More specifically, has anyone of significance wargamed what would have happened had Hitler not made the choices he did regarding Stalingrad?
Note: I'm not asking a /r/HistoricalWhatIf question, I'm asking if other people of note have performed wargames to answer what-if questions, especially related to WW2.
Wikipedia article on Operation Sea Lion
More info on the British-German war game here: http://www.wargaming.co/books/paddysprawling/articles/sealion.htm
What exactly is a war game and how reliable are they for determining how a battle would have unfolded? How can you even say that this particular war game unfolded even remotely close to how a real war would have?
Related question: wasn't this a big part of the peacetime duties of von Moltke's General Staff, as part of the contingency planning that the group was tasked with?
I don't know how much this relates to your question (in fact, on reflection, I don't think it overly does), but for this general kind of "war game", there was a show called "Time Commanders" on the BBC, in which sets of people were tasked with commanding an army in classic historical battles in the Roman/Greek era. If you're interested, you can find most of the episodes on Youtube.