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There are a lot of threads running around talking about "mathhammer", and about how the normal person doesn't want to spend all day calculating probabilities of dice rolls.
Enter the "Comprehensive Probabilistic Combat Statistics."
I have calculated all probabilities for all possible rolls (2+, 3+, etc) for up to 20 dice.
The PDF is downloadable, 11 pages long, and weighs 70kbs.
Download it here (right click save as), or you can click the link for online viewing.
If you find typos, or things that could be better, please let me know.
Last edited by Fizzics; August 25th, 2009 at 19:54.
page 1, first paragraph "introduction [to] the theory"
page 1, third paragraph "zero, one, [two, three,] or four marines"
page 1, first paragraph "binomial distr[i]bution"
page 2, first paragraph "on a single di[e]"
page 2, middle "successive di[e] roll"
page 2, middle "[f]or the number of dice rolled"
Why can't I use your tables with vehicles?
(If my vehicle hits on a 3+ and has 6 shots and I want to know the probability of scoring two hits I can look that up in the table - vehicle or not.
If I have two meltaguns shooting at a Chaos Predator and I want to know the probability of scoring one hit I can look that up in the table - vehicle or not.
Why did you note this exception and what did you mean?)
Nicely done, great you took the time.
I am a fan of mathhammer (because I work with probabilities and statistics professionally). Since calculating the probability for exactly a certain number of successes is fairly easy and quick to do I would find it more helpful to have a table for summarized probabilites (exactly 5 hits _or more_, as in "at least 5 hits") because those force you to do the calculation multiple times if you're doing it all in the head (i.e. with any software or at least pen&paper).
I have incorporated such tables in my tacticas, for example the one on difficult terrain, where it is important to know how likely it is to be able to cover _at least_ a certain distance through difficult terrain as opposed to exactly a certain distance.
Moreover the tables are a little unwieldy. It would be more pleasant to have graphs to read from, the summarized probability functions plotted would make a good source of useful information.
In the end there's still the problem that the probabilities of the tables do not give out the really relevant information but instead only chunks to work with - probabilities that still have to be multiplied with one another in order to get the information that really counts.
Example: most often you want to know the likelihood of killing at least four marines instead of hitting a certain number of them. You would then have to add the probabilities of hitting exactly four marines and all of them failing their save, hitting exactly five marines and four or all of them failing their save, hitting exactly six marines and four, five or all of them failing their saves, etc... up to the maximum number of shots your squad can dish out. [Note that this example was done assuming that all hits succeed to wound. It gets even a hell of a lot more complicated if you put in the to wound rolls - so you see where this is going and what my point is.]
That's a lot of mental work to do, so after all you'll just end up approximating with averages sooner or later. (Example: if I want four marines to die and 1/3 of those fail their saves on average, I will have to hit at least 12 marines. I can add up the probabilities of hitting 12, 13, 14, etc marines up to the maximum number of shots I dish out and work with that probability - better than nothing, while doing all the math without approximating with averages gets practically impossible to do in your head for those situations - much easier and thoroughly possible with two melta guns versus a specific armor value though.)
So your work's usefulness for me is rather limited at this time, but rep nonetheless!
Thanks for the corrections and feedback, I wil correct the typos and see if I can flesh out a few other things for you tomorrow when it is not so late.
u put alot of time and effort, but im probs never gonna use it, haha.
It's time for the grot rebellion!
Orks W:34 D:11 L:0