Suppose we have 2 players, there are 2 territories and we have perfect play. Each controls 1 territory. z is income. Let’s say a territory contains x armies. No (1 army must stand guard) What’s the Lowest starting number armies, y, required to take starting x armies? ex. x = 2, y = 4. The map is https://www.warzone.com/SinglePlayer?PreviewMap=465
The list below assumes 60% kill rate and 70% defense rateINCOME =
*0 y = x+1
Proof for no income: y can keep attacking x with 1 army. 1 army reduces x by 1 and so by y. Eventually, x will have 2 army and y will have 3 armies .
*1 y is almost = 1.0803x
If both kill and defense rate is 0%, y can not take x unless z = 0 and x = 0, which y = 1
If the kill rate is 100%, y = x+z+1 no matter the defense rate
If the kill rate is 0%, y can not take x unless z = 0 and x = 0, which y = 1
The trick is to get y/x as high as possible , modulo come onto play with n/100. We simplify the fraction to 2 coprime number.
We multiply these coprimes to get our r mod q.
Then y attacks with y-r ( So that y can attack most armies while saving most)
The list below assumes 60% kill rate and 70% defense rate
Edited 7/25/2020 02:03:31