They'd still lose. Wars are fought not from individual battles but from logistics. Modern military's don't even engage if there isn't a lopsided power imbalance favoring their success.

So the rational decision is, if you are attacked then you should surrender immediately?

if you find yourself in a fair fight it's time to re-think your strategy

It only takes one side to engage.

Look at the orders of magnitudes differences in casualties in desert storm, iraq, and afghanistan. When Americans battle they ensure they have a massive power advantage for every fight and this is abundantly clear just from the casualty data. Even if the other side engages first like in desert storm, Americans ensure that they don't land boots unless they have a tactical advantage which they had in Desert Storm thanks to technology that Saddam and his army, which was one of the largest and experienced land forces in the world at the time, could not begin to compete with.

Yeah like in Black Hawk Down.

In real life the battle of mogadishu saw Americans with 10x fewer casualties. Most modern battles have numbers like this with an order of magnitude fewer casualties on the American side, because American logistic planners try to ensure a massive power advantage.

And yet...

And yet what? Are you not convinced by the casualty data?

I don't seem to recall Mogadishu being any kind of "victory". It's almost like the casualty data didn't tell the whole story.