08-03-1999 23:06									#1
	The Great Rounding Debate - Resolved! Support Apolyton, buy Civilization: The Boardgame

I'm sure many of you have wondered about how CivII calculates 50% bonuses on odd numbered attack and defense strengths. You've probably also wondered if the bonuses are added together, multiplied, or some combination of addition and multiplication. And when, if ever, are numbers rounded down? Well, amigos, I believe that I have the answers.

I performed a series of tests recently to try and figure out exactly what is happening. The results: all bonuses are multiplied together and no rounding ever occurs.

On to the details: First off, I have Civ II with FW. I changed all units to have 10, i.e. 100, hit points to reduce random fluctuations. I used cheat mode to create all units and reveal the map. After participating in a battle, all survivors were destroyed. In other words, battles were always between full strength units.

I started off by attacking 10 non-vet Warriors with 10 vet Warriors. If there was rounding, the matches should be fairly equal. No contest. The vet Warriors won all 10 times, all still in the yellow.

Then I attacked 10 vet Warriors with non vet Horsemen. If strengths were rounded up, again the matches should be fairly equal. But all 10 Horsemen won handily. Conclusion: vet Warriors have a strength somewhere between 1 and 2. Since the manual explicitly states a 50% bonus, vet Warriors are almost certainly 1.5.

O.K., those tests were all done on Grassland. How about Forests? I attacked 10 non vet Warriors in Forests with 10 non vet Warriors. Sure enough, all the Forest Warriors prevailed. How about fortifying? Same result: fortified Warriors won all 10 times. I repeated the above tests but attacked with Horsemen instead. As you might expect, Horsemen won every time. Conclusion: non vet Warriors in Forests have a defense between 1 and 2. Fortified non vet Warriors also have a defense between 1 and 2. Again, the most likely strength value is 1.5.

What about combinations of bonuses? I attacked 10 vet Warriors in Forests with Horsemen. If the two 50% bonuses were additive, I would expect the matches to be fairly equal. But the Warriors walked away winners every time, although all were in the red. When attacked by Archers however, the Archers easily won. Conclusion: vet Warriors in Forests have a strength between 2 and 3. Multiplying the two 50% bonuses together (1.5 * 1.5) yields 2.25 which seems to be the most likely answer. For completeness, I repeated the above tests using fortified vet Warriors on grass and fortified non vets in Forests. The results were identical except that 1 Horseman won against a fortified vet Warrior. I blame that on random variation.

Finally, I stuck fortified, vet Warriors in Forests and attacked with Archers. 9 out of 10 of the Warriors prevailed. 1 Archer won. When I attacked 10 new, identical Warriors with Knights, all the Knights won. Conclusion: fortified, vet Warriors in Forests have a strength between 3 and 4. Most likely answer is 3.375, 1.5 * 1.5 * 1.5. The one abberation from the expected result I am blaming on random variation.

That's it! That's as far as I got. Still to do: City Walls vs. Fortress vs. fortifying - how many bonuses count. Pikemen and AEGIS special bonuses. Coastal Fortress, SAM and SDI bonuses. Marines vs. walled cities. What bonuses do ships caught in port receive?

	09-03-1999 02:54									#2
	Full PM-box? Change here!

Yeeesh! And I thought I went over the top testing all them damn pikemen. You go, Sieve!

How about a new "you know you've played too much civ when..."

you test the results of percentages in combat.

	09-03-1999 09:45									#3
	Support Apolyton buy from Amazon

Woo-hoo! Now I can quote effective combat strength ratings to my friends at school! I could make them up anyway, because nobody else I know memorizes unit stat tables, but it's still fun. :,\

	09-03-1999 13:45									#4
	Browse Apolyton AD-FREE

Ah, maybe my hair colour will go back from grey to brown again?

There never seem to be consensus about this. I gave up all efforts to figure these things out a long time ago and mostly rely on my gaming experience (often not successfully, I'm a crappy warmonger).

Sieve Too, what about scrambling fighters? Is it their attack or defense factor that counts?

Carolus

	09-03-1999 21:34									#5
	Support Apolyton

Sieve-too;
Could you run those tests with unmodified units? I am always suspicious of modified units. I also note that for warriors, the factors could be additive. A fortified vet warrior could be 1.5x1.5=2.25 as you say. But a vet warrior at 1.5 with a 50% bonus for fortification(.75) added is also 2.25.
I had always assumed that rounding happened at each calculation, but perhaps it only happens at the end. Your tests clearly indicate that a vet warrior is 1.5 not 1.0.

	10-03-1999 10:33									#6
	Increase Your PM Length

geofelt: Vet status never granted the Warrior any better standing than non vet fortifying or non vet sitting in a Forest. In each case, the Warrior's strength was 1.5. Therefore, it's my conclusion that there is nothing special about the vet status bonus.

Also note that a combination of any 2 bonuses (vet-fortifed, vet-Forest, forest-Fortified) yielded the same results: a strength between 2 and 3, almost certainly 2.25.

When all three bonues applied, the strength appeared to be between 3 and 4. Additive bonuses could not have achieved this (1.5 + 0.75 + 0.75 = 3).

My claim is that there is no rounding at any point in the calculation. All tests indicate non-rounded strengths are used in the calculations.

Re: altered units. My goal was to reduce the localized effects of bias in the pseudo random number generator. Battles between 1(10) hp units require only 10 to 19 random numbers. Battles between 10(100) hp units require 100 to 199 random numbers. The chance of bias is far greater in a smaller sequence of pseudo random numbers. We've all seen the occasional unlucky Archer lose when attacking a Phalanx. I was trying to reduce this occurance.

	10-03-1999 00:15									#7
	Lose 30 kilos (of popups)

I doff my hat, and as chairman confer upon you the OKM, Order of the Knights of Meticulosity.

	29-12-1999 00:58									#8
	Lose 30 kilos (of popups)

*bump* per current question...

	15-04-2001 17:58									#9
	Support Apolyton buy from Amazon

{combat formula}
{}{SlowThinker}{end2}

------------------------------
This is a post with keywords. See a thread The Great Library: a hierarchical structure" thread.

	16-04-2001 02:00									#10
	Support Apolyton buy from Amazon

Actually there seems to be consensus that rounding does indeed occur to 1/8th of a point. Although, you have done a good job, Sieve Too, you have got past the point of 1/8th in your tests, so you couldn't see the rounding yet.

	16-04-2001 05:39									#11
	Increase the size of your Attachments

Guess what? This debate has been RESOLVED AND DOCUMENTED in the thread info: Combat Modifiers and Calculation (GL)!

Thanks Marko Polo (in next post), I'll leave just the link for any new readers... I hadn't noticed the start date.
------------------
"There is no fortress impregnable to an ass laden with gold."
-Philip of Macedon
[This message has been edited by Marquis de Sodaq (edited April 16, 2001).]

	16-04-2001 12:35									#12
	Increase Your PM Length

Marquis et al.

This is two years old thread, started at March 1999. The reason why this is now on top is that Slowthinker has written the keywords post. IMHO this old thread could have let forgotten in the dark past of the Civ2 knowlage (spelling?). It's only confusing people.

	16-04-2001 17:18									#13
	Increase Your PM Length

I am sorry. I hope my new signature will solve the problem:
------------------------------
This is a post with keywords. See The Great Library: a hierarchical structure" thread.
This may be an old thread. It has got to the top of the forum because of this post.