Actually, the Americans were not waiting to find out who was going to win the war. Churchill and Roosevelt discussed the inevitability of the Americans entering against the Axis from the beginning. If you've forgotten, the Americans sent supply ships to Britain in the years before they entered WWII. There was really never any doubt the Americans would enter the war or which side they would take (with Germany being the first Axis power to concentrate on defeating). The problem Roosevelt had was justifying American interference in what was largely a European conflict. The American people were used to the Monroe Doctrine and isolationism at the time. But the Japanese took care of that problem once the Americans stopped selling them oil. In fact, after the Pearl Harbor attack, the whole "Germany first" philosophy was almost abandoned because the US could only justify going after Japan. But Hitler made a crucial mistake and declared war on the US which allowed Churchill and Roosevelt to go after him together.
Make sure you get your history right. Try "A World at Arms" by Gerhard L. Weinberg.
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