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This war is unwinnable because there is no possible benefit that will outweigh the cost.

You don't win a war when you cause the most destruction to your enemy. You win when you achieve a political objective.

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Since when do wars have to be profitable?

This isn't middle ages. Most modern wars have dubious cost-benefit at best. Doesn't stop them from being fought and occasionally even won, no.

If US sets its war goal at "secure the strait and the oil fields" or "dismantle the regime" or "dismantle the nuclear program" and pulls that off, doesn't matter how many billions they would have sunk into the affair and how much they would actually have gained from it. From a military standpoint: a war goal was set and accomplished.

Whether US can actually set such a goal and then accomplish it is debatable, but it is not in any way impossible.

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