I understand what you mean and I agree that option 2 is often a good choice. But I´m just pointing out that it could have a big impact if you don´t apply the theory the right way. People can addept it by chosing option 2 most of the time. And yh option 1 is often a defensive option. Option 2 gives you stack in their territory, so that is also often better. Of course it is really depending on the situation, to decide what to do. But that is a whole different story. Also, I just wanted to point out, that 0.6(x-1)<z is an assumption you make.

Ow I just noticed, with (iii) it is always option 1 btw. min(y,0.7(z-0,6(x-1)))= 0.7(z-0,6(x-1), which is really easy to see. So only way to actually chose option 2, is when y is small compared to x, which is pretty much what you want.

Last line is what you expect, not what you want xD. Also that when 0.7z<y, then you have that if you attack with x or y, you get same losses. So you just want to attack with x, that is pretty obvious I must say, wierd that I missed that the first time xD.

Shouldn't it be x-1 and y-1?

"Option 1 - attack with bigger first:
You kill z troops total, you lose (min(x-1,0.7z)+min(y-1,0.7(z-0,6(x-1)))

Option 2 - attack with smaller first:
You kill z troops total, you lose (min(y-1,0.7z)+min(x-1,0.7(z-0,6(y-1)))"

I think it change the outcomes a bit.

Oh yes, that is completely true Monkey, thanks for pointing out that obvious mistake (switched sides of inequality for some reason...), yeah option iii) is obvious option 1 since I get the same losses and that changes a lot actually (I hate making computational errors and noticing only after I make a long debate ;) ). Anyway still trying to push my argument through, it is common knowledge that almost all situations like this (especially in 1vs1 games) are resolved through first variant (unless there are other factors to consider like cards, bigger income, bigger stacks) so I still stand behind what I said (of course except for the obviously wrong part iii).

Yh that is correct, but doesn't change the outcome much, just for exact calculations on where the boundary is. Can calculate it, but don't feel like it :P. I didn't actually pay much time on evaluating this.

I totally agree with you szeweningen, that option 2 is the better option in a lot of 1v1 action.

im asuming you guys really like math