The USA - along with everyone else, except, perhaps, the Ukrainian army, expected a quick Russian vistory. You don't try to get your opponent to gamble everything on the turn of a card when you think you know he has a winning card.
I don’t think the US expected a quick Russian victory. I think this is what they wanted the public to believe, in order to encourage Putin to make the move and fall into the trap.
Like Putin, Biden & European leaders have their own, many of them internal, reasons for what they're doing. They're not sitting around a table playing poker, with nothing else going on. They have to get support within their own parties, & sometimes from other parties, & convince the public they should go along. Scholz, for example, has to struggle with a long-standing policy of friendliness to Russia & trying to tie Russia to the west economically, so that it's against Russia's interests to go to war. I'm sure that he was shocked & surprised by the invasion.
Yes, everyone has different reasons. Scholz didn’t want this war, and he wanted good relations with Russia. Macron had made many efforts to convince Putin not to invade, incouding those humiliating long hours phone calls when Putin gave him history lessons about Peter The Great. Germany and France wanted to continue with the status quo and have good relations with Russia, but the Americans didn’t like that.
For the US, the benefits of this conflict are so great, that it is absurd to dismiss their interests to encourage it. And Biden is an establishment politician. He is old and he doesn’t care much about the voters or another term. He can do the dirty work of the establishment. During his term, many of the previous unfinished problems have been solved quickly (the Afghanistan withdrawal was done quicker than anyone imagined possible, the Fed raised the interest rate faster than anyone expected). The status quo of the last 15 years (American troops in Afghanistan and zero interest rate policy) has been turned upside down in only two years.
What I’m trying to point here is that the Americans had all the reasons to want Putin’s invasion to happen. Also, many of the more nationalist elements in Ukraine wanted this war to happen, as they prepared for it since 2014. Do you think it is a simple coincidence that Ukrainians were shooting at targets in Donetsk in the days before the invasion? They were poking the bear, and they probably had promises of help from the US.
The truth is that the US outmaneuvered Putin and Scholz big time. The German-Russian relations have been destroyed and the US is now exporting LNG to Europe, while European industry is suffering from high energy costs. Finland has joined NATO and Russia has lost a lot of its military capabilities. And all this happened without the US firing a single bullet and losing a single soldier. The economic costs for the US have been insignificant and the benefits enormous. I don’t think the US just got lucky. I think they did their best to mislead their rivals into making foolish mistakes.