I made a spreadsheet to calculate the probabilities of a simple battle under the Civ3 system as I understand it. Inputs are attacker Att, attacker HP, defender Def, defender HP. Outputs are probability of attacker or defender winning, and expectation of remaining HP for attacker and defender.
So to get the 59.2% figure for a Civ2-style 10 round battle for a single HP, I set Att=3, Def=2.7, and both combatants to have 10hp. This gave me 59.2% chance of attacker winning. I then used that figure as the new Att, with a Def of 40.8 making up the rest of the 100%, and set the HP as originally specified: attacker is vet, defender is reg. That spat out 80.96% attacker wins.
OK. The source where I got the info that the Civ2 game broke the hp down into tenths was the Civ2 manual. I've know idea if it was actually used in the game.
For reference, without using subdivided HP, the outcome of this match-up should be 70.42% attacker wins.
That's what the combat calculator came up with. It looked like this:
to 5.034% AI win, no HP loss.
+5.034% - 15.633% AI win, 1 HP loss.
+15.633% - 29.579% AI win, 2 HP loss.
+29.579% - 45.075% player win, 3 HP loss.
+45.075% - 64.703% player win, 2 HP loss.
+64.703% - 85.421% player win, 1 HP loss.
+85.421% - 100% player win, no HP loss.
So on those all too frequent times that the AI spear defeats the player sword without being damaged in those circumstances, the odds are only 1 in 20 that this would happen.
Meanwhile, some preliminary stats from my combat logging: I've fired 42 artillery shots against armour, unfortified on flat land, with more than 2hp.
I got 13 misses, 23 single hits, and 6 double hits.
If I work on the assumption that the artillery's two hits are resolved independently, my spreadsheet calculates the expectations of these outcomes as 15 misses, 20 singles, and 7 doubles. That's pretty close to the observation, actually.
To compare, I can think of two other possible models for artillery rate of fire, which now seem less likely to be the correct one:
(1) Getting to roll for the second hit is dependant on the first hit being a success. In this case the expectations for 42 shots would be 25 : 10 : 7.
(2) There is a single roll to hit, followed by some other function to determine whether the damage is 1 or 2 hp, such as simply a 50/50 chance. In which case expectations would be 25 : 8.5 : 8.5.
So far in my game, the only bombardment has been some AI dromens (stats - 6 off, 2 bom, 2 def, 4 move) bombarding coastal towns of mine. They are hitting something about half the time, but most of the time I cant tell what they have hit since the unit heals up by the time the player turn comes around. A couple of towns shelled didn't have harbors or barracks yet and I was able to see what unit got it.
These were a curragh (stats - 2 off, 2 def bom, 2 def, 3 move) fortified in a mountain tile town. To find the odds for this I don't know what I should use, since ships in port I believe get a special minus. The AI has been hitting the curraghs about 75%.
The other unit I saw being hit was a land unit. It's defense was 3, and the bonus it got was 46%. The AI dromen hit it once, then missed the next time. The odds work out to be a 36% chance of successful bombardment for this. There has only been a couple of AI bombard attacks on this town. That's all I got definite so far on bombardments in this game. The player side doesn't have the resources necessary to build catapults, nor the tech for dromens yet.
I'd like to add that the AI has been showing a little uncharacteristic gray matter in how it's been running its sea forces
. I've captured all the AI cities on the continent we shared and they have a couple left on an island close off shore. Since soon after the war began the AI positioned a couple dromons between the continent and the island, effectively preventing my crossing over to there. Those same 2 dromons close the coast during the AI turn, bombarding coastal towns, then retreating out of range of possible catapult reply during the player turn. Since the player curraghs are no match for these dromons, the risk of loosing ships loaded with expensive troops has prevented the player chancing a crossing till they can build some dromons of their own to escort the troop carrying curraghs.
Meanwhile, the AI sent 2 fleets, each of 2 curraghs escorted by a dromon around the north (the fighting has been on the eastern edge of the continent) towards the west, threatening the player's cities on the northern and western coasts with possible invasion. As each fleet could have up to 8-9 troops, I had to move land forces away from the eastern fighting to follow these fleets. I now doubt the fleets have troops aboard, because they have not tried to land them, but I'll keep the troops near them just in case. But an AI curragh apparently had journeyed around the southern edge of the continent, which is another AI's territory, and dropped off 3 troops next to one of my western cities. This curragh must have got started soon after the war began, or maybe before, since it's a long trip that route. There may be more of these on the way too.
All and all, the AI sea strategy has been pretty good, much better than their land strategy had been. They picked off a few undefended weak player units in the first couple of rounds, but mostly scattered their units about unsupported where they were easy for me to mop up during the player turn. After their losses in the first couple of turns, the AI kept mostly to defending their cities and placed their hope in the rng - which has helped them more than their strategy has.
