A friend had a WWII strategy game, long in the making, come out this fall. The War: Europe 1939-1945, put out by Compass Games, finally started shipping last month. I have only a passing familiarity with this type of extended table game, pioneered decades ago by Avalon Hill, but I expect this to be seriously good. I knew Ernie as a history fanatic and early wargamer at William and Mary, and among his many other fascinating careers, he teaches at a local college (local to him, over in Maine that is). WWII, Europe has long been his favorite era. He is the person that put me on to both Joel Garreau's Nine Nations and David Hackett Fischer's Albion's Seed as they came out, both on my short list of essential reading. He absolutely knows his stuff.
These are the complex and precise games that attract serious students of military history - the cost would certainly daunt the merely curious, but is standard for the genre. Some effort has been made to make it accessible to new gamers with solitaire and some scenarios that can be played more quickly. But it's the real deal otherwise, with expected games of 50 hours.
If this is new to you, you need to know something of what to expect in this type of gaming. What you can do within the game must be something which could plausibly have occurred. To take Copley's example, one cannot posit "What if the Japanese had had an atomic bomb prior to the war?" (I believe the proper response to that is "Yeah well, what if the Belgians had had a magnetic Death Ray? What about that?") But trying on how things would have been different if Stalin hadn't killed so many of his generals during the purges is fair game.
We see this echoed in literary forms redoing history. There is speculative fiction in which even wild possibilities are allowed, steampunk tends strongly to this; then there is the time travel genre, certainly the most common in visual media, in which the plot is confined to the otherwise possible, save that a single wildcard group or individual can act with foreknowledge; then there is counterfactual history, which is more constrained still, in which the author tries to describe what most plausibly would result from a small, realistic change at the outset of some historical event. These are often most attractive in situations that appear in retrospect to have hinged on some small event anyway: what if air reconnaissance had focused more on the northern attack routes at Pearl Harbor; what if the British had pursued at the Battle of Jutland; what if Jeb Stuart had "done his duty" and the Confederate States succeeded at secession. All are a type of alt history - wargaming is most like the last of these, though there is overlap and the categories are not clean.