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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?
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?
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