Maths Question
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- Lorddrittz
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Maths Question
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?
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?
Dark Elf Battles
Win/Draw/Loss
10 : 1 : 4 7th Ed Codex
Win/Draw/Loss
10 : 1 : 4 7th Ed Codex
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).
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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- Daeron
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<CUT: Daeron was wrong about his rules>
Last edited by Daeron on Fri Oct 05, 2012 11:48 am, edited 1 time in total.
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
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
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- Cold One Knight
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- Cold One Knight
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- Daeron
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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.
http://warhammer.orderoftheathanor.eu/flee_catch.html
Seems it checks out. This is much better than I expected.
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
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
- Daeron
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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.
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
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
- Daeron
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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.
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
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
- Lorddrittz
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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...
(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...
"One day I'll have a plan that works to perfection. The shock will likely kill me." -Malus Darkblade
- Lorddrittz
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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 %
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 %
"One day I'll have a plan that works to perfection. The shock will likely kill me." -Malus Darkblade
- Lorddrittz
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- Daeron
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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
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
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
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
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.
"One day I'll have a plan that works to perfection. The shock will likely kill me." -Malus Darkblade
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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?
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?
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
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
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.”
"One day I'll have a plan that works to perfection. The shock will likely kill me." -Malus Darkblade
- Daeron
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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.
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.
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
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
- Daeron
- Malekith's Best Friend
- Posts: 3975
- Joined: Fri Oct 03, 2003 7:36 pm
- Location: Belgium, Brussels
- Contact:
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.
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.
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
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