Maths genius required!

I’d like to know the % chance of successfully casting boosted doombolt (cast value 24), using 6 dice, with:

a) 5 warlocks (single full rank)
b) 10 warlocks (two full ranks, so +1 to cast)

Clearly we either need to miscast (25% chance, I’ve calculated this myself previously using nPr and all that), or meet the casting value. It’s not that simple though as we can’t simply add the % chance of a miscast with the % chance of a successful normal cast, as we need to remove all the permutations of a successful cast which include two or more 6’s. Then we can perhaps add them. Although you’d need a fat spreadsheet to work that out (6^6 = 46,656 different results), or approximate to a Normal distribution which would be a lot easier. Then perhaps you can just add the 25% chance of rolling two sixes. Who knows, it’s very difficult – hence I require a maths genius!

Any input I’d be very grateful,

toots

From:
- http://www.druchii.net/viewtopic.php?t=65664
- http://www.druchii.net/viewtopic.php?t=71090

We have these casting probabilities, -after modifiers-. So if the cast value is 24 and you get +3 to cast (level 2, +1 to cast from extra rank), then look up 21.


. . . . . . . . 1d6 . . . . 2d6 . . . . 3d6 . . . . 4d6 . . . . 5d6 . . . . . 6d6 . . . . 7d6
01+ . . . . 100.% . . 100.% . . 100.% . . 100.% . . 100.% . . 100.% . . 100.%
02+ . . . . 83.3% . . 100.% . . 100.% . . 100.% . . 100.% . . 100.% . . 100.%
03+ . . . . 66.7% . . 97.2% . . 100.% . . 100.% . . 100.% . . 100.% . . 100.%
04+ . . . . 50.0% . . 91.7% . . 99.5% . . 100.% . . 100.% . . 100.% . . 100.%
05+ . . . . 33.3% . . 83.3% . . 98.1% . . 99.9% . . 100.% . . 100.% . . 100.%
06+ . . . . 16.7% . . 72.2% . . 95.4% . . 99.6% . . 100.% . . 100.% . . 100.%
07+ . . . . 00.0% . . 58.3% . . 90.7% . . 98.8% . . 99.9% . . 100.% . . 100.%
08+ . . . . 00.0% . . 41.7% . . 83.8% . . 97.3% . . 99.7% . . 100.% . . 100.%
09+ . . . . 00.0% . . 27.8% . . 74.1% . . 94.6% . . 99.3% . . 99.9% . . 100.%
10+ . . . . 00.0% . . 16.7% . . 62.5% . . 90.3% . . 98.4% . . 99.8% . . 100.%
11+ . . . . 00.0% . . 08.3% . . 50.0% . . 84.1% . . 96.8% . . 99.5% . . 100.%
12+ . . . . 00.0% . . 02.8% . . 37.5% . . 76.1% . . 94.1% . . 99.0% . . 99.9%
13+ . . . . 00.0% . . 02.8% . . 25.9% . . 66.4% . . 90.2% . . 98.0% . . 99.7%
14+ . . . . 00.0% . . 02.8% . . 17.6% . . 55.6% . . 84.8% . . 96.4% . . 99.4%
15+ . . . . 00.0% . . 02.8% . . 12.0% . . 44.8% . . 77.9% . . 93.9% . . 98.8%
16+ . . . . 00.0% . . 02.8% . . 08.8% . . 35.0% . . 69.6% . . 90.4% . . 97.8%
17+ . . . . 00.0% . . 02.8% . . 07.4% . . 26.7% . . 60.5% . . 85.6% . . 96.2%
18+ . . . . 00.0% . . 02.8% . . 07.4% . . 20.5% . . 51.3% . . 79.6% . . 93.9%
19+ . . . . 00.0% . . 02.8% . . 07.4% . . 16.7% . . 42.5% . . 72.5% . . 90.7%
20+ . . . . 00.0% . . 02.8% . . 07.4% . . 14.5% . . 35.0% . . 64.8% . . 86.4%
21+ . . . . 00.0% . . 02.8% . . 07.4% . . 13.5% . . 29.1% . . 56.9% . . 81.3%
22+ . . . . 00.0% . . 02.8% . . 07.4% . . 13.2% . . 24.8% . . 49.3% . . 75.2%
23+ . . . . 00.0% . . 02.8% . . 07.4% . . 13.2% . . 22.1% . . 42.6% . . 68.6%
24+ . . . . 00.0% . . 02.8% . . 07.4% . . 13.2% . . 20.7% . . 37.0% . . 61.9%
25+ . . . . 00.0% . . 02.8% . . 07.4% . . 13.2% . . 20.0% . . 32.9% . . 55.3%
26+ . . . . 00.0% . . 02.8% . . 07.4% . . 13.2% . . 19.7% . . 29.9% . . 49.4%
27+ . . . . 00.0% . . 02.8% . . 07.4% . . 13.2% . . 19.6% . . 28.1% . . 44.4%
28+ . . . . 00.0% . . 02.8% . . 07.4% . . 13.2% . . 19.6% . . 27.1% . . 40.4%
29+ . . . . 00.0% . . 02.8% . . 07.4% . . 13.2% . . 19.6% . . 26.6% . . 37.5%
30+ . . . . 00.0% . . 02.8% . . 07.4% . . 13.2% . . 19.6% . . 26.4% . . 35.5%

A unit of 5 Warlocks casts 24+ on 6D6 with 49.3% chance.
A unit of 10 Warlocks in 2 ranks casts 24+ on 6D6 with 56.9% chance.

is this it? is this what it's come to? me, sat watching a battle report whilst rolling 6 dice TWO HUNDRED (200) TIMES and entering in the results in Excel?

turns out that the 56.9% chance figure below is correct. i got 57.5% so i figure that's close enough...

lol. but yeah, thanks Daeron!

For the future: Use wolframalpha.com

E.g. you could enter "probability for rolling at least 22 with 6 dice" (boosted Doombolt with Warlocks) and get:

Probability of occurrence: 0,4536

Now this is lower that Dearon's correct number (49,3%), because he included the chance of not having 22, but having two sixes, but it is close enough to understand, that it is generally a "fifty-fifty" proposition.

Ohhh more math talk! I like!

Wolfram are the experts and heavy duty programs!
But, you don't need advanced maths to calculate the probability of dice. Regular algebra can be used:
http://wolfr.am/7lXltUab
This expression, for example. Or, linked:



The part between parens is the expression for a single dice. Add the exponent for the number of dice you're throwing and you get all possible outcomes, of the format:
SIGMA x_n R^n
where x_n is the chance to score "n" on as many dice as you rolled.

Which means something as simple as this can calculate it:
http://www.mathpapa.com/algebra-calcula ... 5E6%29%5E6

Or my combat calculator can (implemented as a 100% chance to kill with 6d6 attacks):


But.. That doesn't include IF. That one was tricky.
I calculated that by calculating the chance to score any given value with at most 1 six in it and then added the chance to cast IF. According to the rule of sum, that shouldn't conflict since those are two disjoint possibilities on the same test

I haven't found a simple Algebraic expression for that.

Hey, that's still a very valuable test. Imagine you did have a calculation. How would you make sure it is correct?

I have a question about this and Doomfire Warlocks. If you have 15 are you then basically going to hit 100% of the time?

I fear your question is about Warlocks in Age of Sigmar. The original question was for WFB 8th edition.
But in neither game will you get a 100% hit.

In AoS, you get 6 Mortal Wounds if you cast the spell. In Warhammer you get 2D6 (or 4D6 if boosted) S5 hits if you cast the spell. So you always have to cast the spell.

exactly, it's the IF part that's the difficult bit.

cheers again, Ronny! (daeron)

p.s. i'm quite pleased how my experimental analysis tended towards the theoretical calculated value. nice when that happens, eh?!