Ok, I got another one.
The weird, asymmetric effects of +x% vs Y-type.
In case you didn't know, if a unit has +x% vs Y (Axeman/Rifleman/etc bonuses), it behaves exactly as you'd expect on defense, giving a straight bonus percentage of whatever it states. But when attacking, it does NOT behave that way. The "bonus" is actually a malus applied to the defender. And it starts by first removing bonuses the defender has, and then, if there is any left over "bonus" in excess of the defender's bonuses, it takes the defender's base strength and divides it by (100% + [remaining bonus of attacker]).
Example: City Raider 3 Treb vs fortified Longbow in a hill city with City Defender 2 but cultural defense of 0:
Treb has +100% city attack on its own, which acts exactly like CR does, and gets an additional +75% from CR 3.
The longbow has +25% due to the hill. It's own ability gives it an additional +25% on hills. It has the same but for cities as well, for another +25%. Fortify gives it +25% too. Finally, CD 2 gives it +45% in cities. Total: +145%
So the Trebs first 145% of 175% of bonuses is used to remove the LB's 145% of defensive bonuses. That leaves 30% of attacker bonus, so the longbow strength is then divided by (100% + 30%, or 1.3) and is set to 4.61538.... (probably displayed as 4.62 but maybe 4.61).
Example using one that has defense (as the CR promos and Treb ability don't actually do anything on defense, as they are attacking only):
Infantry vs Marine. Infantry gets +25% vs Gunpowder units, which Marine is. Assuming flat ground, no fortify in each case:
Infantry attacks: 20 vs 19.2. Marine Attacks: 24 vs 25. The power ratio for both is 1.041666 in favour of the infantry, but the infantry has slightly different displayed odds for some reason (honestly, that just surprised me as I wrote this. That's a separate gripe entirely!) 65.0 is displayed for the infantry attack, 35.3 is displayed for the marine attack (This should have added to 100%? but out of this rabbit hole for now).
Give them both combat 1 (where combat promos always adds to the unit's strength _unlike_ +x% vs y for some reason):
Infantry attacks: 22 vs 20.86. Infantry has the advantage. Marine attacks: 26.4 vs 27. The power ratio is now different for the two combats. 1.05465.... vs 1.022727. As such I no longer expect the combat odds to add to 100% and they don't (though they didn't the first time either, when I did expect them to.....). 65.7% vs 36.5%
Give them Combat 2:
Infantry gets 24 vs 22.85 when it attacks and 65.5% odds. Marine gets 28.8 vs 29. Ratios: 1.0503 vs 1.006994 (less than 1% difference for the second one, which is still enough to have the marine down to 37.4%, worse than 3-2 against).
Combat 3:
Infantry gets 26 vs 25.2, Marine gets 31.2 vs 31. The odds are 64.3% for the Infantry attacking and 62.8% for the Marine attacking. Note, again, a greater than 3:2 advantage despite a less-than-1%-greater strength.
Why is this system so needlessly counterintuitive?
This is why the Vulture sucks, when, at first glance, it might seem that it should be equal to or better than an axeman in all situations (and is instead weak to axemen).
Intuitively, you'd think it was 7.5 vs 7.5 in either case, but instead it's 6 vs 6.25 when the vulture attacks and 5 vs 4.8 when the axe attacks and the vulture loses both ways.
If you want a take-away from all of this, it's as follows: when attacking, massive bonuses like that are at their best in terms of hanging the odds when you are "punching up" to a unit with higher base strength and lower bonuses. So your upgraded CR3 Maceman > Rifleman can-opener is affecting the odds the most when he is attacking blimp-damaged unpromoted infantry, not well promoted longbows. But then you don't want to risk losing him, hahaha (also, have to cross that strength differential! 30% difference right there, which is why the infantry in that last example needs to be blimp-damaged)
)
or same situation with machine gun in city with high walls and castle when melee units are attacking
vs one with 3
