Hearthpwn

Quote from STiGY »

Kinda simple math here but just gonna explain if anyone doesn't know.

X = Amount of minions on the board
X+1 = Amount of Possible Targets

So if there is 3 minions on the board, X, then there are 4 possible targets, X+1.

To work out the probability of each of the targets being hit by a single shot then you need to do this (X+1)/100 

So if there is 4 possible targets then its 4/100 which is 25% or 1/4. 

For a minion Y to be hit Z amounts of times you need to do another equation. Let us let Z=3. So if minion Y is hit 3 times then the chance of it hitting each time is 25% but as it is being hit 3 times the chance of it hitting is 25% x 25% x 25% or 25%^3. This works out to be around 0.01%, chance if my math is correct. I believe it as as in Hearth Troldens videos when he points out the chance of something happening X amount of times then it ends up really small. However I do think this only works in consecutive hits on a certain target.

With your questions about killing a 4 health minion. There is a total of 8 shots meaning that a maximum of 4 can go to the minion and a maximum of 8 can go to the character. I cannot answer that as you would need to go even deeper in probability and unfortunately at only 16 I cannot answer that :c but there is basically how it works. If someone can correct me if I'm wrong that would be great (Haven't done maths since my exam 2 months ago xD)

This isn't really correct at all, since 4/100 is 4% not 25%.

I'm pretty sure based off of the "If you die you can't be hit anymore" thing that you want to look at

(# ways to get hit 4 times)/ (# ways to get hit 4 or less times)

Quote from Shakrazam »

(...) To evaluate a probability you need to divide the number of desired outcomes by the number of all posible outcomes. (...)

You can't do that if different outcomes have different probability. In this case they do have different probability.

Quote from Shakrazam »

Quote from wtk300 »

Quote from Shakrazam »

(...) To evaluate a probability you need to divide the number of desired outcomes by the number of all posible outcomes. (...)

You can't do that if different outcomes have different probability. In this case they do have different probability.

by outcome I dont mean certain minion dieing or not. By outcome I mean different combination of missle attacks. For example the first three missles to hit a minion and the next 5 missles to hit the hero has the same probability as the first 4 missles to hit the hero and the second for to hit the minion.

I know. Still, they don't. Probability to hit particular target changes based on what was hit by earlier missiles. If you hit minion with 4 HP 4 times probability to hit it with last missile is 0%. If you kill all minions chance to hit face is 100%.

If we call targets A, B and C. ABBCABBA and BBCAAAAA can have different probabilities depending on the HP of each target.

Quote from tempest8008 »

 

Each time the RNG rolls in this case there is a 50% chance of hitting either target.
There is no probability calculation to make here.

If I toss a coin 1000 times and it comes up heads 999 of them, if you were to ask me the odds on my next toss of it comes up heads again I would HAVE to say 50/50.  The former results do not impact the next toss.  You're multiplying the chances of things happening together here, but the chances do NOT multiply together.  They are distinct events.

Of the 9 possible conditions (0 hits to 8 hits) 5 of them (4,5,6,7,8) mean the minion dies.  It does not matter if the minion is missed by the first 4 hits if the next 4 hit him, the condition is met.  He can't be hit 5,6,7, or 8 times, so those would automatically go to the Hero.  Better to look at it from the other direction.  The minion LIVES if he is hit 0, 1, 2, or 3 times.  There are only 9 possible combinations between the 2 targets and 4 of those combinations mean the minion lives.

There's no true probability calculation to be made here.  With distinct 50/50 events occurring on each hit, you have to look the the number of combinations, not the likelihood of a given combination occurring, because it is irrelevant.  Of the 9 possible things that can happen, 5 of them mean the minion dies.  Each of those possibilities is equally likely.

You are correct in saying that individual events don't affect each other, but you are missing one thing though. The first hit is 1/2, but in order to hit it a second time that is another 1/2 on top of that 1/2. So there is a 1/4 chance of it hitting the minion twice in a row as there are 4 possible outcomes from 2 missiles and 2 targets. (MM, MH, HM, HH where M = minion and H = hero). That is the probability I'm talking about. I hope this clears up the confusion.

Well, taking the whole sequence is just shortcutting taking each one individually. When you shortcut like this you're using a probability algorithm called a distribution, of which there are dozens if not hundreds of different ones. 

And Tempest8008, The probabilities aren't equally likely because there is a greater number of equally likely combinations that lead to certain results. if you don't believe Tehstool, believe me. I'm an actuary.  ;)

Quote from Shakrazam »

Quote from wtk300 »

Quote from Shakrazam »

Quote from wtk300 »

Quote from Shakrazam »

(...) To evaluate a probability you need to divide the number of desired outcomes by the number of all posible outcomes. (...)

You can't do that if different outcomes have different probability. In this case they do have different probability.

by outcome I dont mean certain minion dieing or not. By outcome I mean different combination of missle attacks. For example the first three missles to hit a minion and the next 5 missles to hit the hero has the same probability as the first 4 missles to hit the hero and the second for to hit the minion.

I know. Still, they don't. Probability to hit particular target changes based on what was hit by earlier missiles. If you hit minion with 4 HP 4 times probability to hit it with last missile is 0%. If you kill all minions chance to hit face is 100%.

If we call targets A, B and C. ABBCABBA and BBCAAAAA can have different probabilities depending on the HP of each target.

Yes ,but what was hit earlier is a part of the combination. The way I handle it is  that combination ABBBBBAAC cannot exist if minion B has 4 health so I dont count it (substract it from all possible combinations) and its not part of the equation. You take the probabilities of the individual missle hits occuring whereas you should take the probability of the whole sequence of missles occuring.

Let's make it simpler. One minion with one HP - target A. And your opponent with 8 HP - target - B. There are 9 outcomes

ABBBBBBB, BABBBBBB, BBABBBBB, BBBABBBB, BBBBABBB, BBBBBABB, BBBBBBAB, BBBBBBBA, BBBBBBBB

Do you think they are equally likely?

You are correct; once a minion's health has been exhausted the distribution calculation breaks down. We can, however, calculate the probability of the minion not dying and subtract from 1 to get the probability of it dying using the distribution.

I presented this calculation on the previous page of this thread and it is indeed 63.7%.

Okay, now I'm looking at it more like a bell curve with 0 damage at one end and 8 at the other.

There's a greater distribution in the middle of combinations of 4 damage hits, covering more of the curve.

I can see why it would be higher than my 5/9.

Thanks to Tehstool and Betterliving.  My afternoon has just flown by, and now it is the weekend!
(and no, I won't attempt to explain any of this to my 5yr old :P, though I will tell her Daddy was wrong today, and learned something)

 

Quote from Shakrazam »

Quote from wtk300 »

Let's make it simpler. One minion with one HP - target A. And your opponent with 8 HP - target - B. There are 9 outcomes

ABBBBBBB, BABBBBBB, BBABBBBB, BBBABBBB, BBBBABBB, BBBBBABB, BBBBBBAB, BBBBBBBA, BBBBBBBB

Do you think they are equally likely?

Are they not? Ofcourse they are.

 

They are not. Probability to hit minion with the first missile is 50%. With the last one is 0.5 ^ 8. Just imagine it, killing that Young Priestess with last shot of Avenging Wrath is far less likely than with the first one.

No it isn't.  Ignore the first 7 shots in this case, because each is a 50/50 chance to hit and it's a one hit kill.

Your last shot is a 50/50 chance to kill, same as the first one.

The probability of getting that particular combination is low, but the chance to hit that Young Priestess on the 8th Avenging Wrath hit is 50%, assuming only the minion and the Hero are targets.

Thanks guys. I was making the same mistake tempest was. Thinking about it harder obviously a 4/4 distribution is way more likely than 8-0 :) 

Quote from Elitesparkle »

(...)
The chance to kill a 7 health minion alone on the battlefield is the same as the one to kill a 3 health and a 4 health minions.
(...)

Your answer is correct for one 7 hp minion, but this assumption above is wrong. It is more likely to kill two minions than one even if their total hp is the same. Chance to hit face is different in each case. More than that, it would be different if we change minions hp from 4 and 3 to 5 and 2.

Quote from Elitesparkle »

The chance to kill a 7 health minion alone on the battlefield is the same as the one to kill a 3 health and a 4 health minions.

This assumption is not correct unless you consider the 7 health minion's P to be 2/3.
I don't believe we can use this shortcut, however, because if either of the minions die the probability of the minion getting hit becomes 50%. That's why Avenging wrath with 3+ targets is difficult to calculate; the distribution changes partway through on SOME BUT NOT ALL strings of outcomes, so we can't use just a multinomial or just a binomial distribution to calculate it.

So i did the math (actually my script did) and the answer is 11.86% - thats the chance to kill both 4hp and 3hp minions with Avenging Wrath.

Going back to the OPs question. The simple, not mathy, answer is that it is higher than 50% because of the limiting factor of the minions health. I will attempt to explain using only the concepts and logic. I do not know upper level maths well enough to explain beyond this and my explanation may not be the best. But my limited understanding of probabilities leads me to believe that so far everyone's explanations have been SUPER confusing.

Think of it this way. Basically probabilities is a shortcut way to look at EVERY SINGLE possible outcome. So if you had two targets and 8 shots, there are 256 orders that the shots could hit in. Lets call that our logical outcome. Where did I get that number? Its simple. I just multiplied the number of targets (2) together for each shot (8). So 2x2x2x2x2x2x2x2, later denoted as 2^8 = 256. (Quick Proof of concept. Lets say you had 2 targets, A and B, and 3 shots. So 2^3 is 2x2x2=8 They could hit 8 ways 1.AAA 2.AAB 3.ABA 4. ABB 5.BAA 6.BAB 7.BBA 8.BBB, no other combos right? okay moving on)  

So, there are 256 logical outcomes when there are 2 targets and 8 shots. Of those 256 logical outcomes there are 128 outcomes in which the minion gets hit 4+ times. So on the surface it is a 50/50 chance that the minion gets hit 4 times. However in the example given the minion only has 4 health. So rather than being a quick calculation of finding our logical outcomes, it is a calculation that needs to take whether or not those outcomes or possible or impossible. (Obviously our minion cant get hit 5+ times)

I dont even know how to get into the calculations to eliminate the impossible outcomes but suffice it to say that if you were looking at ONLY the possible outcomes then 63% of those have the minion getting hit 4 times.

Quote from Sparker700 »

the math is wrong. Every time it hits something it increase the chance of hitting the other one. 

1st Hit - Target 1 (50%) / Target 2 (50%) 

2nd Hit - Target 1 (33%) / Target 2 (66%)

and so on....

This is only right if something dies after a hit. The probabilities of something getting hit does not change unless the number of targets changes. Otherwise it isnt truely random

Chance to kill all enemies with Avenging Wrath when opponent controls:

Young Priestess - 99.61%

Concealed Auctioneer - 63.37%

Concealed Auctioneer with 7 hits - 50%

Concealed Auctioneer + Thalnos - 48.92% (50.53% just to kill Auctioneer)

Boulderfist Ogre - 3.52%

3/3 + 4/4  - 11.87%

2/2 + 5/5  - 9.36%

If someone is interested in details, here are all 280 possible outcomes for the 4 and 3 hp minions case with probabilities of each outcome next to it:

0 - face, 1 - 4hp minion, 2 - 3hp minion

<pre>[0,1,1,1,1,2,2,2] 0.051440329218107005
[0,1,1,1,2,1,2,2] 0.03429355281207134
[0,1,1,1,2,2,1,2] 0.022862368541380892
[0,1,1,1,2,2,2,1] 0.022862368541380892
[0,1,1,2,1,1,2,2] 0.03429355281207134
[0,1,1,2,1,2,1,2] 0.022862368541380892
[0,1,1,2,1,2,2,1] 0.022862368541380892
[0,1,1,2,2,1,1,2] 0.022862368541380892
[0,1,1,2,2,1,2,1] 0.022862368541380892
[0,1,1,2,2,2,1,1] 0.03429355281207134
[0,1,2,1,1,1,2,2] 0.03429355281207134
[0,1,2,1,1,2,1,2] 0.022862368541380892
[0,1,2,1,1,2,2,1] 0.022862368541380892
[0,1,2,1,2,1,1,2] 0.022862368541380892
[0,1,2,1,2,1,2,1] 0.022862368541380892
[0,1,2,1,2,2,1,1] 0.03429355281207134
[0,1,2,2,1,1,1,2] 0.022862368541380892
[0,1,2,2,1,1,2,1] 0.022862368541380892
[0,1,2,2,1,2,1,1] 0.03429355281207134
[0,1,2,2,2,1,1,1] 0.051440329218107005
[0,2,1,1,1,1,2,2] 0.03429355281207134
[0,2,1,1,1,2,1,2] 0.022862368541380892
[0,2,1,1,1,2,2,1] 0.022862368541380892
[0,2,1,1,2,1,1,2] 0.022862368541380892
[0,2,1,1,2,1,2,1] 0.022862368541380892
[0,2,1,1,2,2,1,1] 0.03429355281207134
[0,2,1,2,1,1,1,2] 0.022862368541380892
[0,2,1,2,1,1,2,1] 0.022862368541380892
[0,2,1,2,1,2,1,1] 0.03429355281207134
[0,2,1,2,2,1,1,1] 0.051440329218107005
[0,2,2,1,1,1,1,2] 0.022862368541380892
[0,2,2,1,1,1,2,1] 0.022862368541380892
[0,2,2,1,1,2,1,1] 0.03429355281207134
[0,2,2,1,2,1,1,1] 0.051440329218107005
[0,2,2,2,1,1,1,1] 0.0771604938271605
[1,0,1,1,1,2,2,2] 0.051440329218107005
[1,0,1,1,2,1,2,2] 0.03429355281207134
[1,0,1,1,2,2,1,2] 0.022862368541380892
[1,0,1,1,2,2,2,1] 0.022862368541380892
[1,0,1,2,1,1,2,2] 0.03429355281207134
[1,0,1,2,1,2,1,2] 0.022862368541380892
[1,0,1,2,1,2,2,1] 0.022862368541380892
[1,0,1,2,2,1,1,2] 0.022862368541380892
[1,0,1,2,2,1,2,1] 0.022862368541380892
[1,0,1,2,2,2,1,1] 0.03429355281207134
[1,0,2,1,1,1,2,2] 0.03429355281207134
[1,0,2,1,1,2,1,2] 0.022862368541380892
[1,0,2,1,1,2,2,1] 0.022862368541380892
[1,0,2,1,2,1,1,2] 0.022862368541380892
[1,0,2,1,2,1,2,1] 0.022862368541380892
[1,0,2,1,2,2,1,1] 0.03429355281207134
[1,0,2,2,1,1,1,2] 0.022862368541380892
[1,0,2,2,1,1,2,1] 0.022862368541380892
[1,0,2,2,1,2,1,1] 0.03429355281207134
[1,0,2,2,2,1,1,1] 0.051440329218107005
[1,1,0,1,1,2,2,2] 0.051440329218107005
[1,1,0,1,2,1,2,2] 0.03429355281207134
[1,1,0,1,2,2,1,2] 0.022862368541380892
[1,1,0,1,2,2,2,1] 0.022862368541380892
[1,1,0,2,1,1,2,2] 0.03429355281207134
[1,1,0,2,1,2,1,2] 0.022862368541380892
[1,1,0,2,1,2,2,1] 0.022862368541380892
[1,1,0,2,2,1,1,2] 0.022862368541380892
[1,1,0,2,2,1,2,1] 0.022862368541380892
[1,1,0,2,2,2,1,1] 0.03429355281207134
[1,1,1,0,1,2,2,2] 0.051440329218107005
[1,1,1,0,2,1,2,2] 0.03429355281207134
[1,1,1,0,2,2,1,2] 0.022862368541380892
[1,1,1,0,2,2,2,1] 0.022862368541380892
[1,1,1,1,0,2,2,2] 0.0771604938271605
[1,1,1,1,2,0,2,2] 0.0771604938271605
[1,1,1,1,2,2,0,2] 0.0771604938271605
[1,1,1,1,2,2,2,0] 0.154320987654321
[1,1,1,2,0,1,2,2] 0.03429355281207134
[1,1,1,2,0,2,1,2] 0.022862368541380892
[1,1,1,2,0,2,2,1] 0.022862368541380892
[1,1,1,2,1,0,2,2] 0.051440329218107005
[1,1,1,2,1,2,0,2] 0.051440329218107005
[1,1,1,2,1,2,2,0] 0.10288065843621401
[1,1,1,2,2,0,1,2] 0.022862368541380892
[1,1,1,2,2,0,2,1] 0.022862368541380892
[1,1,1,2,2,1,0,2] 0.03429355281207134
[1,1,1,2,2,1,2,0] 0.06858710562414268
[1,1,1,2,2,2,0,1] 0.03429355281207134
[1,1,1,2,2,2,1,0] 0.06858710562414268
[1,1,2,0,1,1,2,2] 0.03429355281207134
[1,1,2,0,1,2,1,2] 0.022862368541380892
[1,1,2,0,1,2,2,1] 0.022862368541380892
[1,1,2,0,2,1,1,2] 0.022862368541380892
[1,1,2,0,2,1,2,1] 0.022862368541380892
[1,1,2,0,2,2,1,1] 0.03429355281207134
[1,1,2,1,0,1,2,2] 0.03429355281207134
[1,1,2,1,0,2,1,2] 0.022862368541380892
[1,1,2,1,0,2,2,1] 0.022862368541380892
[1,1,2,1,1,0,2,2] 0.051440329218107005
[1,1,2,1,1,2,0,2] 0.051440329218107005
[1,1,2,1,1,2,2,0] 0.10288065843621401
[1,1,2,1,2,0,1,2] 0.022862368541380892
[1,1,2,1,2,0,2,1] 0.022862368541380892
[1,1,2,1,2,1,0,2] 0.03429355281207134
[1,1,2,1,2,1,2,0] 0.06858710562414268
[1,1,2,1,2,2,0,1] 0.03429355281207134
[1,1,2,1,2,2,1,0] 0.06858710562414268
[1,1,2,2,0,1,1,2] 0.022862368541380892
[1,1,2,2,0,1,2,1] 0.022862368541380892
[1,1,2,2,0,2,1,1] 0.03429355281207134
[1,1,2,2,1,0,1,2] 0.022862368541380892
[1,1,2,2,1,0,2,1] 0.022862368541380892
[1,1,2,2,1,1,0,2] 0.03429355281207134
[1,1,2,2,1,1,2,0] 0.06858710562414268
[1,1,2,2,1,2,0,1] 0.03429355281207134
[1,1,2,2,1,2,1,0] 0.06858710562414268
[1,1,2,2,2,0,1,1] 0.051440329218107005
[1,1,2,2,2,1,0,1] 0.051440329218107005
[1,1,2,2,2,1,1,0] 0.10288065843621401
[1,2,0,1,1,1,2,2] 0.03429355281207134
[1,2,0,1,1,2,1,2] 0.022862368541380892
[1,2,0,1,1,2,2,1] 0.022862368541380892
[1,2,0,1,2,1,1,2] 0.022862368541380892
[1,2,0,1,2,1,2,1] 0.022862368541380892
[1,2,0,1,2,2,1,1] 0.03429355281207134
[1,2,0,2,1,1,1,2] 0.022862368541380892
[1,2,0,2,1,1,2,1] 0.022862368541380892
[1,2,0,2,1,2,1,1] 0.03429355281207134
[1,2,0,2,2,1,1,1] 0.051440329218107005
[1,2,1,0,1,1,2,2] 0.03429355281207134
[1,2,1,0,1,2,1,2] 0.022862368541380892
[1,2,1,0,1,2,2,1] 0.022862368541380892
[1,2,1,0,2,1,1,2] 0.022862368541380892
[1,2,1,0,2,1,2,1] 0.022862368541380892
[1,2,1,0,2,2,1,1] 0.03429355281207134
[1,2,1,1,0,1,2,2] 0.03429355281207134
[1,2,1,1,0,2,1,2] 0.022862368541380892
[1,2,1,1,0,2,2,1] 0.022862368541380892
[1,2,1,1,1,0,2,2] 0.051440329218107005
[1,2,1,1,1,2,0,2] 0.051440329218107005
[1,2,1,1,1,2,2,0] 0.10288065843621401
[1,2,1,1,2,0,1,2] 0.022862368541380892
[1,2,1,1,2,0,2,1] 0.022862368541380892
[1,2,1,1,2,1,0,2] 0.03429355281207134
[1,2,1,1,2,1,2,0] 0.06858710562414268
[1,2,1,1,2,2,0,1] 0.03429355281207134
[1,2,1,1,2,2,1,0] 0.06858710562414268
[1,2,1,2,0,1,1,2] 0.022862368541380892
[1,2,1,2,0,1,2,1] 0.022862368541380892
[1,2,1,2,0,2,1,1] 0.03429355281207134
[1,2,1,2,1,0,1,2] 0.022862368541380892
[1,2,1,2,1,0,2,1] 0.022862368541380892
[1,2,1,2,1,1,0,2] 0.03429355281207134
[1,2,1,2,1,1,2,0] 0.06858710562414268
[1,2,1,2,1,2,0,1] 0.03429355281207134
[1,2,1,2,1,2,1,0] 0.06858710562414268
[1,2,1,2,2,0,1,1] 0.051440329218107005
[1,2,1,2,2,1,0,1] 0.051440329218107005
[1,2,1,2,2,1,1,0] 0.10288065843621401
[1,2,2,0,1,1,1,2] 0.022862368541380892
[1,2,2,0,1,1,2,1] 0.022862368541380892
[1,2,2,0,1,2,1,1] 0.03429355281207134
[1,2,2,0,2,1,1,1] 0.051440329218107005
[1,2,2,1,0,1,1,2] 0.022862368541380892
[1,2,2,1,0,1,2,1] 0.022862368541380892
[1,2,2,1,0,2,1,1] 0.03429355281207134
[1,2,2,1,1,0,1,2] 0.022862368541380892
[1,2,2,1,1,0,2,1] 0.022862368541380892
[1,2,2,1,1,1,0,2] 0.03429355281207134
[1,2,2,1,1,1,2,0] 0.06858710562414268
[1,2,2,1,1,2,0,1] 0.03429355281207134
[1,2,2,1,1,2,1,0] 0.06858710562414268
[1,2,2,1,2,0,1,1] 0.051440329218107005
[1,2,2,1,2,1,0,1] 0.051440329218107005
[1,2,2,1,2,1,1,0] 0.10288065843621401
[1,2,2,2,0,1,1,1] 0.0771604938271605
[1,2,2,2,1,0,1,1] 0.0771604938271605
[1,2,2,2,1,1,0,1] 0.0771604938271605
[1,2,2,2,1,1,1,0] 0.154320987654321
[2,0,1,1,1,1,2,2] 0.03429355281207134
[2,0,1,1,1,2,1,2] 0.022862368541380892
[2,0,1,1,1,2,2,1] 0.022862368541380892
[2,0,1,1,2,1,1,2] 0.022862368541380892
[2,0,1,1,2,1,2,1] 0.022862368541380892
[2,0,1,1,2,2,1,1] 0.03429355281207134
[2,0,1,2,1,1,1,2] 0.022862368541380892
[2,0,1,2,1,1,2,1] 0.022862368541380892
[2,0,1,2,1,2,1,1] 0.03429355281207134
[2,0,1,2,2,1,1,1] 0.051440329218107005
[2,0,2,1,1,1,1,2] 0.022862368541380892
[2,0,2,1,1,1,2,1] 0.022862368541380892
[2,0,2,1,1,2,1,1] 0.03429355281207134
[2,0,2,1,2,1,1,1] 0.051440329218107005
[2,0,2,2,1,1,1,1] 0.0771604938271605
[2,1,0,1,1,1,2,2] 0.03429355281207134
[2,1,0,1,1,2,1,2] 0.022862368541380892
[2,1,0,1,1,2,2,1] 0.022862368541380892
[2,1,0,1,2,1,1,2] 0.022862368541380892
[2,1,0,1,2,1,2,1] 0.022862368541380892
[2,1,0,1,2,2,1,1] 0.03429355281207134
[2,1,0,2,1,1,1,2] 0.022862368541380892
[2,1,0,2,1,1,2,1] 0.022862368541380892
[2,1,0,2,1,2,1,1] 0.03429355281207134
[2,1,0,2,2,1,1,1] 0.051440329218107005
[2,1,1,0,1,1,2,2] 0.03429355281207134
[2,1,1,0,1,2,1,2] 0.022862368541380892
[2,1,1,0,1,2,2,1] 0.022862368541380892
[2,1,1,0,2,1,1,2] 0.022862368541380892
[2,1,1,0,2,1,2,1] 0.022862368541380892
[2,1,1,0,2,2,1,1] 0.03429355281207134
[2,1,1,1,0,1,2,2] 0.03429355281207134
[2,1,1,1,0,2,1,2] 0.022862368541380892
[2,1,1,1,0,2,2,1] 0.022862368541380892
[2,1,1,1,1,0,2,2] 0.051440329218107005
[2,1,1,1,1,2,0,2] 0.051440329218107005
[2,1,1,1,1,2,2,0] 0.10288065843621401
[2,1,1,1,2,0,1,2] 0.022862368541380892
[2,1,1,1,2,0,2,1] 0.022862368541380892
[2,1,1,1,2,1,0,2] 0.03429355281207134
[2,1,1,1,2,1,2,0] 0.06858710562414268
[2,1,1,1,2,2,0,1] 0.03429355281207134
[2,1,1,1,2,2,1,0] 0.06858710562414268
[2,1,1,2,0,1,1,2] 0.022862368541380892
[2,1,1,2,0,1,2,1] 0.022862368541380892
[2,1,1,2,0,2,1,1] 0.03429355281207134
[2,1,1,2,1,0,1,2] 0.022862368541380892
[2,1,1,2,1,0,2,1] 0.022862368541380892
[2,1,1,2,1,1,0,2] 0.03429355281207134
[2,1,1,2,1,1,2,0] 0.06858710562414268
[2,1,1,2,1,2,0,1] 0.03429355281207134
[2,1,1,2,1,2,1,0] 0.06858710562414268
[2,1,1,2,2,0,1,1] 0.051440329218107005
[2,1,1,2,2,1,0,1] 0.051440329218107005
[2,1,1,2,2,1,1,0] 0.10288065843621401
[2,1,2,0,1,1,1,2] 0.022862368541380892
[2,1,2,0,1,1,2,1] 0.022862368541380892
[2,1,2,0,1,2,1,1] 0.03429355281207134
[2,1,2,0,2,1,1,1] 0.051440329218107005
[2,1,2,1,0,1,1,2] 0.022862368541380892
[2,1,2,1,0,1,2,1] 0.022862368541380892
[2,1,2,1,0,2,1,1] 0.03429355281207134
[2,1,2,1,1,0,1,2] 0.022862368541380892
[2,1,2,1,1,0,2,1] 0.022862368541380892
[2,1,2,1,1,1,0,2] 0.03429355281207134
[2,1,2,1,1,1,2,0] 0.06858710562414268
[2,1,2,1,1,2,0,1] 0.03429355281207134
[2,1,2,1,1,2,1,0] 0.06858710562414268
[2,1,2,1,2,0,1,1] 0.051440329218107005
[2,1,2,1,2,1,0,1] 0.051440329218107005
[2,1,2,1,2,1,1,0] 0.10288065843621401
[2,1,2,2,0,1,1,1] 0.0771604938271605
[2,1,2,2,1,0,1,1] 0.0771604938271605
[2,1,2,2,1,1,0,1] 0.0771604938271605
[2,1,2,2,1,1,1,0] 0.154320987654321
[2,2,0,1,1,1,1,2] 0.022862368541380892
[2,2,0,1,1,1,2,1] 0.022862368541380892
[2,2,0,1,1,2,1,1] 0.03429355281207134
[2,2,0,1,2,1,1,1] 0.051440329218107005
[2,2,0,2,1,1,1,1] 0.0771604938271605
[2,2,1,0,1,1,1,2] 0.022862368541380892
[2,2,1,0,1,1,2,1] 0.022862368541380892
[2,2,1,0,1,2,1,1] 0.03429355281207134
[2,2,1,0,2,1,1,1] 0.051440329218107005
[2,2,1,1,0,1,1,2] 0.022862368541380892
[2,2,1,1,0,1,2,1] 0.022862368541380892
[2,2,1,1,0,2,1,1] 0.03429355281207134
[2,2,1,1,1,0,1,2] 0.022862368541380892
[2,2,1,1,1,0,2,1] 0.022862368541380892
[2,2,1,1,1,1,0,2] 0.03429355281207134
[2,2,1,1,1,1,2,0] 0.06858710562414268
[2,2,1,1,1,2,0,1] 0.03429355281207134
[2,2,1,1,1,2,1,0] 0.06858710562414268
[2,2,1,1,2,0,1,1] 0.051440329218107005
[2,2,1,1,2,1,0,1] 0.051440329218107005
[2,2,1,1,2,1,1,0] 0.10288065843621401
[2,2,1,2,0,1,1,1] 0.0771604938271605
[2,2,1,2,1,0,1,1] 0.0771604938271605
[2,2,1,2,1,1,0,1] 0.0771604938271605
[2,2,1,2,1,1,1,0] 0.154320987654321
[2,2,2,0,1,1,1,1] 0.11574074074074076
[2,2,2,1,0,1,1,1] 0.11574074074074076
[2,2,2,1,1,0,1,1] 0.11574074074074076
[2,2,2,1,1,1,0,1] 0.11574074074074076
[2,2,2,1,1,1,1,0] 0.2314814814814815
11.8655%
I'm curious if someone can come up with correct answer without using brute force method like this.</pre>

Quote from Sparker700 »

the math is wrong. Every time it hits something it increase the chance of hitting the other one. 

1st Hit - Target 1 (50%) / Target 2 (50%) 

2nd Hit - Target 1 (33%) / Target 2 (66%)

and so on....

No. Not at all, in any realm of reality that I am aware of, is this even close to being correct. If their are two targets, then the chance to hit each is 50/50. Math doesn't care about what happened last hit. It is always 50/50 because each hit is a completely isolated incident with no statistical relationship to the previous hits. 

Quote from Snow_King »

Quote from Sparker700 »

the math is wrong. Every time it hits something it increase the chance of hitting the other one. 

1st Hit - Target 1 (50%) / Target 2 (50%) 

2nd Hit - Target 1 (33%) / Target 2 (66%)

and so on....

No. Not at all, in any realm of reality that I am aware of, is this even close to being correct. If their are two targets, then the chance to hit each is 50/50. Math doesn't care about what happened last hit. It is always 50/50 because each hit is a completely isolated incident with no statistical relationship to the previous hits. 

This would only be the case if there was some sort of pseudo-random distribution going on, which as far as I know isn't the case. This is how a lot of the math works in various MOBAs though.

Quote from Elitesparkle »

There is something strange since I've got a different value of probability with my simulation.
My result is around 6.5368% but I've used a less accurate method compared to yours.

I'd like to find a formula as well.

I've run my code and got correct results for situations that are easy to calculate with other methods, so I'm somewhat confident in it. Still, maybe i missed something for 3+ targets. Do you mind sharing your code?