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View Full Version : Anybody good with maths? Weapon calculations.

13-06-2009, 12:45
This might seem like an out of place post but I'm looking at doing calculations in regards to dice rolls in order to get an average chance of inflicting wounds, glances, penetrations etc.

My maths is horrible so I thought I'd try here as a first stop to see if anybody else is better with numbers than I am.

I'm trying to work out the average chance a gun has of causing a glancing hit on a vehicle with an AV of 12.

Lets assume I have a BS of 3 and a weapon that fires 4 times at strength 6, and my target has an AV of 12.

For each dice I have 0.5 chance of getting 4+ After this I require a 6+ which is 0.167 chance

So that would be 0.5 x 0.167 = 0.0835 So I have approximately an 8% chance of scoring a glance with a single dice out of four. Am I then able to multiply 8% by 4 dice to get approximately 32% chance of scoring a glance with said weapon?

Am I even close?

Thanks for any help in advance.

GooDice!

Amareo Davion
13-06-2009, 13:20
.........

:wtf:

Just find out how what you need to role to get the hit and and role the dice.
Even Inquisitor dosen't require you to find out the percentage of getting a hit.

susu.exp
13-06-2009, 13:31
Correct up to the last sentence. You will get a mean number of 0.33 glacing hits. But the probability of getting at least one glancing hit are 1-(1-0.0835)^4 = 29.4%.
Generally if you have n shots the probability of inflicting h hits is:
h!/((n-h)!*n!)*p^h*(1-p)^(n-h) where p is the probability of inflicting a glancing hit with one shot.

The same can be used if you fire at a unit, say 5 Marines rapid fire their bolters at a Squad of CMS:
To hit: 3+: 2/3
To wound: 4+ :1/2
Failed save 2-: 1/3
p=1/9~0.11
5 Marines have 10 shots, so the probability to kill h marines is:
h!/((10-h)!*10!)*0.11^h*(0.89)^(10-h)
Now, if there are less targets than shots, you add up the probabilities for h greater or equal to the number of targets to get the probability of wiping them out. The true mean number of casualties is the sum of h*p(h).

Dark Muse
13-06-2009, 13:34
This might seem like an out of place post but I'm looking at doing calculations in regards to dice rolls in order to get an average chance of inflicting wounds, glances, penetrations etc.

My maths is horrible so I thought I'd try here as a first stop to see if anybody else is better with numbers than I am.

I'm trying to work out the average chance a gun has of causing a glancing hit on a vehicle with an AV of 12.

Lets assume I have a BS of 3 and a weapon that fires 4 times at strength 6, and my target has an AV of 12.

For each dice I have 0.5 chance of getting 4+ After this I require a 6+ which is 0.167 chance

So that would be 0.5 x 0.167 = 0.0835 So I have approximately an 8% chance of scoring a glance with a single dice out of four. Am I then able to multiply 8% by 4 dice to get approximately 32% chance of scoring a glance with said weapon?

Am I even close?

Thanks for any help in advance.

GooDice!

The first half is right but the second half is wrong. It is a common mistake though. To get the probability of an event occurring at least once across multiple attempts you do not multiply by the number of attempts. You instead should figure out the odds of the event not occurring at all.

So

.5 * .167 = .0835 (probability of success with one attempt)
1 - .0835 = .9165 (probability of failure with one attempt)
.9165^4 = .7055 (probability of failure on all four attempts)
1-.7055 = .2945 (probability of success on at least one out the four attempts)

.2945 happens to be close to .32 for 4 attempts but compare 12 attempts and the flaw becomes more evident (.96 vs .649)

13-06-2009, 13:49
Cool thanks guys!

Templar Ben
13-06-2009, 14:02
I find it better to keep fractions until the final calculation so rounding errors don't skew your results.

13-06-2009, 14:21
And now whe know why this is called math hammer. It should be a game on having fun, with units you like, not trying to find a powergaming way of playing.

But I can see how effective you want to see a weapon is.

13-06-2009, 14:51
We all have different ideas as to whats fun. Personally I enjoy working out which weapon will work best in what situations or has the best chance on average of destroying something.

For me I find just as much fun off the table, preparing and theorizing about lists and stratagies as I do actually employing them.

Just different perspectives :)

Griefbringer
13-06-2009, 15:18
Generally if you have n shots the probability of inflicting h hits is:
h!/((n-h)!*n!)*p^h*(1-p)^(n-h) where p is the probability of inflicting a glancing hit with one shot.

And if my memory is working properly, this is called as "binomial distribution".

For those interested to learn more on the subject, visit your local library and look for introductory books to probability and statistics - they should cover the topic. Some also have handy charts demonstrating binomial distributions for various probabilities.

susu.exp
13-06-2009, 15:26
TBH, I wouldn´t use it for list building. But it generally doesn´t hurt to know whether you´ll be better of firing RF weapons and then taking the charge from your opponent next turn, or to forgoe shooting them and charge yourself. Now, I may not be the average person, but I do maths for fun. And if tactics is the taking of calculated risk, being able to claculate them helps. If you know what your units can do, you can use them better. And seriously, somebody who understands the maths and uses their units well will beat somebody who has C&Pd the "mathhammer effective list" from the web, without understanding it.

Plus understanding probability theory has a great many uses in all walks of life. Learning to understand the basics through 40k may make you able to get why that headline gets discussed by Mr Goldacre...

Oh, your memory serves correctly, Griefbringer. It´s a binomial distribution. Always remember that 40k is a game of left-skewed binomial distributions, and you know the most important bit: You will do worse than expected over 50% of the time.