Eve of the Apocalypse: Twilight

4th revision >_<

As I have to learn stochastic, I'm taking another try to find out Heartstops kill chance.
For the DarkNemesis under you who dont know what Heartstop is, it is a talent that kills a unit when Exhaustion stuns it, if it is already stunned.

Exhaustion on level 6 has a 16% chance per second to stun a unit for 3 seconds and lasts 85 seconds.

Units:

Every second there is a 16% chance to cause a stun. Then there is a 0.84³= 59.3% chance in the next 3 seconds not to die or 40.7% chance to die.

So we have a 0.16*0.407= 6.5% chance to die per second.

For 83 seconds we have 0.935^83 = ~0.377% to survive one cast of Exhaustion.

But units tend to not live that long anyway, so we take a look at smaller times:

5 seconds: 28.5% kill chance
10 seconds: 49% kill chance
15 seconds: 63.5% kill chance

Heroes:

8% to get stunned, 22% to get another stun while stunned (=stunlocked).

Of course that calculation may be completly wrong, so feel free to correct me.
Also not sure if 2 or 3 stuns can happen during another stun which trigger Heartstop.

for one thing pick commas or periods, don't mix

but uh, I think stuns can be reapplied when a unit is already stunned, although it depends on the way it was coded.

anyway the rest of it looks good I think

Alright, my statistical skills're a little rusty, but I'll do my best

Every second there is a 14% to cause a stun. Then there is a 0,86³= 63,6% chance in the next 3 seconds not to die or 36.4% to die.

EDIT: Nevermind, actually went back and familiarized myself with what the spell did. Numbers, so far as I can tell, work.

Also t1 and t3. >_>

There are essentially three rolls for a twice in a row stun. In which case, would be (.14^2) then there's three rolls for that, now we calc for of those three rolls, chances of -not- getting that chance, to get chance of not of the chance you would inverse it via 1-(.14^2). To calculate the chance of -not- within three rolls, it's [1-(.14^2)]^3. To go back to chance of twice within three rolls inverse back to chance of, 1-{[1-(.14^2)]^3}

.14^2 = a
1 - a = b
b^3 = c
1 - c = d
d = chance

Yeah, yeah, as I said, my stats're a little rusty. Been a couple years since I took the course. Although I was pretty sure it was (1-p)^n, so (1-.14)^2, not 1 - (.14)^2.

EDIT: Also, plug'n'chugging with what Perhaps said comes out with a chance to die of 5.76%. Assuming those numbers are correct.

Cleaned up the first post a bit.

Periods - commas mixup was propably due to constant rewriting of the first post until I found the right way to tackle this problem.

You do consecutive chance of something to the power of how many rolls/tries. When you look at "at least once," you need to calculate with "not" because the "not" chance would have to be consecutive for the "at least once" to never happen, or otherwise, the chances of it not happening decrease per roll, which means the chances of it happening increase.

In this case the 14% chance has to happen twice, each consecutive time that's called for the lesser the chances of it happening so in this case .14^2 will be a less of a chance giving your chance for instant kill to happen. Assuming it will do an instance for all 3 second, "1, 2, 3", you would have, 1|2, 1|3, 2|3, 3 possibilities. Of course the more possibilities of instant kill, the greater the chance that the instant kill will happen. .14^2 is chance for instant kill, incorporating the consecutive occurrence of not happening for that chance in 3 rolls would be [1-(.14^2)]^3.

I forget the quick way to calculate a total amount of possibilities without counting. -_-

Gotcha, starting to come back to me now.

Updated with the far more interesting hero kill chance:

7% to get stunned, 20% to die when stunned, 1.4% chance to die per second. 44.1% to survive one minute of exhaustion.

The kill chance only applies to units.

And i'm pretty damn sure I tested it and found it to be working...

DarnYak

I just tested it again and didnt score a single kill between lvl 19 and 26 with it (Exhaustion level 4 and 5). I even saw a sorc getting multiple stuns in rapid succession without any effect.

I hoped but didn't believe the instantkill works with heroes.
Could you tell us if 2 or 3 stuns can trigger Heartstop during another stun = if the stun duration is rather 2.99 or 3.01 seconds.

The actual spell values for level 6 are 8% chance and 85 seconds duration.
Units:
5 seconds: 28.5% kill chance
10 seconds: 49% kill chance
15 seconds: 63.5% kill chance

Dekar wrote:Could you tell us if 2 or 3 stuns can trigger Heartstop during another stun = if the stun duration is rather 2.99 or 3.01 seconds.

Probably not.

And just incase it isn't clear, the instant death triggers while the unit is stunned from anything, not just exhaustion.

DarnYak

Hmm, I only thought about stunned by something else and then stunned by Exhaustion again, not the other way around.
Cluster rockets and magic gen come to mind, as there is no hero with a good unit stun skill.

And if Heartstop works it may be good enough on its own to make people take Exhaustion instead of his chain plague.

exhaustion with gravel's tremor might make for a deadly combo.

What about flare?

Like anyone is using that!
... ok, fine, I dont like to play Ember so I forgot about that.

Tremor and Exhaustion will be the ultimate AoE slow/stun combo in -AP, someone should test it.