You’re looking too far into the details. The value of the territory is irrelevant for this hypothetical scenario. But I’ve been catching a lot of flak in the comments for it, so you know what? I’ll humor you, let’s change the formula.

Let’s say tomorrow, Russia announces that because they feel that they were cheated in 1867, they are refusing to recognize the sale of the Alaska territory to the United States and are reestablishing their control over the land as it’s sole owner. They send an invasion force and they capture the land in a swift blitzkrieg-style assault, the United States is caught completely by surprise.

Now, the United States fights, but we can’t really conduct ground operations without the support of Canada. They are our not just our neighbors, but our staunchest allies in this fight. However, a new Prime Minister is sworn in and they suddenly decide to take a massive shift in foreign policy, and try to broker a “peace deal” between Russia and the USA in which we agree to sign over the rights to future drilling operations to Canada in exchange for a ceasefire from Russia, but Russia gets to keep Alaska since they occupy it now anyway. Refusal means Canada pulls their support, forbids US soldiers from operating in Canadian waters or on Canadian soil, and conducting operations in the occupied Alaskan territory becomes virtually impossible. And, let’s not forget, no security agreements even if we do sign the agreement. So, if Russia decides to attack Hawaii or California next, nobody will be compelled to aid us.

Is that a better comparison? Alaska has massive economic and strategic value, so there’s a good reason for Russia to want it. They’ve been regretting ever selling it to us in the first place.