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I failed my stat class. Whatever, it's not important. It's only school. What IS important though is figuring out probabilities in gaming! (i'm joking of course. i mean i really did fail stat but, yeah...)
Anyway, i was wondering how to calculate the probability when you have dependent dice rolls (specifically trying to figure out 40k stuff if anyone was wondering).
IE if chance to hit is X, to wound is Y and to not save is Z, then X*Y*Z=chance to kill (for infantry). If i however get multiple to hit rolls, how do i figure out the net chance to kill?
For a 96 year old I'd be surprised if you remembered any of your stats class even if you had passed:rolleyes:
http://www.librarium-online.com/foru...earchid=265166
Ciao
Stonehambey
Just out of curiosity, wouldn't it be better to work out what they will save as opposed to what they won't? Or is it dependant on what their save is? Or does it really matter the way its worked out?
Not to reward failure to search, or anything, but this isn't really a hard question to answer.
I'm assuming that you are asking what the overall probability to hit is if you get a re-roll. Let's say that your probability to hit without the re-roll is p. The probability that you don't hit on the roll of the die, then, is 1-p. But you have a re-roll, so you get to roll again. The probability that you miss the first time, and the second time as well, is (1-p)^2 as the rolls are statistically independent. Now the probability that you hit either time is just the probability that you don't miss both times, and that is 1-(1-p)^2. Substitute this number in for X (in the formula in your original post).
For example, suppose you are shooting with BS 4, twin-linked (in 40K), that you are shooting a Strength 4 weapon against a target with toughness 4 and that your target gets a 3+ save. The probability that you hit on the roll of a die is 2/3. So the probability that you hit with your re-roll is 1-(1-(2/3))^2=8/9. The probability that you deal an unsaved wound is 8/9 * 1/2 * 1/3 = 4/27.
Edit: I noticed that in your original post you described the To Hit, To Wound, and Save rolls as "dependent". I should note that they are statistically independent. That's why you can work out overall probabilities by multiplying them together, after all.
Tyranids / Skaven / Pan Oceania
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no, not reroll. multiple rolls. assault 3, heavy 4, and so on. not twin linked, twin linked is simple enough to figure out. ie what's the chance to kill at all when you have 4 shots?
and chance to not save works better because then all the chances are "chances to fail", it's just less confusing to calculate, don't have to reverse it or nothing. though i suppose you COULD do chance TO save.
and i did a search, and searched extensively google, so stop telling me to just search... i did...
So you are asking: given n shots, each with probability p of dealing an unsaved wound, what is the probability that at least one unsaved wound is dealt?
The probability that a given shot fails to deal an unsaved wound is 1-p. Since the shots are independent, the probability that each shot fails to deal an unsaved wound is (1-p)^n. The probability that at least one shot deals an unsaved wound is then 1-(1-p)^n.
For example suppose you are firing 4 shots, with BS 3, non-twin-linked, strength 4 versus toughness 4 with a 4+ save. (The example is contrived to make the calculation easy.) The probability of a given shot dealing an unsaved wound is 1/2 * 1/2 * 1/2 = 1/8. The probability over all four shots of dealing at least one unsaved wound is 1-(1-(1/8))^4 = 1695/4096.
Edit: inadvertent smiley
Tyranids / Skaven / Pan Oceania
UK Student? Take part in the Student Nationals at Sheffield University, the weekend after Easter weekend 2008 - wargaming, roleplaying, CCGs, board games - see www.studentnationals.org for more details!
Suppose you fire n shots, each with probability p of dealing an unsaved wound, and you want to know what the probability is of dealing PRECISELY k unsaved wounds with those n shots. This probability is nCk * p^k * (1-p)*(n-k) where nCk is the binomial coefficient. So if you were firing 4 shots, each with probability 1/8 of dealing an unsaved wound (as in the last example), the probability of dealing PRECISELY 2 unsaved wounds is 4C2 * (1/8)^2 * (7/8)^2 = 6 * (1/8)^2 * (7/8)^2 = 6 * 7^2 / 8^4 = 6 * 49 / 4096 = 147 / 2048 which to four decimal places is 0.0718.
If you wanted to know what the probability is of dealing AT LEAST or AT MOST k unsaved wounds then it becomes impractical to do using calculations by hand once n gets beyond the artificially small numbers I've been using. You would have these options:
1) If your computer has an office suite with a spreadsheet application, find and learn how to use the cumulative distribution function of the binomial distribution.
2) If you have a programmable calculator or access to a computer algebra package then you can program it to do the calculation for you.
3) You could obtain a set of statistics tables from somewhere and use the table of the cumulative distribution function for the binomial distribution. If working with very large numbers of shots you would also want to find out about Poisson and normal approximations to the binomial distribution and learn how to use those tables too.
Tyranids / Skaven / Pan Oceania
UK Student? Take part in the Student Nationals at Sheffield University, the weekend after Easter weekend 2008 - wargaming, roleplaying, CCGs, board games - see www.studentnationals.org for more details!
Coo Hammerite.
You seem to imply it is possible to calculate PV using statistical calculatiuons based on statistical data on the stat lines.(How logical !!)
For a given 'phase space' of nominal game, minus variable variables that can cancel each other out ,so can be ignored.
So a PC program could accuratley allocate PV, in seconds ,so all the devs would have to do is restrict certian overpowering unit combos/sizes in the army/force composition lists.
That would certainly speed up codex releases wouldnt it?
And lead to a more provable 'ballanced' game?
But then GW wouldnt be able to 'massage' PV /in game cost effectivness, to aid marketing of certain models ,minatures would they? :shifty:
No ,just let GW list 'artisticaly creative' rules and PV to go with thier artistically creative hobby.:wacko:
I mean its not like gamers pay good money, for poorly written unballanced subjective rules and army composition lists is it?:cry:
Oh they do dont they!!!(
TTFN
Lanrak.