Friday, March 20, 2009

Mathhammer: Scatter dice Probability II

I've been asked since writing my previous article on scatter dice probability how to calculate the probability of a certain distance of scatter, not just a direct hit. This is actually pretty easy to calculate using the same forumla.

How do you calculate the prob of scattering 1 inch or less for a BS of 4?
- Use the same formula I showed you before, but use a BS of 5 instead of 4
- For 2 inches or less use a BS of 6 instead of a 4

That gives me the probability of 1 inch or less, how do I get the probability of just scattering 1 inch?
- Calculate the probability of scattering 1 inch or less, then subtract the probability of not scattering at all, to get the probability of just scattering 1 inch.

Lets go over some examples

To calculate the probability of a blast template scattering 2 inches or less with a BS of 4
- there are 15 ways to roll a 6 (BS of 4+2) or less on 2D6
P = ( 1/3 ) + ( ( 15 / 36 ) * 2/3 ) = .611 = 61% chance of scattering 2 inches or less with a BS of 4

To calculate the probability of a blast template scattering just 2 inches
- Subtract the probability of a blast template scattering 1 inch or less from the probability of scattering 2 inches or less
- P = 61% - 52% = 9%

You can check your results against these

BS of 2
scatter of 0 = 35%
scatter of 1 = 4%
scatter of 2 = 5%

BS of 3
scatter of 0 = 39%
scatter of 1 = 5%
scatter of 2 = 8%

BS of 4
scatter of 0 = 44%
scatter of 1 = 8%
scatter of 2 = 9%

- Hope this helps!

3 comments:

  1. So if the BS 4 scatter is 8% for one inch, does that stack with the 44% for the scatter of zero? Meaning, that I have a 52% chance of it landing within one inch of target, 53% chance of hitting within two inches, etc?

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  2. Loyal Guardsman, that is correct. But if you just want to know the chances of the template landing within 1 inch for a BS of 4, then calculate the formula with a BS of 5. That will give you the 52%. You get the 8% by subtracting the formula done with a BS 4 from the formula done with a BS of 5.

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  3. Is farseer still being worked on and will it be released for use outside of a blackberry (i.e. on a pc)?
    I stumbled upon this while wondering about the chance for an Imperial Griffon's barrage to hit / not scattering or not scattering more than 2 inches. The Griffon has a special rule that allows you to reroll the scatter dice.

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