Of course it's not sufficient. What leader will fight if he has nothing to gain, and more importantly, expects to lose?
And, it should go without saying: People can be wrong. Both about thinking that they will win, and can take into account irrelevant factors like "guts" or "purity", and that they have something to gain (e.g. irrational concepts like "honor" or "pride"), but in modern, literate societies those factors are less common and less prevalent, varying from society to society and individual to individual.
Wars pretty much happen because of scarcity of resources and imbalance of information. Both sides think they can win (even factoring in the cost of war) and both sides can't have the resources. Structuring languages and governments can make more slightly less likely, but not significantly so.
You can't fix the imbalance of information as no society will believe a simulation all the time, especially of war, which depends on all sorts of human factors. The only way out, really, is to have unlimited resources. That is actually the main thesis implied by the push for globalization: That through capitalism, we can have a non-zero sum game (drastically increase available resources to all nations) and avert real war. And it seems to work -- but it leads to the (reasonable) criticism of the anti-globalists: that there is still a finite amount of resources and sooner or later capitalist technological innovation won't be able to extend them any further.
Which leads to the basic final disconnect: Are you fundamentally optimistic about technology or pessimistic? If you're an optimist, we've already solved the long term problems that create world wars, and the last two were simply a painful transition period. If you're a pessimist, we've only delayed the inevitable and they were merely a preview of coming attractions -- which increased resource use is hastening.
Factorials were someone's attempt to make math LOOK exciting.