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Maths Question 
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Beastmaster
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The odds of an infantry unit chasing down an infantry unit is 2D6 v. 2D6 the odds are 55% chance of running down the fleeing unit.

What are the odds of a Cavalry/Flyer running down an infantry unit?

3D6 pick the best 2 vs. 2D6. The mathematicians should be able to help here?

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Fri Oct 05, 2012 2:55 am
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Interesting. Unfortunately, I have no time to figure out.
I only have the most likely distances that will be ran.
For infantry, that’s 6-9” (2D6, with 72% chances for 6”, 28% chances for 9”).
For cavalry/flyers, that’s 8-11” (best 2 of 3D6, with 68% chances for 8”, 36% chances for 11”).
But I don't have the combined result for catching up a fleeing foe.

It might be interesting also to figure out what becomes of these figures when there is a corsair among the winners (note: there might be simultaneously corsairs and fast runners among winners).

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Fri Oct 05, 2012 9:56 am
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Malekith's Best Friend
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<CUT: Daeron was wrong about his rules>

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Last edited by Daeron on Fri Oct 05, 2012 11:48 am, edited 1 time in total.



Fri Oct 05, 2012 10:49 am
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Cold One Knight

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I have a table which says 75.3% (Made by Aaron Chapman).

His site (which I cannot access from this computer) may explain how he arrived at this figure.


Fri Oct 05, 2012 11:00 am
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Cold One Knight

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Sorry didn't see Daeron's post please ignore previous post


Fri Oct 05, 2012 11:10 am
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Hm. I was so surprised by seeing the odds were so strong in favor of cavalry, that I decided to build a quick simulator for the sake of proof.

http://warhammer.orderoftheathanor.eu/flee_catch.html

Seems it checks out. This is much better than I expected.

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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


Fri Oct 05, 2012 11:33 am
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Prince Fabulas wrote:
I have a table which says 75.3% (Made by Aaron Chapman).


Hmm.. you confuse me now. Swiftstride means you can roll 3 dice and discard the lowest, right? But.. cavalry still uses 3D6? or am I still mixing up the old edition?

I'll double check when I get home.

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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


Fri Oct 05, 2012 11:37 am
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Prince Fabulas wrote:
I have a table which says 75.3% (Made by Aaron Chapman).

His site (which I cannot access from this computer) may explain how he arrived at this figure.


Right. I redid my simulation. The link is still
http://warhammer.orderoftheathanor.eu/flee_catch.html

I end up with around 72.5% chance. This is notably more challenging to calculate with maths, but I'll give it a shot none the less. That'll take me more time though.

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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


Fri Oct 05, 2012 11:59 am
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Interesting not as high as I thought it would be but 75% is pretty good odds.

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Fri Oct 05, 2012 2:21 pm
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After some number crunching I've got the following results:
(If I have been able to correctly keep track of all the possible results...)

normal unit pursuing normal unit:
721/1296 = 55.633...%
normal unit pursuing swiftstrider:
2964/7776 = 38.117...%
swiftstrider pursuing normal unit:
5631/7776 = 72.415...%
swiftstrider pursuing swiftstrider:
26271/46656 = 56.308...%


The rest of the results require even more complicated calculations. Maybe I'll give it a try sometimes...

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Fri Oct 05, 2012 8:49 pm
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Also factoring in chasing down Skaven which get +1 to their Flee rolls and Dwarves with -1 to theirs.

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Tue Oct 09, 2012 12:10 am
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As somebody who loves mathhammer this is a question that intrigues me. The original question has already been answered, but as Calisson wrote there are lots of similar questions. So, today when I didn't have anything else to do, I did some more calculations.

The possibility for the pursuer/pursuers to catch the fleeing unit:

normal unit pursuing normal unit:
721/1296 => 55.633 %
normal unit pursuing swiftstrider:
2964/7776 => 38.117 %
swiftstrider pursuing normal unit:
5631/7776 =>72.415 %
swiftstrider pursuing swiftstrider:
26271/46656 => 56,308 %
2 normal units pursuing normal unit:
33621/46656 => 72.061 %
2 normal units pursuing swiftstrider:
152530/279936 = >54.487 %
2 swiftstriders pursuing normal unit:
1441791/1679616 => 85.841 %
swiftstrider and normal unit pursuing normal unit:
225819/279936 => 80.668 %
swiftstrider and normal unit pursuing swiftstrider:
1103760/1679616 => 65.715 %
2 swiftstriders pursuing swiftstrider:
7203021/10077696 => 71.475 %

If one of the pursuing units is Corsairs!
In the calculations I have used the following conditions:
- If the highest dice is equal to or greater than 4 the fleeing unit re-rolls
- If the fleeing unit is a swiftstrider and rolls a triple it doesn't re-roll

Corsairs pursuing normal unit:
5441/7776 => 69,972 %
Corsairs pursuing swiftstrider:
25074/46656 => 53,742 %
Corsairs and normal unit pursuing normal unit:
235971/279936 => 84,295 %
Corsairs and normal unit pursuing swiftstrider:
1191588/1679616 => 70,944 %
Corsairs and swiftstrider pursuing normal unit:
1514515/1679616 => 90,170 %
Corsairs and swiftstrider pursuing swiftstrider:
8084922/10077696 => 80,226 %

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Tue Oct 09, 2012 8:23 pm
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Nice Statistical analysis

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Tue Oct 09, 2012 9:48 pm
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While I don't doubt your maths (I may actually try to reproduce them for the sake of exercise at some point) I could toss in a simulation program that could verify your results. And your results would verify my simulation :D

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"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 10, 2012 7:30 am
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Daeron wrote:
While I don't doubt your maths (I may actually try to reproduce them for the sake of exercise at some point) I could toss in a simulation program that could verify your results. And your results would verify my simulation :D

That would be really helpful. I’ve tried to double check the results and make sure they seem reasonable, but I can’t give any guarantees. The risk that something goes wrong when there are more than 1 000 000 possible combinations to keep track of isn’t insignificant.

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Wed Oct 10, 2012 8:15 am
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For a moment I was thinking: hey.. can't you combine the results from 1 unit to get the results from 2 pursuing units... but then I realized they aren't independent tests.

My simulator is built, but the uploader is having trouble. Will update this post with the link when I got it to work.

normal unit pursuing normal unit:
55.5% - 55.8% matches
normal unit pursuing swiftstrider:
38.1% - 38.3% matches
swiftstrider pursuing normal unit:
72.2% - 72.6% matches
swiftstrider pursuing swiftstrider:
56.1% - 56.5% matches
2 normal units pursuing normal unit:
72.0% - 72.3% matches
2 normal units pursuing swiftstrider:
54.2% - 54.4% matches
2 swiftstriders pursuing normal unit:
85.7% - 85.9% matches
swiftstrider and normal unit pursuing normal unit:
80.5% - 80.7% matches
swiftstrider and normal unit pursuing swiftstrider:
65.6% - 65.8% matches
2 swiftstriders pursuing swiftstrider:
73.1% - 73.4% slight deviation

In the calculations I have used the following conditions:
- If highest dice is 4+ then a dice is rerolled.
- If fleeing unit has swiftstriding, then the swiftstriding is worked out first.

Corsairs pursuing normal unit:
71.5% - 72.0% slight deviation
Corsairs pursuing swiftstrider:
62.0% - 62.3% Notable deviation
Corsairs and normal unit pursuing normal unit:
86.7% - 86.9% slight deviation
Corsairs and normal unit pursuing swiftstrider:
79.6% - 79.7% Notable deviation
Corsairs and swiftstrider pursuing normal unit:
92.3% - 92.6% slight deviation
Corsairs and swiftstrider pursuing swiftstrider:
87.3% - 87.5% Notable deviation

I think we interpret the combination of Slaver rule and Swiftstrider rule differenty which yields the difference in outcome. Is there a FAQ telling how those two combined are worked out?

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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


Thu Oct 11, 2012 12:09 pm
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Daeron wrote:
...
I think we interpret the combination of Slaver rule and Swiftstrider rule differenty which yields the difference in outcome. Is there a FAQ telling how those two combined are worked out?


Not a FAQ, but an amendment: :)

GW wrote:
Page 45 – Slavers
Add “Against opponents that have Swiftstride, the Dark Elf
player may force the opponent to re-roll the highest of the 3D6
they roll, before it is decided which two dice will be used.”

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Thu Oct 11, 2012 4:09 pm
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Right:
http://warhammer.orderoftheathanor.eu/flee_catch.html

Corsairs pursuing normal unit:
72% - 74.0% Deviation
Corsairs pursuing swiftstrider:
59% - 61% Notable deviation
Corsairs and normal unit pursuing normal unit:
86% - 88% Deviation
Corsairs and normal unit pursuing swiftstrider:
75% - 78% Notable deviation
Corsairs and swiftstrider pursuing normal unit:
91% - 93% Deviation
Corsairs and swiftstrider pursuing swiftstrider:
84% - 86% Notable deviation


Weird. Still some differences. I'll refactor a few things in my calculator so it produces a log of all rolls as verification. But that's for tomorrow.

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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


Thu Oct 11, 2012 7:29 pm
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The update is in. The link is still:
http://warhammer.orderoftheathanor.eu/flee_catch.html

I discovered that my slavers enforced too many rerolls. With the log I double checked the results and they seem to work. Now, for the scores:

Corsairs pursuing normal unit:
69.8% - 70.1% Matches
Corsairs pursuing swiftstrider:
53.6% - 53.7% Matches
Corsairs and normal unit pursuing normal unit:
84.3% - 84.3% Matches
Corsairs and normal unit pursuing swiftstrider:
70.7% - 70.9% Matches
Corsairs and swiftstrider pursuing normal unit:
90.2% - 90.2% Matches
Corsairs and swiftstrider pursuing swiftstrider:
80.2% - 80.3% Matches

Pretty neat. Everything except "2 Swiftstriders vs 1 Swiftstrider" matches.

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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


Mon Oct 15, 2012 11:47 am
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