Carvan Delivery Payoff formula

[William Keenan]

I've just published a paper on a topic near and dear to the hearts of many of the posters in this forum. It is, I believe, an improved formula. Feedback is welcome.

Caravan Delivery Payoffs

[La Fayette]

... and the paper is also goodlooking.
I suppose you have run a few tests (since this 48.5 makes me think of a programmer with an empty bottle of cognac besides him).
Nothing contrary to my knowledge in your formula.
IMO worth direct entrance into the GL (if you and the SGs agree, of course)

[Scouse Gits]

Outstanding!

Certainly seems to capture everything except ...

Science bonus - is the same as gold except when 'capped' by the imminent completion of a discovery - there was about 18 months ago a commonly held view that the cap was 2/3 of the required number of beakers - but I never saw this confirmed. Certainly there is a capping mechanism of some sort in action - does it ever effect the gold reward?

As a programmer myself I suspect the rounding mechanism proposed here - why should it be completely different from that apparently used in the combat calculations - but then why not?

Whatever my reservations - I still think this is a splendid piece of work....

[William Keenan]

La Fayette

I would prefer that the algorithm prove itself a bit before it is entered in the Great Library. In test scenarios the formula was dead on 80% of the time and within 1.2% otherwise. However, testing in a controlled environment is not the same as testing in a real game. Thus, there may be flaws that have not yet come to light.


SG

You are an astute observer. In fact, there is a rounding error in the algorithm. As a former programmer, I must admit that the rounding in the formula is contrived and unlikely. However, attempts to refine it resulted only in compromising the algorithm's balance.

Capping of gold (science was not check separately) was not seen in test scenarios. Deliveries paying 1000 to 1450 gold with only 8 to 15 techs discovered were frequent. Seeing no cap on gold in evidence, further research into the topic seemed unprofitable.

There may be a connection between beakers and the payoff. In testing, strange results were produced when a civ had fewer than five techs. Beyond that though, no other connection was discernable.

[Marquis de Sodaq]

First, you ought to change the zero multipliers to something other than x0. That makes the total 0, n'est-ce pas?

Second, there was recently a thread here in which someone (I forget who ) posted a graphic depicting exactly which road connections counted toward making the bonus work. That would be a good addition to your paper.

Excellent summary! This is one worth saving to the hard drive, to be sure.

[William Keenan]

Originally posted by Marquis de Sodaq
First, you ought to change the zero multipliers to something other than x0. That makes the total 0, n'est-ce pas?

There are no zero multipliers in the formula.

Second, there was recently a thread here in which someone (I forget who ) posted a graphic depicting exactly which road connections counted toward making the bonus work. That would be a good addition to your paper.

Excelent suggestion!

[Marquis de Sodaq]

From the linked document:
X⅔ if Railroad has been discovered

Now that I copy/paste from the document, it appears that the railroad and flight bonuses, second bullet, is not a zero, but some character I cannot read. What is in each of these slots?

[Marquis de Sodaq]

I've found the thread containing the graphic and discussion in question:

Interesting effects of roads on trade, started by Ceasar the Great

[Scouse Gits]

Marquis - the character is a "two thirds" symbol 2/3 for both the Railroad & Flight modifiers - and there are several places where the multiplier is given as x1 followed by a symbol which you may or may not be able to read which is in fact a 'half' 1/2 - hope this clarifies the situation ...

[fittstim]

I think the post is good. Three suggestions though:

1) Fix the problem with the symbols. They sure look like 0's to me so I was confused about the multipliers for flight and railroad.

2) There are two "multipliers" listed as "halving factors" and one listed as "modifier". I'm not sure of the difference between a modifier and a multiplier. And the halving factors might be changed to decimals and restated as "multipliers.

3) A single, long drawn out formula with each of the "multipliers" listed out would be nice - so as to avoid the confusion I listed above.

Otherwise, you have my congratulations!

[Marquis de Sodaq]

Thanks, SG. The halves do show up, apparently my font does not care about thirds...

[William Keenan]

Originally posted by fittstim
I think the post is good. Three suggestions though:

1) Fix the problem with the symbols. They sure look like 0's to me so I was confused about the multipliers for flight and railroad.

2) There are two "multipliers" listed as "halving factors" and one listed as "modifier". I'm not sure of the difference between a modifier and a multiplier. And the halving factors might be changed to decimals and restated as "multipliers.

Both fixed.

3) A single, long drawn out formula with each of the "multipliers" listed out would be nice - so as to avoid the confusion I listed above.

Please draft an example of what you have in mind so that I can understand your suggestion better.

[Scouse Gits]

William, you still state at the top of the paper that the formula gives both the gold & science bonus - until the science capping is fathomed this is not true ...

Term has just started here (I give my first lecture in a couple of hours) so I probably will not have any time for testing, but if I find some time I shall run some independent tests for you ...

[DaveV]

Nice work. Please take the following as constructive criticism.

1) I think the document should include an explanation of how distance is calculated, since that's been a topic of some discussion on the board. I calculated distance as 1 per square, 1.5 per diagonal, so in my attached files the distances to Carthage are Utica 3.5, Malaca 4, Panormus 4.

2) Some differences in trade route bonuses (see attached files). For 650 BC file, if I maximize arrows, Carthage has 24 arrows and Malaca 8. Bonus from your formula is 19; actual payoff is 16. If I move workers to generate 17 and 5 arrows, formula bonus is 13; actual is 10.

For the 600 BC file, if I maximize arrows, Carthage has 34, Panormus 7, and Utica 9. Calcuated payoff Utica->Carthage (with road bonus): 28; actual is 30. Calculated payoff Panormus->Carthage (with demand bonus): 48; actual is 40.

*** Spoiler alert! The attached files are from the "laugh at a Scouse Git" game! ***

[William Keenan]

Originally posted by DaveV
Nice work. Please take the following as constructive criticism.

The whole reason I posted this thread was to garner the wisdom and experience of this forum. Input is more than welcome.

1) I think the document should include an explanation of how distance is calculated, since that's been a topic of some discussion on the board. I calculated distance as 1 per square, 1.5 per diagonal, so in my attached files the distances to Carthage are Utica 3.5, Malaca 4, Panormus 4.

Yes. I'll add this, just as soon as I understand it.

2) Some differences in trade route bonuses ...

This is really good news! I had no idea how where in the formula the flaw(s) were, but now I have a clue - my distance calculations may not have been accurate. Thanks Dave.

[DaveV]

William,

See the Diplomats and Spies thread for a complete explanation of how to calculate distance (4.31ff).

[La Fayette]

There is a very clear explanation of distance calculation in civ2 given by SlowThinker in the thread 'Info: diplomats and spies'
(tested it myself many times: always OK)

[La Fayette]

It seems that your connection is slightly faster than mine
(BTW I did notice that Alexandria was in civil disorder, but SG1 explained that I probably forgot to press Ctrl+N, so I played it as it was = nice gift to the Romans and other second class civs)

[Xin Yu]

Should "flight" be "advanced flight"?

Building airports on both cities will cancel the effect of discovering "advanced flight"; also, connecting two cities with railroad will cancel the effect of discovering "railroad". Strangely the prerequisite for building airports is "radio", not "advanced flight".

[William Keenan]

Originally posted by Xin Yu
Should "flight" be "advanced flight"?

Nope. Flight is the one.

Building airports on both cities will cancel the effect of discovering "advanced flight"; also, connecting two cities with railroad will cancel the effect of discovering "railroad". Strangely the prerequisite for building airports is "radio", not "advanced flight".

The Airport bonus has no connection to the Flight, Advanced Flight, or Radio techs. If two cities with airports get the bonus whether or not that civilization knows how to fly. Funny, eh?

Similarly, the railroad trade bonus is not diminished by a civilization's inability to build box-cars.

[William Keenan]

distance = (length of longer side of rectangle) + 0.5 * (length of shorter side of rectangle)

This is the distance formula, right?

[Scouse Gits]

Yes WK - that is correct - and the same as that given by Smash above - travel diagonally at 1.5 a square until you are orthogonal and then run home at 1 per square - I shall try an ASCII diagram ...
O . . . . . .
. x . . . . .
. . x . . . .
. . . x z z O

Distance = 3 'x' @ 1.5 each + 3 'z' @ 1 each = 7.5
or
Distance = 6 + 0.5(3) = 7.5

or at least this is how I understand it - I would be happy to be corrected if I am in error ...

[La Fayette]

Originally posted by Scouse Gits
- I shall try an ASCII diagram ...
O . . . . . .
. x . . . . .
. . x . . . .
. . . x z z O

Distance = 3 'x' @ 1.5 each + 3 'z' @ 1 each = 7.5
or
Distance = 6 + 0.5(3) = 7.5

or at least this is how I understand it - I would be happy to be corrected if I am in error ...

No need to correct you AFAIK.
This is also how I understand it, and I have tested it many times.

[debeest]

Am I wrong in thinking that under "Foreign Delivery" you've accidentally placed the text from the beginning of "Commodity Demand" instead of the text you meant to put there?

[debeest]

I just tried delivering three caravans, and in each case the actual payoff was almost exactly 90% of that predicted by your formula. I'm pretty sure that I did the calculations and measurements and so on correctly, but I'd be happy to send you a save if you want to check it out yourself (and if I can remember how). The fact that the results are wrong is disappointing, but the consistency is encouraging because it might mean that only one factor needs tweaking.

Oops. I just realized that I saved AFTER delivering. Still, there are numerous camels lurking in my capital, and I'd bet that a test with remaining ones would give similar results.

[debeest]

Tried it myself with a bunch more caravans. Mostly they came in at about 10% less than predicted by your formula, some closer, one exactly right. Of course, this is all from one game situation, post-navigation, pre-flight, etc. Clearly the formula isn't entirely right, and sadly it's probably not just one factor that's off, but it's far closer than anything I've previously seen. For a long time I've been looking for a way to predict payoff in order to figure out whether it's worth delivering caravans at all. This will help a lot. Thanks!

[William Keenan]

Originally posted by debeest
Am I wrong in thinking that under "Foreign Delivery" you've accidentally placed the text from the beginning of "Commodity Demand" instead of the text you meant to put there?

You are exactly right, debeest. It's fixed now. Thanks.

Originally posted by debeest
Tried it myself with a bunch more caravans. Mostly they came in at about 10% less than predicted by your formula, some closer, one exactly right. Of course, this is all from one game situation, post-navigation, pre-flight, etc. Clearly the formula isn't entirely right ....

When I did the derived the formula I incorrectly counted diagonals as 1 instead of 1.5. This, of course, caused a big problem with the formula. I'm currently working on a revised formula.

[SlowThinker]

Originally posted by DaveV
William,

See the Diplomats and Spies thread for a complete explanation of how to calculate distance (4.31ff).

DaveV, your link link goes to the old Apolyton forum. This is the link to the updated Info: diplomats and spies thread.

[markusf]

In trying to brush away the rust, I have been combing civ2 sites for basic info and have come across the nitty-gritties of trade routes which might bear reproducing here (as I have not seen this tabling in the threads I have come across here). Source is the Scrolls of Wisdom website which acknowledged the original post by Robert Lancaster to alt.games.civ2
"The amount of trade and the bonus payment you get for establishing a trade route between two cities with a caravan or a freight depends on quite a few factors. The formulas below contain all the details.
Trade = ( trade of home city + trade of destination city + 4 ) / 8
Note that it does not directly depend on city size or distance. The following (cumulative) modifiers apply:
Both cities are yours -50%
Freight instead of caravan +50%
Cities connected by road +50%
Cities connected by rail +50%
Cities on different continents +100%
Airports in both cities +50%
Superhighways in home city +50%
The one time bonus payment is calculated as follows:
Payment = ( ( distance + 10 ) x ( trade of both cities ) ) / 24
It increases if the destination city demands one of these goods (double these figures if the city is not yours):
Silver, Cloth, Wine +50%
Silk, Spice, Gems, Gold +100%
Oil +150%
Uranium +200%
The final bonus payment figure is then doubled during the first 200 game turns or until both Navigation and Invention are discovered. It is reduced by one third after the discovery of Railroad, and by another third after the discovery of Flight. "

[La Fayette]

Originally posted by markusf
have come across the nitty-gritties of trade routes which might bear reproducing here (as I have not seen this tabling in the threads I have come across here). Source is the Scrolls of Wisdom website which acknowledged the original post by Robert Lancaster to alt.games.civ2

It is very kind of you to provide this, markusf.
But this is already in the GL (look at 'scrolls').
The problem is that many of us think that R. Lancaster's results need to be improved, and that's what William is trying to do.