Need some help from the math/statistics folks

[JoeHollywood]

Have a couple quickies, if someone could run the numbers for me.

3 warriors attacking 1 warrior.

no upgrades
defending warrior has full 25% fortified bonus for 5 rounds
inside a city
culture of 40%

What are the odds the 3 warriors wins

What about if the 3 are aggressive (corresponding 2v1 stats would be nice there as well)

What about if the 3 were non upgraded and the defender was aggressive

 

[Kid R]

Stack win/lose calculations like that aren't easy to do, because if the defender wins his first fight he will be damaged by a random amount, making the odds on the second fight dependent on the random result of the first. I too would be interested to see if anyone can express a simple method of calculating it.

What's the situation? Is it really going to help if somebody else does the sums this time - won't you just be stuck next time?

 

[AutomatedTeller]

It's not 100%, but they will almost certainly win.

The first 1 should hit twice, for 28 HP. The second should hit 3 times, for another 51 hp, which would leave the defender at 21, which is pretty close to 100%.

 

[cain3456]

AT, how exactly is damage calculated? By your figures, the first warrior does 14 damage per hit x2, and the second does 17 damage per hit x3.

 

[Revenant]

It mostly depends on the attack and defense and health of all the units involved. The easiest way to check this is by checking the notification logs and looking at the combat page, unfortunately this is only possible after combat. (I didn't know this existed for such a long time, it's the button underneath where it shows your income and gold. Looks like a piece of paper and a pencil.

It can help tell you if you got screwed by the RNG or not, which seems to happen to me frequently when it's a barb galley vs my galley.

Somehow this is a battle I frequently lose despite have ~66% odds of winning.

 

[Kid R]

Combat explained:

http://www.civfanatics.com/civ4/strategy/combat_explained.php

 

[AutomatedTeller]

Well, if you have a 66% chance of losing, you should lose 1/3 of the time. Which means that if your one galley fights 3 barb galleys, it will probably lose one of those fights.

I figured damage, btw, by using one of the combat calc spreadsheets.

2 completely even units (say, 2 undamaged axes on flat land without fortification) each have a 50% chance of hitting each combat round and will do 20 HP of damage, both taking 5 rounds to die and having an overall 50% chance.

When you have 2 units of different strengths, the weaker unit will do less damage per round and win less often.

The combat odds will give 100% chance of winning sometimes, which isn't strictly true - there's no such thing as automatic victory. But the odds can be so long as to be essentially 100%.