H. G. Muller wrote on Tue, Dec 11, 2018 11:55 AM UTC:
Perfect play is usually not helpful at all in determining piece values. Because piece values are a heuristic aid to be used by inperfect players to begin with. In perfect play the only thing that matters is distance to mate, and you don't care at all about which pieces get lost or gained in the process of forcing or delaying the mate. And all moves that draw are equally good. There is no such thing as a 'nearly won' or 'nearly lost' position with perfect play; both are just draws. The difference is only determined by how large the chances are that an imperfect player will make the mistake that will push him over the edge.
We now do have perfect play (theough End-Game Tables) for all end-games of orthodox Chess with 7 men or less. Amongst those are B vs N with 1 vs 1 or 2 vs 1 Pawns. But you would be hard-pressed to deduce anything about the B vs N value from those. Counting the fraction of won and lost positions isn't very helpful, as these are completely dominated by the trivially won and lost positions, where either the N or the B is hanging and captured on the first move. And then there is the somewhat deeper tactics that loses a minor, through a fork or skewer. Even if you weed all those out the remaining positions are often of a type that you would never encounter in real games. To make any sense of it you would really have to know the probability that each 7-men position will be reached by simplifying from a more complex one in games. It tends to be that the 'silly' positions have the largest probability to be a win or loss.
I think this whole obsession with (near) perfect play is a fallacy. This is well known in technology. There exists for instance a device called a 'strip detector', used to measure the position where a particle (be it light or elctrons) hits a screen. It consists of a number of 'collector' strips next to each other. If you let the particles fall directly on the strips, you could never get a resolution better than the width of the strips: you would know which strip it its, but you would have no clue whether this was close to the edge or to which edge. So it is typically used behind a 'diffuser', which blurs the incoming particles (by disturbing their trajectory in a random way) to about the width of a stip. Then it always hits multiple strips, and the fraction that falls on one strip and that on its neighbor make it possible to see if it was just on the boundary between the two, or in the center (almost no overspill on either side). The imperfection of the imaging allows you to determine the point of arrival an order of magnitude more precise than with perfect imaging, to a fraction of the strip with.
Now this is exactly what we have in Chess: a detector with 3 stips, a narrow 'draw' strip in the center, and 'win' and 'loss' strips on either side of it. Precisely imaging a set of positions with a certain material imbalance onto this detector, by perfect play, will make it completely invisible whether you hit the draw strip in the center or near an edge. Blurring the imaging by imperfect play, however, increases your resolution, and makes it very easy to determine if the positions were on average 'nearly lost' or 'nearly won'. The thing of interest is how much perspective the material imbalance offers when you are up against an imperfect player, taking into account that you might make errors yourself as well.
Perfect play is usually not helpful at all in determining piece values. Because piece values are a heuristic aid to be used by inperfect players to begin with. In perfect play the only thing that matters is distance to mate, and you don't care at all about which pieces get lost or gained in the process of forcing or delaying the mate. And all moves that draw are equally good. There is no such thing as a 'nearly won' or 'nearly lost' position with perfect play; both are just draws. The difference is only determined by how large the chances are that an imperfect player will make the mistake that will push him over the edge.
We now do have perfect play (theough End-Game Tables) for all end-games of orthodox Chess with 7 men or less. Amongst those are B vs N with 1 vs 1 or 2 vs 1 Pawns. But you would be hard-pressed to deduce anything about the B vs N value from those. Counting the fraction of won and lost positions isn't very helpful, as these are completely dominated by the trivially won and lost positions, where either the N or the B is hanging and captured on the first move. And then there is the somewhat deeper tactics that loses a minor, through a fork or skewer. Even if you weed all those out the remaining positions are often of a type that you would never encounter in real games. To make any sense of it you would really have to know the probability that each 7-men position will be reached by simplifying from a more complex one in games. It tends to be that the 'silly' positions have the largest probability to be a win or loss.
I think this whole obsession with (near) perfect play is a fallacy. This is well known in technology. There exists for instance a device called a 'strip detector', used to measure the position where a particle (be it light or elctrons) hits a screen. It consists of a number of 'collector' strips next to each other. If you let the particles fall directly on the strips, you could never get a resolution better than the width of the strips: you would know which strip it its, but you would have no clue whether this was close to the edge or to which edge. So it is typically used behind a 'diffuser', which blurs the incoming particles (by disturbing their trajectory in a random way) to about the width of a stip. Then it always hits multiple strips, and the fraction that falls on one strip and that on its neighbor make it possible to see if it was just on the boundary between the two, or in the center (almost no overspill on either side). The imperfection of the imaging allows you to determine the point of arrival an order of magnitude more precise than with perfect imaging, to a fraction of the strip with.
Now this is exactly what we have in Chess: a detector with 3 stips, a narrow 'draw' strip in the center, and 'win' and 'loss' strips on either side of it. Precisely imaging a set of positions with a certain material imbalance onto this detector, by perfect play, will make it completely invisible whether you hit the draw strip in the center or near an edge. Blurring the imaging by imperfect play, however, increases your resolution, and makes it very easy to determine if the positions were on average 'nearly lost' or 'nearly won'. The thing of interest is how much perspective the material imbalance offers when you are up against an imperfect player, taking into account that you might make errors yourself as well.