it is) when considering 9/10 of a B as one component for the compound piece's value as I estimated it. For calculating chess values, this happens too, when one makes the compound piece Q=R+B+P and takes its value from the equation just given, without in any way discarding the colourbound penalty a B has built in (whatever it is).

A Q is as a result not a colourbound piece, similar to the compound piece that I estimated the value of is not a compound piece, in spite of having a colourbound piece as one of its components (i.e. the same story as for a Q). So, secondly, note that for either compound piece there is no now-non-colourbound-piece bonus explicitly used in the equations involved (for a Q, the lack of any binding it has is implicitly taken into account, along with any other factors created by the combining of its B and R components, by the Ps worth of cooperativity between the two components). Hopefully it will not confuse things to note also that a wazir and ferz are worth about the same (I treat them as =) in spite of a ferz being colourbound - in that case the pieces are very small in value, plus other factors are involved that help the ferz' value. Thus, I get a Waffle (WA) the same value as a ferfil (FA) in the case of those compound pieces, in spite of the fact one is colourbound and the other is not. This happens once again because an equation for compound pieces is being used, where I choose to use a P as the amount of cooperativity involved (I may get things significantly wrong on some occasions by normally using a pawn for cooperativity in the case of compounds, but at least it greatly simplifies my life, for the time being anyway).

There could perhaps be some piece type dreamt up that I could have big trouble handling as a compound piece, as a way of handling the masking of binding that occurs in a case like that of a Q. I thought such a type of piece improbable or uncommon, and it certainly might force me to see binding penalties in a different light. Otherwise, treating pieces as compounds whenever possible seemed attractive to me early on when estimating values, and I try to milk that cow for all it's worth. :)

If you ask me how I might assign a B a binding penalty etc. when evaluating it from scratch, I'd have huge trouble being sure I'd weighed all of the possible significant factors, but to try to meet you halfway, here's how I'd use my least well worked out method, a sort of crude weighing of pros and cons, between two piece types I'm considering, where the first one has a known value - in this case it'll be a knight (on 8x8), which I'll say is worth 3.5.

Characteristics of a N:

1) Leaper (thus x2 bonus. e.g. compared to a B, is built into its value, if what I've read on CVP is the common wisdom);

2) Average cells reached on empty (8x8) board = 5, which is half of a B's average of 10 (thus B deserves about a x2 bonus compared to a N, IMHO);

3) Short-range compared to a B, i.e. lacks speed in comparison (thus B deserves about a x2 bonus compared to a N, IMHO);

4) Can reach every cell on the board (i.e. B is colourbound, deserving a x0.5 penalty, as compared to a N, IMHO [thus before this final stage you might say I was tentatively thinking a B worth 2xN's value, further bonuses or penalties pending]).

At this point I've pretty well used up all the big pros and cons I can think of, and happily they balance (suggesting B roughly or exactly = N), which may make you somewhat happy given your computer study results, though I'd note there are many finer things I did not try to weigh (impossible as it is even to list them all), which might ever so slightly tilt the balance in favour of a B, such as that a B can at times trap a N on an edge of the board, while a N cannot do the same.

My problem is, without treating a 9/10 B combined with 1/4 wazir as a compound piece, this crude method would probably fail to work out so well for me when comparing the piece to a N, as colourbinding is no longer something that's clearly on the table (though one thing to note is that making a 1/4 wazir move in order to change the colour of cell the piece is on costs a tempo (as often/normally is the case) plus a lot of speed, but it's not so clear why such would carry a big penalty, and about how big it might be, trying to weigh things crudely). Fortunately for me (and my sleep at night) I can treat the aforementioned piece as a compound one.

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