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[ 9 posts ] 

Maths genius required! boosted doombolt calculation
Author 
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toots
Beastmaster
Joined: Wed Mar 19, 2014 10:25 pm Posts: 334

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

Wed Sep 30, 2015 10:54 am 


Daeron
Malekith's Best Friend
Joined: Fri Oct 03, 2003 7:36 pm Posts: 3863 Location: Belgium, Brussels

From:  http://www.druchii.net/viewtopic.php?t=65664 http://www.druchii.net/viewtopic.php?t=71090We 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.
_________________I love me a bowl of numbers to crunch for breakfast. If you need anything theoryhammered, I gladly take requests. Furnace of Arcana, a warhammer blog with delusional grandeur. "I move unseen. I hide in light and shadow. I move faster than a bird. No plate of armour ever stopped me. I strike recruits and veterans with equal ease. And all shiver at my coldest of whispers."  The stiff breeze

Wed Sep 30, 2015 11:03 am 


toots
Beastmaster
Joined: Wed Mar 19, 2014 10:25 pm Posts: 334

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!

Wed Sep 30, 2015 10:42 pm 


DarkSky
Corsair
Joined: Mon Jun 15, 2015 1:20 pm Posts: 83

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 "fiftyfifty" proposition.
_________________My Blog containing battle reports and painting updates: https://bleaklegion.wordpress.com

Tue Oct 06, 2015 1:29 pm 


Daeron
Malekith's Best Friend
Joined: Fri Oct 03, 2003 7:36 pm Posts: 3863 Location: Belgium, Brussels

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/7lXltUabThis 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/algebracalcula ... 5E6%29%5E6Or 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.
_________________I love me a bowl of numbers to crunch for breakfast. If you need anything theoryhammered, I gladly take requests. Furnace of Arcana, a warhammer blog with delusional grandeur. "I move unseen. I hide in light and shadow. I move faster than a bird. No plate of armour ever stopped me. I strike recruits and veterans with equal ease. And all shiver at my coldest of whispers."  The stiff breeze

Tue Oct 06, 2015 2:08 pm 


Daeron
Malekith's Best Friend
Joined: Fri Oct 03, 2003 7:36 pm Posts: 3863 Location: Belgium, Brussels

Hey, that's still a very valuable test. Imagine you did have a calculation. How would you make sure it is correct?
_________________I love me a bowl of numbers to crunch for breakfast. If you need anything theoryhammered, I gladly take requests. Furnace of Arcana, a warhammer blog with delusional grandeur. "I move unseen. I hide in light and shadow. I move faster than a bird. No plate of armour ever stopped me. I strike recruits and veterans with equal ease. And all shiver at my coldest of whispers."  The stiff breeze

Tue Oct 06, 2015 2:08 pm 


Phox532
Executioner
Joined: Wed Sep 09, 2015 4:11 am Posts: 173 Location: Hohhot, China

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

Wed Oct 07, 2015 6:21 am 


Daeron
Malekith's Best Friend
Joined: Fri Oct 03, 2003 7:36 pm Posts: 3863 Location: Belgium, Brussels

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.
_________________I love me a bowl of numbers to crunch for breakfast. If you need anything theoryhammered, I gladly take requests. Furnace of Arcana, a warhammer blog with delusional grandeur. "I move unseen. I hide in light and shadow. I move faster than a bird. No plate of armour ever stopped me. I strike recruits and veterans with equal ease. And all shiver at my coldest of whispers."  The stiff breeze

Wed Oct 07, 2015 7:48 am 


toots
Beastmaster
Joined: Wed Mar 19, 2014 10:25 pm Posts: 334

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?!     Daeron wrote: 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/7lXltUabThis 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/algebracalcula ... 5E6%29%5E6Or 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.     

Wed Oct 07, 2015 12:52 pm 



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