Carvan Delivery Payoff formula

[markusf]

i don't think it can be improved to much. The problem is the trade system is riddled with as many bugs as the rest of the game.

[debeest]

When I discovered the Scrolls of Wisdom, I immediately started comparing the values I got from trade with the values predicted by the formulas there, and I found that the Scrolls formulae were thoroughly inadequate (for example, they only list demanded-commodity multipliers for about half of the commodities). The values for the ongoing trade bonus are especially inaccurate, usually about 3-6 times as high as I actually get. I've posted about this several times; I even posted actual outcomes versus predicted outcomes at one point, hoping to stimulate the Apolyton geniuses to derive better equations. While William Keenan's current formula is not entirely accurate, and doesn't even try to address the ongoing trade bonus, it is indeed a substantial improvement over the Scrolls of Wisdom formula. I thank William for his work and look forward to his continued refinement of the formula. I hope he'll be able to develop a formula for the ongoing bonus, too.

[markusf]

Originally posted by debeest
When I discovered the Scrolls of Wisdom, I immediately started comparing the values I got from trade with the values predicted by the formulas there, and I found that the Scrolls formulae were thoroughly inadequate (for example, they only list demanded-commodity multipliers for about half of the commodities). The values for the ongoing trade bonus are especially inaccurate, usually about 3-6 times as high as I actually get. I've posted about this several times; I even posted actual outcomes versus predicted outcomes at one point, hoping to stimulate the Apolyton geniuses to derive better equations. While William Keenan's current formula is not entirely accurate, and doesn't even try to address the ongoing trade bonus, it is indeed a substantial improvement over the Scrolls of Wisdom formula. I thank William for his work and look forward to his continued refinement of the formula. I hope he'll be able to develop a formula for the ongoing bonus, too.

The ongoing trade formula is correct. Just because you have a road between 2 cities doesn't mean you will get the road bonus. The bonus's only applies when you build along the optimal path. I have gotten up to size 68 routes.. There are a couple of things missing from the formula but they deal with mine improvements.

[debeest]

My experience, carefully and repeatedly observed, convinces me that the Scrolls' ongoing trade formula is far from correct. Invariably the trade bonus is much smaller than predicted. The arbitrary road-connection path requirement does not explain it. It's possible that I'm miscalculating somehow, but I've gone over it again and again, and if the error is mine, I don't see where it is. No sense arguing; I've tested it and it doesn't work for me. If others test it and it works for them, I'd like to find out what I'm doing wrong. Anybody else tested it?

[markusf]

I use it all the time to get +60 trade routes....

The only bug is Airports and your own cities (you can't get over 24 trade using a airport and your own cities)

[SlowThinker]

Originally posted by debeest
It's possible that I'm miscalculating somehow, but I've gone over it again and again, and if the error is mine, I don't see where it is. No sense arguing; I've tested it and it doesn't work for me. If others test it and it works for them, I'd like to find out what I'm doing wrong. Anybody else tested it?

Could you post a savefile?

[debeest]

If I am successful in attaching it, here is a save file from the game I'm playing now (OK, you can see that I'm no great shakes at the game). The freight from Peanut to Pinpoint will generate an ongoing bonus of 7 trade. The formula in the Scrolls of Wisdom predicts about 30 trade. The base calculation is

(49 trade + 70 trade + 4) / 8 = 15.375

Modifiers include +50% for freight versus caravan, -50% for both cities being mine, and +100% for different continents. I suspect that the figures should be multipliers rather than additive, but I don't think that matters much. This result, about 1/4 of the predicted bonus, is thoroughly consistent with my experience.

Is the formula wrong, or am I making some mistake?

If I could generate trade bonuses as high as this formula predicts, I'd sure play the game differently!

[markusf]

Originally posted by debeest
If I am successful in attaching it, here is a save file from the game I'm playing now (OK, you can see that I'm no great shakes at the game). The freight from Peanut to Pinpoint will generate an ongoing bonus of 7 trade. The formula in the Scrolls of Wisdom predicts about 30 trade. The base calculation is

(49 trade + 70 trade + 4) / 8 = 15.375

Modifiers include +50% for freight versus caravan, -50% for both cities being mine, and +100% for different continents. I suspect that the figures should be multipliers rather than additive, but I don't think that matters much. This result, about 1/4 of the predicted bonus, is thoroughly consistent with my experience.

Is the formula wrong, or am I making some mistake?

If I could generate trade bonuses as high as this formula predicts, I'd sure play the game differently!

Well your adding it wrong because only base trade counts.

(49 trade + 59 trade + 4) / 8 = 14

deduct 50% for them being yours and you end up with 7 trade.

+50% freight only applies to the cash bonus, and +100% for different continents ONLY applies for the cash bonus .

[debeest]

So, in this case I'm making a small error (15+ versus 14), and the main error is that the Scrolls formula incorrectly includes large multipliers for freight and for different continents? Are there other errors in the Scrolls formula, or does that cover it? I'd be surprised if the same-civilization penalty applies but none of the bonuses apply.

And how do you get trade routes up to 68? Even with superhighways in both cities, base trade's not likely to total much more than 130 for the two cities. Call it 132, add the 4, divide by 8, you get 17. No freight multiplier, no continent multiplier; that only leaves 50% each for road, rail, airports, and superhighways. That only gets you to 51. And does it seem likely that all those bonuses count, but not the two that I happened to have with that particular freight?

Fortunately, this can be checked, eh?

[markusf]

i will create one in cheat mode later and post it.... superhighways are needed....

[debeest]

So, markusf, you say that the freight multiplier and the different-continent multiplier apply only to the delivery payoff and not to the ongoing trade route? Do you think that the other multipliers are exactly as stated in the Scrolls of Wisdom, or are there other errors as well?

And, I'd love to see a +68 trade route. I haven't paid as much attention to trade as I ought to, but I know I've never had a trade route greater than about +15 or so.

[markusf]

I have been really busy..


In cheat mode Build 2 cities side by side. make sure each is a different civ. Then put in a superhighway in both cities, and railroad every single square between the 2 cities. that should give you +50 assuming there are no specials between the 2 cities and that both cities have all grassland or water

[William Keenan]

Personally, I have never seen a trade route over 30 in a standard, unmodified game - and I do pay close attention to these things.

When there were no formulas those found in the Scrolls of Wisdom were ground breaking. It mattered little that they were not exact becuse they were a vast improvement over blind speculation. As time pasts, the civ player evolves. He demands a greater level of clarity and accuracy then was considered necessary when the Scrolls were written.

The "Caravan Delivery Payoff" paper is about evolving the documentation to match the new generation of civ player.

[debeest]

William, have you done any work on the trade route equation?

Has anyone else seen a trade route greater than 30?

[William Keenan]

Originally posted by debeest
William, have you done any work on the trade route equation?

Yes, I am still working on it. The distace caculation continues to be my nemisis in completing. Assist my understaning, if you would, by walking me though the calculation with this example:

Rome: 50, 28
Paris: 42, 36

What is the distance?

[debeest]

Yes, I found the distance formula to be thoroughly unintuitive too. But if I can explain it to you properly, it's really pretty simple.

First, it may help to imagine the game map rotated 45 degrees so that it looks like a checkerboard instead of a collection of diamonds.

In that orientation, if you move horizontally or vertically, you're moving from one square to a square that shares an edge with it. That move is a distance of 1. (Thus, in your Xexample, the distance is 8. Your example is the rare simple case where straight-line movement gets you there without any diagonal adjustment.) If you move diagonally, to a square that shares only a corner, the distance is 1.5, rounded down. Thus, in the actual orientation of the game map, the diagonal edge-to-edge move is 1, and the horizontal or vertical corner-to-corner move is 1.5. If I'm counting along that line, I just count "1,3,4,6,7,9,10,12....)

There is a second way to calculate the distance, mathematically equivalent, but more intuitive or less intuitive according to individual mindset. Measure the lengths of the sides of the right triangle formed by moving from one space to the other space via edge-to-edge squares. Add the length of the longer side plus one half the length of the shorter side: L + S/2. (In your example, of course, it's a straight line; the longer "side" L = 8.)

I have not tried to determine a formula for calculating distance just based on Civ2's thoroughly unintuitive tile-numbering system, although I suspect it wouldn't be too hard. I just count it out manually in view mode.

Does this help?

[debeest]

Oh, and I think I wasn't clear: I was asking whether you've done any work on a formula for the ongoing trade route bonus. I find that your delivery bonus formula is already good, though usually inexact (usually a bit too high). Whatever factors need to be altered there, they're nothing major.

[La Fayette]

william
debeest's explanation is perfectly correct.
Perhaps I can try to explain it my way (the result is exactly the same and I have tested it many times):
You can always join 2 cities by travelling NW then NE (or NE then NW). Combining those 2 routes always give you a rectangle.
Each square (or tile or rhomboid) along the longer side of the rectangle has a value of 1. Along the shorter side this value is reduced to 0.5 (and you don't forget to round down the result if needed).
Example:
I join my cities by travelling 8 squares NW + 5 squares NE.
The distance is 8 + 5*0.5 = 12.5, rounded down to 12.

AFAIK all distances in civ2 are measured that way.

[SlowThinker]

Originally posted by William Keenan
Roundown ((BTA of SC + BTA of DC + 1) * (D +10) * FD / 48.5)

BTA = Base Trade Arrows
SC = Source City
DC = Destination City
D = Distance
FD = Foreign Delivery

I suggest some changes for the formula:

Roundown ((BTA of SC + BTA of DC) * (D +10) * FD / 48)


It works with basic conditions (no foreign delivery, undemanded commodity, no halving factor, no multiplier) perfectly. I attach my test world and the spreadsheet that shows results of testing.

Should be verified with various multipliers: is the rounddown function placed correctly?

[SlowThinker]

Originally posted by William Keenan
Continental Multiplier
X1 source and destination cities are on the same continent
X2 source and destination cities are on different continents

Airport Multiplier
X1 neither city has an Airport
X1 one city has an Airport
X1.5 cities are on the same continent and both have Airports
X2 cities are on the different continents and both have Airports

Do both multipliers work together or not? In other words, is there a x4 bonus if the cities with Airports are on different continents?

[SlowThinker]

I found out that my suggested formula is very similar to the Scrolls one:

Originally posted by Scrolls of Ancient Wisdom
Payment = ( ( distance + 10 ) x ( trade of both cities ) ) / 24

I suppose there is 24 in place of 48 because of halving factor included.

[William Keenan]

Do both multipliers work together or not? In other words, is there a x4 bonus if the cities with Airports are on different continents?

yep.


The formula is constructed to minimize the number of fractional numbers created, thus eliminate rounding errors.

[markusf]

Like i said, trade routes are 2x is big if the 2 cities are on the same landmass. Soon as you put one on a island its /24 not 48

[SlowThinker]

Originally posted by William Keenan
The formula is constructed to minimize the number of fractional numbers created, thus eliminate rounding errors.

See the .xls file in the caravan payoff.zip attachment.
There are both formulas (your and mine) compared in the sheet: My formula has no rounding error, everything is accurate.

But I didn't test it with various multipliers: did you choose BTA+1 and 48.5
because of multipliers?

[debeest]

Originally posted by markusf
Like i said, trade routes are 2x is big if the 2 cities are on the same landmass. Soon as you put one on a island its /24 not 48

Markusf, if a foreign continent payoff is /24 rather than /48, doesn't that mean it's twice the value, not half the value? I've been checking William Keenan's formula with every freight I deliver, and using a 2x multiplier for foreign continent, and finding the formula to be in the general vicinity of accurate.

Have you had time to generate an example of a 60+ trade route yet?

[SlowThinker]

Originally posted by William Keenan
Distance = (length of longer side of rectangle) + 0.5 * (length of shorter side of rectangle)

You should note that the distance is (always - AFAIK in all the civilization) rounded down.

Originally posted by William Keenan
Railroad Multiplier
X1 if Railroad has not been discovered
Flight Multiplier
X1 if Flight has not been discovered

better: source civilization has not discovered ...

[markusf]

Originally posted by debeest


Markusf, if a foreign continent payoff is /24 rather than /48, doesn't that mean it's twice the value, not half the value? I've been checking William Keenan's formula with every freight I deliver, and using a 2x multiplier for foreign continent, and finding the formula to be in the general vicinity of accurate.

Have you had time to generate an example of a 60+ trade route yet?

cash bonus to another continent is 2x normal and the ongoing route is X. If its on the same landmass cash bonus is x and the on going route is 2x.

I created a real simple save. one city pair has +47 trade, another has +55 trade to get more you would need 4 gold mines in each city and rivers. I think the max was +70 or something.

[debeest]

Aaarrgh! I downloaded your file and saved it to disk, but my 2.42 tells me it isn't a saved game. You're probably using some other version of Civ, and 2.42 is all I've got. I don't suppose you can post a 2.42 version for me? If not, I'll just have to continue to wonder.

[markusf]

mines the march 26 patch from 1999 for MPG

[William Keenan]

Markusf, you are right.