How to determine the value of a piece from scratch? Assume we have a standard chess set setup, but we make a slight change so that (for example) pawns can now move two squares forward on any move rather than just on their initial move. Even assuming that we can still use the established point values for the pieces (Knight=Bishop=3 Rook=5 Queen=9 or whatever system you wish to use), how would one go about finding out how much our modified pawn would be worth?
My initial thought would be to (re-)program a chess engine with the modified piece ability, change the internal values for it in several different ways, and then hold a series of engine tournaments until an approximate value can be narrowed down. This would work (as all point values are approximate and situational anyway), but point values for pieces have been around longer than computers, so there must be other methods available.
Any ideas?
Note: I am not actually looking for software recommendations, etc. to do this. I'm just curious what the best way of doing this would be.
It's possible to use logistic regression (a statistical method) to estimate the predictive values. This way, you wouldn't need anyone to try the game at all.

http://www.sumsar.net/blog/2015/06/big-data-and-chess has the details. I personally tried the method, and it was a good start.

The method estimates the value of each piece by predicting how they relates to  the log-odd of winning.