The following is to clarify the text of p. 42 of the Rules Books a bit (not overly clear).
The tradegood distance formula is sensitive to variations in both the X and the Y directions. So to maximize returns, move to a sale that is diagonally distant from your goods’ province of manufacture.
The number of provinces travelled. Diagonal movement is dealt with using Pythagoras’ theorem … for those of you who have completely forgotten high school math, distance is the square root of the sum of the X distance squared plus the Y distance squared.
SQR([X2-X1]*[X2-X1] + [Y2-Y1]*[Y2-Y1])
with [X2-X1] and [Y2 – Y1] being the absolute (i.e. positive) differences between the X and Y coordinates of the two provinces involved (place of manufacture and place of sale).
3 crowns times distance.
A random factor added to the Base value of 3 crowns; the maximum of this factor is based on what percent of the possible map you have travelled. Your bonus will range from +.01 crown up to the percent you have travelled (divided by 100%), with a maximum of +1 crown.
The largest difference you can possibly travel on a map of 130/80 coordinates (the normal Legends map) is:
SQR (129*129 + 79*79) = 151,
or rather as seems to be used (cf. p. 42; not totally correct IMHO):
SQR (130*130 + 80*80) = 152
travel 10% of the map: bonus of .01 to .10 crowns per tradegood
travel 50% of the map: bonus of .01 to .5 crowns per tradegood
travel 100% of the map (ie from 1/1 to 130/80): bonus of .01 to 1 crown per tradegood.
The total crown value of a tradegood is thus 3 plus the bonus, times the distance.
1) Tradegoods from 10,10 are sold in province 10,60.
The distance is 50, which is about 1/3 of the maximum possible with a 130/80 map, so the value per tradegood will range from 3.01 to 3.33 times 50:
minimum value : 150
maximum value : 166
average return: 158
2) Tradegoods from 17,20 are sold in province 82,60.
The distance is 76 [82-17 = 65, 60-20=40; SQR(65*65+40*40)= 76], which is about 1/2 the maximum possible , so the value will range from 3.01 to 3.5, times 76:
minimum value : 229
maximum value : 266
average return: 248
Note these values are before any bonuses from Merchant skills!
Tradegoods show in their name where they have been made – but with a random margin of a few provinces. Also in their id# they show their production center, thus (as stated by Mons Johnson): “Tradegoods (TGs) are marked as being produced in an even/even province. So if your location was in p23/45 or in p23/46 then the TG would ID as being produced in p24/46. The TGs are numbered from left to right, top to bottom. Starting from the number 3001 for the first spot (i.e. province 2/2). This gives us the formula:
TG id# = 3000 + X/2 + 65*(Y-2)/2, where X & Y are the province numbers
This article is reproduced with kind permission from “Aayko’s The Legends Corner”.