Would he do it? (Updated with solution and follow-up question)

[アイドンノウくん]

A wizard is planning to kill a barb with hp charm, who is also afk outside sirry. However, based on his experience, he determines that he is only managed to reduce the barb's hp by 30% without critical hit, and 60% with critical hit, for every skill he uses. The barb uses a script which activates AD automatically when his hp is below 30% and his charm is in cooldown. The wizard has a critical rate of 25%; and he will stop attacking and run back to sz after the first five skills. Each skill takes 2 seconds to deal damage on the target. He wants to know his odd of killing the barb before he runs back to sz. If it is more than 50%, then he will do it; else he will not do it.

Question: Would he do it?

Answer: His odd of killing the barb is 20.313%, which is lower than 50%. So, he would not do it.


A wizard is planning to kill a barb with hp charm, who is also afk outside sirry. However, based on his experience, he determines that he is only managed to reduce the barb's hp by 30% without critical hit, and 60% with critical hit, for every skill he uses. The barb uses a script which activates AD automatically when his hp is below 30% and his charm is in cooldown. The wizard has a critical rate of 25%; and he will stop attacking and run back to sz after the first five skills. Each skill takes 2 seconds to deal damage on the target. He wants to know his odd of killing the barb before he runs back to sz. If it is more than 50%, then he will do it; else he will not do it. 

Question: Would he do it?

Answer: His odd of killing the barb is 20.313%, which is lower than 50%. So, he would not do it.

Below are the only possible scenarios (in the sequence of 1st-2nd-3rd-4th-5th skill) where the barb will die:
Crit - Crit - Crit 
Crit - No Crit - No Crit - Crit
No Crit - Crit (does not trigger AD since charm is not in cd when the skill hits) - Crit - Crit
No Crit - No crit - Crit - Crit
No crit - Crit (does not trigger AD since charm is not in cd when the skill hits) - No crit - No crit - Crit
No crit - No crit - No crit - No crit - Crit

Thus, the chance of having one of the six scenarios is 20.313%. 

Follow-up questions:
Anyway, the wizard decided to do it since he is a tryhard. An archer and a sin are watching from sz. They see that the wizard had at least two skills that did not crit out of his first three skills. Based on this information, before the wizard casts his fourth skill, they make a bet. If the wizard successfully kills the barb at the end, the archer would pay the sin 5k ec; else if the barb does not die at the end. the sin would pay the archer 3k ec. 

The sin is very happy with the deal; because he thinks his expected return is higher than the archer's. On the other hand, the archer thinks the sin is stupid to accept the bet; since the sin is in obvious disadvantage. 

Who is correct?

[ABBADON]

Wouldn't a better question be "Will he fire combo and relieve himself of all that stress by making it a 1 shot?" 

[Calamity]

Wouldn't a better question be "Will he fire combo and relieve himself of all that stress by making it a 1 shot?"  

no he won't, we will bet and see who wins

[๖ۣۜĐomgrath]

Cool equation, but you're not factoring in the fact that 'Spark' exists.

Assuming the barbarian is AFK, his Cornered Beast would likely be off of cooldown, therefore once 'Spark' skill has been used, it's likely the barb will be killed within that first critical hit, or the one following the initial hit.

Also, we're not factoring in the barbarians gear. All contributing factors to this equation of survival. 

[eternalagony23]

Wouldn't a better question be "Will he fire combo and relieve himself of all that stress by making it a 1 shot?"

I agree +1 

[Moon]

Someone do the math dude

[Nea]

case 1
we assume he critics the 1st skill (25%)
he now ticked the target
he now critics once again , barb's hp reaching 40%
he critics once again, dropping from 40% to 0% without triggering the script  = this leaves a 1.56% chance of doing it, doing 3 critics in a row in 6 seconds out of 10 mentioned above
case 2
we assume he doesnt critic the 1st skill
60%, 2 seconds passed
ticked, 4 seconds passed
he now has full hp
he hits the target , lowering hp to 70%, 6 seconds passed
he hits the target, lowering hp to 40% , 8 seconds passed
25% chance of hiting last one critic and killing target, 10 seconds passing
case 3
we assume he doesnt critic 1st skill
60%, 2 secs passed
full hp , 4 seconds passed
he critics, 25% chance, 40% hp , 6 secs passed
he critics once again, 25% chance, dead , 8 secs passed
there are around 12 scenarios that may occur
he has a nice chance of killing
anyway , all this sums up around 8% chance of doing it w.o ticking the script
+ if we take in consideration AD's cooldown
he will do it after 20 seconds anyhow
but since u wanna know the chance of doing it be4 going to sz
guess its around 8% as i said, im not that good at maths but i guess it sums around right...

[Nea]

ugh im stupid
sec
he can kill with
70 - full - 40 - 0 = win
70 - full - 70 - 40 - 0 = win
70- full - 70 - 40 - 10 - fail kill ( 4be4 + 6 seconds after charm tick + AD lasting 5 , 11 , full hp again)
40 - full - 40 - 10- fail kill he has used only 4 seconds after , ad triggers  lasts 5 seconds, he has 1 sec left, casts last skill = kill succeed with ad triggering
40 - full -40 - 0 = win
70- full - 70 - 10 - AD triggered, 4 seconds +5 =, 1 sec left after  AD triggers, kills = kill success

he has
5/6 chance of doing it
which leads to 83% ?

im sure i've missed a scenario sorry
fck i forgot the times 1st time
well if i failed , sorry
did my best

[Gio]

the WB is afk so u can freely switch to fire, gaining 15% = 40% crit.
 Now u didnt say if the WB is vit or str neither if the wiz is Demon or Sage, but anyway:
IF its just 5 damaging skills then the wiz is free to 3 spark,ice prisoning,virtue and so on, but ill just drop u down a scenario of a wiz vs a vit WB with a total of 5 skills without fire spark:
there r many ways but i wanna go  back watching my movie so ill tell u a fast one: if the wiz can drop off by 30% at max with one skill, even counting it crit so 15% per normal one, with a 3 spark u can get it hitting for at least 65% which leads the WB using his AD, u can even use ur extreme poison to make it sure.4 skills left, go to max distance, drop undine, a projectile skill and an insta damage one, there u heiro the WB if u crit, otherwise u can drop ice prison, undine and extreme poison and going for a lucky crit on a BiD or on a MS even tho BiD hits harder so i suggest that one, or u ice prison, undine use some projectile and some delayed skill to get em hitting at same time and heiroing, in all those combos u can add a mortal reversion at half HP just to make it all safer.I could keep going forever, spark aint needed not cuz Wizs r OP but cuz u need to think about how chaning ur skills thing that 99,9% of wizs dont. On a side note if u are sage the best way is dropping a BiD at half hp and going for direct heiro or for that nice 70%+ crit bonus.
See best is me i win ingame and on fanta-PVP on forum

[Burdette]

hmm after reading question I thought "Aight lets just scroll down and see Sebi's answer" ...always there

[アイドンノウくん]

Cool equation, but you're not factoring in the fact that 'Spark' exists.

Assuming the barbarian is AFK, his Cornered Beast would likely be off of cooldown, therefore once 'Spark' skill has been used, it's likely the barb will be killed within that first critical hit, or the one following the initial hit.

Also, we're not factoring in the barbarians gear. All contributing factors to this equation of survival.

The problem specifies that the wizard will only attack with his first 5 skills, each reduces the barb's hp by either 30% (without crit) or 60% (with crit), subject to a crit rate. Of course, in practice, things are much more complicated. 

[アイドンノウくん]

ugh im stupid
sec
he can kill with
70 - full - 40 - 0 = win
70 - full - 70 - 40 - 0 = win
70- full - 70 - 40 - 10 - fail kill ( 4be4 + 6 seconds after charm tick + AD lasting 5 , 11 , full hp again)
40 - full - 40 - 10- fail kill he has used only 4 seconds after , ad triggers  lasts 5 seconds, he has 1 sec left, casts last skill = kill succeed with ad triggering
40 - full -40 - 0 = win
70- full - 70 - 10 - AD triggered, 4 seconds +5 =, 1 sec left after  AD triggers, kills = kill success

he has
5/6 chance of doing it
which leads to 83% ?

im sure i've missed a scenario sorry
fck i forgot the times 1st time
well if i failed , sorry
did my best

You did very well, almost there. But it seems like you got a little confused when you said the chance was 5/6 or 83%, based on 5 out of the 6 scenarios succeed. By saying that, you mean all the 6 scenarios have an equal chance to happen. However, in your previous reply, you said the chance of killing the barb with 3 crits in a row was 1.56%, which is correct. So, how is this 1.56% translated to the 1/6 or 16.67% as the chance of having 1 of the 6 scenarios, which is the scenario of having 3 crits in a row in your second reply?
Leaving that aside, there are actually 26 scenarios in total, of which 6 of them have a dead barb at the end, and the rest have a barb afk with AD in effect at the end. So, the barb's script does make a huge difference. 
After doing some calculations, the chance of having one of the 6 successful scenarios is 20.313%. 

[Nea]

You did very well, almost there. But it seems like you got a little confused when you said the chance was 5/6 or 83%, based on 5 out of the 6 scenarios succeed. By saying that, you mean all the 6 scenarios have an equal chance to happen. However, in your previous reply, you said the chance of killing the barb with 3 crits in a row was 1.56%, which is correct. So, how is this 1.56% translated to the 1/6 or 16.67% as the chance of having 1 of the 6 scenarios, which is the scenario of having 3 crits in a row in your second reply?
Leaving that aside, there are actually 26 scenarios in total, of which 6 of them have a dead barb at the end, and the rest have a barb afk with AD in effect at the end. So, the barb's script does make a huge difference.
After doing some calculations, the chance of having one of the 6 successful scenarios is 20.313%.

well as i said, im not a big fan of maths, i just did my best with the 'knowledge' i had
im glad i got some points right LOL
could u tho, explain how u reached to that answer of 26 scenarios stated? im rlly curious of the ones i've missed

[アイドンノウくん]

well as i said, im not a big fan of maths, i just did my best with the 'knowledge' i had
im glad i got some points right LOL

Yes, the way you came up with the 1.56% is the right way; and it can get you to the correct answer, after you figure out the rest of the possible scenarios, which is not that difficult at all. But you probably need a big piece of paper...LOL  

[Burdette]

nerds