💡📝Kevin Pacey wrote on Mon, Dec 24, 2018 05:22 AM UTC:
The one thing I've done so far is to treat a super-bishop (aka promoted bishop in shogi) as a compound piece where I add a B's value plus a wazir's value plus a pawn, on 10x10 (for my Sac Chess variant). On 10x10 I rate a B worth 3.5 (as opposed to a N being just set=3 there, unlike on 8x8), and I rate a wazir as worth 0.75 there (half of what I rate it as on 8x8). So Super-bishop=B+wazir+P=3.5+0.75+1=5.25 on 10x10, which feels about right to me, especially as most people seem to value it as about worth a rook on 8x8. Note I'd similarly rate a super-B as worth 6 on 8x8, slightly more than R (I set to 5.5), in line with Greg's post about the super-B compared to the R a while back in another thread, i.e. re: (8x8) Pocket Mutation Chess (both are put in the same piece type class in terms of value by that game's inventor).
Observe also that colour-binding is built into a B's known value, and having a B as a component of a compound piece still includes that built in binding penalty (whatever it is) for the B; the masking of the colour-binding by the addition of another component (in this case, a wazir) is taken into account by (in addition to adding a wazir's value) adding a pawn's value (only), much as Q=R+B+P in chess. So, there is no sudden doubling of the Bs value as it were, in the case of a super-B (or a Q) compound piece, the way I do this particular calculation (i.e. as a sum).
At the risk of repetition, that (not always perfectly applicable) Q=R+B+P analogy, when used for estimating the value of compound pieces, often seems (to me at least) to produce results that aren't too badly off, when I've run with it in order to make many of my estimates. The case of valuing an archbishop on 8x8 being one quite possible exception, however, though on 10x10 at least, I wonder if that piece might be nearly as potent as on 8x8 - I sense this when I play 10x10 Sac Chess, though I do sense a certain potency of an Archbishop when I play 10x8 Capablanca Chess. My guess is that the N component of the archbishop suffers from less influence on 10x10, the largest size of these three sizes. It's also quite possible a B enjoys a 10x8 board even more than a 10x10 one (indeed I rate a B as 3.75 on 10x8), so that may explain why an archbishop seems extra strong to me on 10x8, in spite of a slightly less influential N component (than if it were on 8x8).
One thing that still makes no sense to me, btw, is if Amazon at best =Q+N in value (as I recall the wiki for that piece implies), then why zero co-operativity between the Q and N components? That's why I feel still more comfortable with Amazon set=Q+N+P at the moment. There also may be a similar problem for Guard set=3.2 on 8x8, if ferz and wazir are each approx. 1.5 (as I vaguely recall the wiki for each more or less gave), as the co-operativity seems all but shockingly low between ferz and wazir, if so.
Note I still rate a rook as worth 5.5 on 10x10 (as I would for any number of board sizes), since for one thing I don't believe a B's value should ever be 4 or greater (since it can't often restrain 4 pawns in an endgame - though a problem for me may be that if I set Guard=4 [incidentally =ferz+wazir+P, perhaps] on 8x8, as some chess authorities have done similarly for a K's fighting value, the same reasoning, about not restraining 4 pawns in an endgame, might be argued), and a rook should pretty well be worth about a B and 2 pawns on any board size, at least for square or rectangular boards.
There are, I imagine, many things I have yet to try to take into account when tentatively evaluating piece values, such as what Betza has written about pieces with negative values.
Note a colourbound penalty of e.g. x0.5 can be just one part of an estimating process, possibly. There can be offsetting bonuses, such as a x2 bonus for a leaper. There can also be a x0.5 penalty for non-capturing movements that make up part of how a piece moves, too (then there's forward as opposed to sideways or backward movements by a piece, and how to reckon with the valuation of that). At the moment my repertoire of formulae and methods is limited, but, again, I try to keep my life simple when possible, and I hope to compare my estimates with existing ones, if any, to get a feeling for if I am in the right ballpark before giving an estimate of my own.
In the case of the (colourbound, but 8-target leaper) camel, its value of 2 is still close to N/2 on 8x8 (especially if N set to =3.5 is used, which is even close to Guard, if that's set to =4), coincidence or not, which gives me some encouragement. Incidently, I assume a leaper bonus is not used for pieces (or components of them) that take just a one cell step, which is why I see a N in a way more different from a ferfil than a N is from a camel, in spite of a ferfil being closer to a N in value (on 8x8, in all cases).
Aside from all that, I hope you (and everyone else) are enjoying the holiday season, H.G.
The one thing I've done so far is to treat a super-bishop (aka promoted bishop in shogi) as a compound piece where I add a B's value plus a wazir's value plus a pawn, on 10x10 (for my Sac Chess variant). On 10x10 I rate a B worth 3.5 (as opposed to a N being just set=3 there, unlike on 8x8), and I rate a wazir as worth 0.75 there (half of what I rate it as on 8x8). So Super-bishop=B+wazir+P=3.5+0.75+1=5.25 on 10x10, which feels about right to me, especially as most people seem to value it as about worth a rook on 8x8. Note I'd similarly rate a super-B as worth 6 on 8x8, slightly more than R (I set to 5.5), in line with Greg's post about the super-B compared to the R a while back in another thread, i.e. re: (8x8) Pocket Mutation Chess (both are put in the same piece type class in terms of value by that game's inventor).
Observe also that colour-binding is built into a B's known value, and having a B as a component of a compound piece still includes that built in binding penalty (whatever it is) for the B; the masking of the colour-binding by the addition of another component (in this case, a wazir) is taken into account by (in addition to adding a wazir's value) adding a pawn's value (only), much as Q=R+B+P in chess. So, there is no sudden doubling of the Bs value as it were, in the case of a super-B (or a Q) compound piece, the way I do this particular calculation (i.e. as a sum).
At the risk of repetition, that (not always perfectly applicable) Q=R+B+P analogy, when used for estimating the value of compound pieces, often seems (to me at least) to produce results that aren't too badly off, when I've run with it in order to make many of my estimates. The case of valuing an archbishop on 8x8 being one quite possible exception, however, though on 10x10 at least, I wonder if that piece might be nearly as potent as on 8x8 - I sense this when I play 10x10 Sac Chess, though I do sense a certain potency of an Archbishop when I play 10x8 Capablanca Chess. My guess is that the N component of the archbishop suffers from less influence on 10x10, the largest size of these three sizes. It's also quite possible a B enjoys a 10x8 board even more than a 10x10 one (indeed I rate a B as 3.75 on 10x8), so that may explain why an archbishop seems extra strong to me on 10x8, in spite of a slightly less influential N component (than if it were on 8x8).
One thing that still makes no sense to me, btw, is if Amazon at best =Q+N in value (as I recall the wiki for that piece implies), then why zero co-operativity between the Q and N components? That's why I feel still more comfortable with Amazon set=Q+N+P at the moment. There also may be a similar problem for Guard set=3.2 on 8x8, if ferz and wazir are each approx. 1.5 (as I vaguely recall the wiki for each more or less gave), as the co-operativity seems all but shockingly low between ferz and wazir, if so.
Note I still rate a rook as worth 5.5 on 10x10 (as I would for any number of board sizes), since for one thing I don't believe a B's value should ever be 4 or greater (since it can't often restrain 4 pawns in an endgame - though a problem for me may be that if I set Guard=4 [incidentally =ferz+wazir+P, perhaps] on 8x8, as some chess authorities have done similarly for a K's fighting value, the same reasoning, about not restraining 4 pawns in an endgame, might be argued), and a rook should pretty well be worth about a B and 2 pawns on any board size, at least for square or rectangular boards.
There are, I imagine, many things I have yet to try to take into account when tentatively evaluating piece values, such as what Betza has written about pieces with negative values.
Note a colourbound penalty of e.g. x0.5 can be just one part of an estimating process, possibly. There can be offsetting bonuses, such as a x2 bonus for a leaper. There can also be a x0.5 penalty for non-capturing movements that make up part of how a piece moves, too (then there's forward as opposed to sideways or backward movements by a piece, and how to reckon with the valuation of that). At the moment my repertoire of formulae and methods is limited, but, again, I try to keep my life simple when possible, and I hope to compare my estimates with existing ones, if any, to get a feeling for if I am in the right ballpark before giving an estimate of my own.
In the case of the (colourbound, but 8-target leaper) camel, its value of 2 is still close to N/2 on 8x8 (especially if N set to =3.5 is used, which is even close to Guard, if that's set to =4), coincidence or not, which gives me some encouragement. Incidently, I assume a leaper bonus is not used for pieces (or components of them) that take just a one cell step, which is why I see a N in a way more different from a ferfil than a N is from a camel, in spite of a ferfil being closer to a N in value (on 8x8, in all cases).
Aside from all that, I hope you (and everyone else) are enjoying the holiday season, H.G.