George Duke wrote on Fri, Jul 27, 2007 04:04 PM UTC:
John Conway's fairy piece Angel jumps to any square that can be reached by
n King moves. Let Pawns = 1.0 point. On 8x8 with n=7, what is the value of an Angel? Anything greater than 1.0 that you want. 60.0 would probably be convenient [Then n=6 makes Angel-prime about 40.0 points], but a variate piece could be more valuable than that if stipulating it cannot be captured. What model-system(s) is trying to be emulated? Chess piece-values may be like predicting the weather, or selecting stocks to maximize profit, or handicapping horse races. However, those systems have measureable successes to compare. Or do they? Does 'weatherman' get credit if it rains in the suburbs but not city? If stocks generally go up 7% over x years, and one's value appreciates 8%, does your formulaic selection method amount to much? In handicapping thoroughbreds, a steady 5% loss is already above average because of government take-outs of 15% and more: methods-players must be well up that bell-shaped curve reliably to average net $100 per $1000 bet over the long-run. There is extensive literature in all three of those fields. In latter two, any profit or win(at all skilled gambling like Poker) is indicative of good, or useful, 'system' behind it. In Falcon Chess we now assign Pawns 1.1(it may yet change toward 1.05) in order to keep Rook 5.0; we just like that set-off better than Rook 4.6 or 4.7. The first step, after some play of a variate, is to ask deeply within many alternate positions which would be preferred, 4 Pawns or 1 Rook, and so on. [To be developed is how we know values are close to 'correct']