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Question for you logical ones.: 9/26/2015 11:17:48


Smithereens
Level 27
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Help me.

I started thinking about this and unfortunately found that I am unable to solve this with my own maths skills. Now it's keeping me awake at night.

If x is defined as the number of defending troops, find a function of x that gives the minimum number of troops required for a positive outcome in battle, where positive outcome is defined as the point where more defenders die than attackers.

I'm not interested in taking the territory. Assume standard attrition rates of 60%vs70%. Def vs Att respectively.

Then, factor attrition rates in. let y be a percentage attrition rate for defenders, and z be for attackers.

So ultimate question: Find a function with x,y and z that gives the minimum number of troops required for a positive outcome for the attacker, where x is the number of defenders, y is the defender attrition rate and z is the attacker attrition rate.
Question for you logical ones.: 9/26/2015 11:22:04


Nogals 
Level 58
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or you can use the analyse attack button, whatever floats your boat
Question for you logical ones.: 9/26/2015 11:23:12


Bayern München is the best!
Level 60
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or you can use the analyse attack button, whatever floats your boat


right
Question for you logical ones.: 9/26/2015 12:25:58


Beren • apex 
Level 63
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a > (dk/ak) * d

a is # of attacking armies
d is # of defending armies.
dk is defensive kill rate
ak is offensive kill rate
Question for you logical ones.: 9/26/2015 12:34:20

Widzisz • apex 
Level 60
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I believe Beren got it right...

More interesting question is this:

Assuming Defender income Di, Attacker income Ai, current armies in defending territory D, in attacking A, find a function that indicates whether attacker will capture a territory some time in the future turns, assuming both put all income to attack / defend.

(default kill rates, pick whichever rounding mode you like)

I wonder if you find easier answer than mine.

Edited 9/26/2015 12:42:21
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