What is the formula to calculate the minimum amount of armies needed to take a territory with a counterattack?

I need it for a game where I know with how many armies i will be attacked with, at multiple places.

Surcumstancise:
Off. kill rate: 60%
Dif. kill rate: 70%
SR, 0% luck.
one armie stand guard: On

Formula:
D*0,7+(D-A*0,6+1)*0,6=A+1
D= Difensive armie
A= Attacking armie

When 1000 armies attack, then you need to deploy 1047 to take the territory with counterattack.

Edit: When using clamping I get a formula like this: (A+1)*1,046=D

But what is the correct formula?

Edited 7/1/2016 01:19:58

Edited 7/1/2016 00:36:40

@Wapo, you can't use analyze during the game to calculate the amount of armies needed to take a territory with a counterattack.

@ayy lmao, dont spam ouside the Off-topic forum please.

As far as taking over a territory goes, doesn't it just require two things?:

- all defensive armies are killed

- at least 1 offensive army survives to take the territory

So on face you just need to meet two requirements:

ROUND(A * .6) >= D
ROUND(D * .7) <= (A-1)

Second one simplifies to (A-1) >= ROUND(D * .7), which becomes A >= ROUND(D * .7) + 1.

That second one's only relevant for D = 1, as (D - .5)/.6 < (1 - D * .7) doesn't work for any integer values of D above 1.

So we're really concerned by the first constraint, which becomes (D - .5)/.6 <= A, so you need to just subtract .5 armies (due to the straight rounding) and then divide by .6 (and round up since we're only working with integer values here).

Unless I missed something, it's pretty simple with a few adjustments.

@kynte, I dont understand... If I'm attacked with 1234 armies, how manny armies must i have to take the territory with order delay?

Reduce your variables.


OFF : nb of attackers

DEF : nb of defenders


X : Remaining attackers

Y : Remaining defenders

---

Y * 0.6 = X ; Y * 6/10 = Y / (10/6) = Y / (5/3) ; Y = X * 5/3

---

OFF - DEF * 0.7 = X

DEF - OFF * 0.6 = Y

---

5/3 * (OFF - DEF * 0.7) = DEF - OFF * 0.6

5/3 * 0FF - DEF * 35 / 30 = 5/3 * OFF - DEF * 6/5



Edit :

5/3 * (OFF - DEF * 7/10) = DEF - OFF * 0.6

5/3 * 0FF - DEF * 35 / 30 = 5/3 * OFF - DEF * 6/5

---

5/3 * OFF - DEF * 7/6 = DEF - OFF * 3/5

DEF + DEF * 7/6 = 5/3 * OFF + 3/5 * OFF


DEF * 13/6 = OFF * (25/15 + 9/15) ; DEF * 13/6 = OFF * (34/15)

---

DEF = OFF * ((34/15)/(13/6)) ; DEF = OFF * (34/15 * 6/13) ; DEF = OFF * 204/195

---

DEF = OFF * 204/195





[QED]

Edited 7/1/2016 00:32:32

I edited.


I calculated 35/30 as equal to 6/5 instead of 7/6.

for 1234 i calculated 1291 to take the territory in a counter attack. But i may be wrong (it is close to what hostile said, but not exactly -> 1%). Would need to do some equations to be sure - what im not.

Edit.: the new equation (def = off * 204/195 ) that hostile did is correct now

Edited 7/1/2016 00:38:13

Example :


1000 attackers need 1046.15 defenders with counter attack.



Defenders : 1046.15 - 0.6 * 1000 = 446

Attackers 1000 - 0.7 * 1046.15 = 267.70


267.7 / 0.6 = 446.166666666


Formula works. =)



I am a Math Wolf

@OP: Yeah, looks like I missed the counterattack part. Will recalculate and see if I can get better accuracy than Hostile.

1% might be due to rounding, since remaining defenders aren't actually off * .6 but really off * .6 rounded.

Edited 7/1/2016 00:41:07

"DEF = OFF * 204/195" --> This is not working.

with OFF=10, the DEF= 10 * 204/195 = 10,46= 10?

But with 10 attacking armies I need 12 to counter...
(10*0,6=6 dmg...12*0,7=8 dmg
10-8= 2+1 remaining...12-6= 6-1 remaining
5*0,6 = 3dmg)

no kynte, he changed his formula. instead of 204/195 was 180/170.. Now the result of "204/195" was 1290.95, and my result 1291, a good result.

he forgot about one army stands guard option, correct formula is D=(1.36*A+1.6)/1.3

yes, i forgot that too, GiantFrog formula works better.

D=(1.36*A+1.6)/1.3

A=7
D=(1.36*7+1.6)/1.3 = 9, while 8 needed.

A=10000
D=(1.36*10000+1.6)/1.3 = 10463, while 10462 needed.


Is a correct formula not possible because of rounding?

my forumla obviously still wasnt including rounding, but i really wouldnt go for that.
The resulting formula wouldnt be handy at all. You d still be way faster calculating D this way and checking D-1 if D worked or go with D+1 in case it didnt.

(1.36 / 1.3) * 150/150 = 204 / 195

---

(1.6 / 1.3) * 150/150 = 240 / 195

---

(204 / 195) * A + 240 / 195 = D

---

OFF - DEF * 0.7+ 1 = X

5/3 * 6/13 = 30 / 39 = 240 / 312 = 0.77

0.77 * 1.3 = ~ 1.


:P

1290.9 for 1234 is really close.

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If there is one extra army guarding the territory, you only need to add an extra attacker.


It is the same as adding [0.6]. [0.6] rounded up is 1.

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Only defenders may have a decimal part.

You use the floor function to get real number of defenders needed.


Also, add one extra army if [1 army stand guard] setting enabled.

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The degree of error due to rounding for two "battles" is not big.

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I am the ultimate MATH WOLF.

Edited 7/1/2016 01:20:41

When A= 1234 then D=1292, not 1291.

My own Formula: (A+1)*1,046=D
seems the most accurate...