7 replies to this topic

[Tino]

As you might know, I enjoy debating Fire Emblem, especially its characters. However, sometimes you need to talk about how durable a unit is compared to the other, and then it's handy to know what the chance of dying of your unit after x attacks is compared to the chance of dying of your opponent's unit after x attacks.

Often, people just use the average chance. This is incorrect though, because it doesn't take into account several deviations and all kinds of complicated things you don't need to worry about. So after I saw some people use this "better" method I started to try figuring out how it worked, and I think I found out, but I would like someone to confirm my math to be either correct or wrong.

Let's say a unit is 4HKOed at 60% true hit.

The true chance of that unit dying after four attacks would be (0.60)^4 * 100 = 12.96%

That was still easy. But if I want to calculate his chance of dying after, say, 8 attacks, I would do this:

(8!/(4!6!)) * (0.60)^4 * (1-0.60)^(10-4) = 23.22%

Am I doing it right? If somebody can confirm, please do so.

[Fire Blazer]

That makes no sense to me... why can't you just do (0.60)^8?

[Tino]

Since then you would be talking about if the unit would be 8HKOed if he would be hit on every attack, but he's 4HKOed, so that's impossible.

To make it a bit easier to understand:

(8 choose 4) * (0.60)^4 * (1-0.60)^(10-4) = 23.22%

[Fire Blazer]

Oh, I see... Can't you just like double the previous answer to get a good estimate?

[Tino]

Nah. ~26% =/= ~23%, and that 3 percentage points of difference can easily make the difference between which unit has the better durability.

And that would be incorrect math as well. At least, it would be incorrect for this formula (granted I did it right :/). Simply multiplying it by two would bring it back to the simple average, which isn't what I'm looking for. If you know the difference between simple average stats and real average stats (those that take the stat cap into account), you can see this as something similar, I suppose.

[Felover3]

I don't take AP Stat, so going of Algebra II/Trig...


In a geometric Sequence

Un= Ui(Un-i)^r

So Ui should be whatever it starts as .6 perhaps?
r is .6
Uviii


so

Uviii = .6(7)^.6 = 1.8

180%......I think not

So I don't have much to say until I think of something...



Edit:

I did the wrong formula....


Uviii = .6(.6)^7 = .016786

Or in percentage...

1.679%

Still think that is wrong...

[Tino]

Perhaps I should elaborate a bit on the formula I'm using...

(A choose B) * (C )^B * (1-C)^(A-B)

A = Total number of attacks
B = Total hits needed to get killed
C = True hit rate divided by 100

[Fire Blazer]

That looks right/makes sense to me.