Need help with Blade Cascade math

[ac_noj]

I thought I had the math for Blade Cascade all worked out, but something has come to light that makes me doubt the result.

I was calculating it's damage by working out the chance of each result:

Miss Chance
Hit Chance x Miss Chance
Hit Chance x Hit Chance x Miss Chance
Hit Chance x Hit Chance x Hit Chance x Miss Chance
Hit Chance x Hit Chance x Hit Chance x Hit Chance x Miss Chance
Hit Chance x Hit Chance x Hit Chance x Hit Chance x Hit Chance
------------------------------------
Sum of the probabilities above

My problem is that the sum of the probability of every result does not equal 1...and I'm pretty sure that when you look at chance of every event occuring and add them together, they're supposed to total 1.

So either my math is wrong, or I've missed a possible outcome, or they don't need to total 1....which is it?

 

[spinmd]

The last outcome would implicitly include other outcomes that can't occur due to the artificial 5 attack limit. So since you know the probabilities of the first 4 outcomes, the 5th becomes 1- those 4 probabilities.

At least that's how I think it would work.

 

[ac_noj]

Urgh never mind, I just realised that I was adding the miss chance on the last entry. >_<

 

[MeMeMeMe]

Here's probably the simplest way to calculate the damage:
Hit Chance + Hit Chance ^2 + Hit Chance ^3 + Hit Chance ^4 + Hit Chance ^5
(Hit chance as a percentage, a fraction of 1)
Yes, the total can exceed 1.
Multiply that by the damage for a single attack.

 

[ac_noj]

Don't worry I've got it all sorted now. The top one is the Blade Cascade / Armor Splinter combo, both builds are humans and demigods: