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Hi chaps trying to work out the odds of a vindicare using a quad gun to kill a model with a 4+ save is the calculation someting like (im saying wounding on 2's)

(4*5*5*3) and then add 0,17 (from http://mathhammer.blogspot.co.uk/) giving me 1.625

so on average i score just over 2 wounds a turn?

http://mathhammer40k.com/

This is what i use out of interest sometimes. Hardly effects what happens in game though.

Mark kelly wrote:
Hi chaps trying to work out the odds of a vindicare using a quad gun to kill a model with a 4+ save is the calculation someting like (im saying wounding on 2's)

(4*5*5*3) and then add 0,17 (from http://mathhammer.blogspot.co.uk/) giving me 1.625

so on average i score just over 2 wounds a turn?

I'm away from books so not sure what the BS of your assassin is. But basically, to get the total chance of something you just keep multiplying the odds together, same way that when you're counting something, you just keep adding things together.

So if you hit on a 3+ and damage on a 2+, the chance of getting both is

(2/3)*(5/6) = 0.56 = 56%

That first 2/3 is just a simplified fraction: you hit on 3,4,5 & 6 (4 results) out of 1, 2, 3, 4, 5 & 6 (6 possibilities) so that's 4/6 which is the same as 2/3. The 5/6 is of course your wound on 2+.

Now the model has a 4+ Save so we're not done yet. 4+ is 3/6 chance, i.e. 1/2, so our calculation now becomes:

(2/3)*(5/6)*(1/2) = 0.28 = 28%

So with a single shot, your chance of scoring an unsaved wound is 28%.

If that's all good so far, then the final stage is actually pretty simple. You want to know your chance of killing the model, i.e. that there's at least one unsaved wound. Average wounds wont actually tell you that, they just tell you whether you're more or less likely to kill the model than 50:50. I.e. if the average wounds is greater than 1 then you know you're MORE likely to kill the model than not, but you don't know if you're 60% likely to kill it, 97% likely, or anything else!

What you actually want is an easy trick. You just need to work out the chance of not scoring any wounds at all. Which we do by doing the same thing we just did - multiplying chances together.

We've worked out that the chance of scoring an unsaved wound is 0.28 (i.e. 28%). So the chance of NOT scoring an unsaved wound must be 1 - 0.28 . 1 is certainty in probability, you see, i.e. 100%. So that's 0.72 chance.

What do we do to get cumulative probabilities again? Yep - multiply.

So with four shots out chance of NOT scoring an unsaved wound is as follows:

0.72 * 0.72 * 0.72 * 0.72

As you can see, 0.72 * 0.72 is smaller than 0.72, which makes sense - everytime you throw in another shot, the chance of not scoring an unsaved wound is getting smaller. Anyway,


0.72 * 0.72 * 0.72 * 0.72 = 0.268 = 26.8%

So that's your final answer: chance of NOT scoring an unsaved wound is 26.8%, so the chance of getting one or more is 73.2%.

Now I'm away from my books so if the assassin isn't hitting on a 3+ then you'll need to recalculate. But hopefully the above should have explained the process. If you want to calculate multi-wound results, you have to go into aomething called Binomial Distribution. I'm happy to go into as much detail as you like on any if this. I hope this is useful.

Btw, I did all if the above long-hand for the sake of explanation. You can collapse the whole thing down to the following if you like:

(1 - (1-((2/3)*(5/6)*(1/2))))^4

Cool man thanks for that - and yes its on a milti wound model - looking at killing a herald so how do you do Binomial distribution (note his bs is 8) but its a twin linked quad gun

Mark kelly wrote:
Cool man thanks for that - and yes its on a milti wound model - looking at killing a herald so how do you do Binomial distribution (note his bs is 8) but its a twin linked quad gun

Okay. Then it gets a bit more fun. You can do it all long-hand the way I just showed you, but once you get into re-rolls, multi-wounds, etc. it becomes pretty long and a lot to keep track of. That's where you get into Binomial Distribution. It streamlines things. Unfortunately you need to be either (a) good at maths or (b) have a spreadsheet or maths program. The simple and imprecise way of doing things is to work out

Give me the chance to hit, the chance to damage, the chance to save and the number of wounds and I'll give you the cumulative chances of each possible result. If you have Excel, I'll upload a spreadsheet with the formulae in so you can see how it all fits together.

So its 2+ to hit with a re-roll 2+ to wound and a 4+ save the model has 2 wounds and yes i have excel

Mark kelly wrote:
So its 2+ to hit with a re-roll 2+ to wound and a 4+ save the model has 2 wounds and yes i have excel

Okay. well as its BS8 and has a re-roll to hit, your average number of Wounds would be 1.62. So if the Herald has > 1.62 Wounds at the time that you shoot it, it will on average survive. Give me a few minutes to set up the formulae for this and I'll get you the precise chances of each outcome.

Cool thanks budy

Okay. Sorry for the delay - friend called.

I have uploaded a spreadsheet to show how this is calculated. It's on my Skydrive here: http://sdrv.ms/1cNJdpX

(And this is why I love my Surface tablet - when I need to whip up a spreadsheet in Excel and share it with gaming friends online, I can. )

There are some variables in the top left that can be adjusted - chance to hit, number of shots, etc. Over to the right of that are some basic calculations on chance to hit or damage per shot. Those are worked out as discussed in my initial reply. If you're familiar with Excel, you should be able to follow the maths in those formula.

Down the bottom is the more interesting stuff: Binomial Distribution.

Explaining the maths of that... I can do if you're really interested but it's a bit beyond the scope of a quick forum post and I don't know where you're starting from mathematically. But Excel has a function (BINOM.DIST) which does it for you - it takes a given chance, the number of trials (how many shots you have in this case) and then works out the chance of getting exactly a given number of successes. So the left column shows you the exact chance of getting 0 wounds, 1 wound, 2 wounds, etc. The column to the right of it, I sum the probabilities so that you get the cumulative chance, e.g .1+ wounds, 2+ wounds, etc.

Given that the Herald you want to take down has 2 wounds, you're looking at the probability of scoring 2 wounds, which is 35%, plus 3 wounds which is 16%, etc. So you basically have a 53% chance of one-shotting the Herald (column 3 below). Tough bugger, isn't it?

Basically, the probabilities are:

Wounds Individual Chance This number of Wounds or greater 0 13% 100% 1 34% 87% 2 35% 53% 3 16% 19% 4 3% 3%


EDIT: You'll notice a discrepancy with my comment about the average score from earlier. I was a doofus. The mean score may be 1.62 but of course it's impossible to score that on a 1d6. The fact that the numbers are discrete values (you never roll a value between 3 and 4) throws everything off when it comes to just multiplying averages. 1.62 wounds is the average you'd do per turn, but of course that doesn't tell you whether you'd kill it in a single turn, because 1.62 rounds up by necessity to 2 wounds. I believe the above values (the 53% of 2+ wounds) to be the correct values. I welcome comments from anyone if you think I've made a mistake.

That is interesting so a vindacre has a slightly better then chance to take out the herold turn1 but very likly if he gets a 2nd shot this is interesting :-). thanks again for all the help ;-)

Mark kelly wrote:
That is interesting so a vindacre has a slightly better then chance to take out the herold turn1 but very likly if he gets a 2nd shot this is interesting :-). thanks again for all the help ;-)

It's a pleasure. I enjoy probability maths. Just to clarify what I think you're saying - yes, the Vindicare with a quad-gun twin-linked (i.e. 4 shots at 2+, with re-rolls to hit), has a slightly better than 50:50 chance to one-shot a Herald. It would drop to around 43% without Twin-Linked though. If it went to Turn 2 and he took a second attempt, that's very likely a dead Herald (it's got about a 1/20 chance of surviving two turns of that, which isn't great).

Moral of the story is that anything with BS8 on a twin-linked, multi-shot, high-strength weapon, is pretty horrifying.

Yep and with his abilty to allocate wounds and they cant be look out sired away that makes me a happy camper also haveing a looks at the maths he has a 75% chance to kill the Herald if he only has a 5+ save and a 72% chance to kill a 1 wound 3+ save eg eldar warlock :-)

Thanks again there budy you have been a big help ;-)

Mark kelly wrote:
Yep and with his abilty to allocate wounds and they cant be look out sired away that makes me a happy camper also haveing a looks at the maths he has a 75% chance to kill the Herald if he only has a 5+ save and a 72% chance to kill a 1 wound 3+ save eg eldar warlock :-)

Thanks again there budy you have been a big help ;-)

I enjoyed it.

Watched some of the battle report in your sig (the Escalation one) and am half way through - so a few equations are the least I can do.

Glad you enjoyed well in the not to distant future you might well see the fruits of your labour with my grayknights/tau list

 Swastakowey wrote:
http://mathhammer40k.com/

This is what i use out of interest sometimes. Hardly effects what happens in game though.

This one is good, but leaves out FNP etc.