George Duke wrote on Sat, Feb 5, 2005 07:43 PM UTC:
The mathematical formula I worked out a year ago for M(=#Moves) helps
explain the flatness of play in Medieval Chess in Game Courier. It simply
can be expected to have a large number of turns on average for its 76
squares. Building on Smith's Exchange Gradient, #M = 3.5N/(P(1-G)), with
P Power Density and G calculated as (PV1/PV2 + PV1/PV3...+ PV1/PVn +
PV2/PV3...+ PV2/PVn...+ PV(n-1)/PVn))/(n(n-1)/2). That gives Gradient, but
we want (1-G) for right directionality. For Medieval with Q9, P1, R5, and
excluding K all the other pieces 3 points, G is 0.614, very high,
representing not much benefit in exchanges. Plugged in above, it
translates to predicted long-term average of 62 moves, long games for 76
squares. Contrast that to Orthodox Chess(64sq) Design Analysis giving just ave. 34
#M and Capablanca(80sq) ave. 38 #Moves in Comments there.