The butterfly effect in the Civil War

Michael Schermer investigated whether at any point in the Civil War an insignificant, contingent event had a substantial effect.
He suggested this happened on Sept. 13, 1862, at Antietam Creek near Sharpsburg, Maryland.
The brilliant Lee had 50,000 troops in the region, the more timid McCllelan had 80,000. A southern victory could have redirected foreign support to the Confederacy, possibly changing the outcome of the war. Here is what happened.
While resting in a field near Frederick, Maryland, two Union soldiers happened to notice three cigars wrapped in paper lying on the ground. On the paper was written Special Order 131, the detailed plans of southern troup movements, signed by Lee. With this information, McClellan, by all accounts a substantially inferior strategist to Lee, engaged in a battle in which he lost 10,293 troops and Lee lost 10,318. A draw in terms of casualties, this battle forced Lee to retreat to friendly territory in order to recover his losses. McClellan declared a victory, because he had succeeded in driving the Confederate forces from Maryland. Emboldened, within a week Lincoln announced the emancipation of the slaves would occur on January 1, 1863. This was a major factor in keeping Great Brittain and France from recognizing Confederate independence from the Union, and thus brought a quicker conclusion to the Civil War. Indeed, had Britain and France recognized the Confederacy, they may have broken the Union naval blockade of the south, and the war could have ended differently.
The Union victory in the Civil War may have been the result of a tiny chance, that two Union soldiers happened to be resting near the cigar wrapper on which Lee's plans for troop movements were written.
Perhaps the Union would have prevailed even without McClellan's victory, but it is likely the war would have lasted much longer, and been much more devastating to both sides.
 
In contrast, the scenario outlined in MacKinlay Kantor's short book If the South had won the Civil War (Bantam Books, 1965) is not such a good example of the butterfly effect. The death of General Grant before the Battle of Vicksburg is hardly a small change in initial conditions. No chaos is needed for a large change to have large effects, in this case the formation of the independent nation, the Confederate States of America. Then Texas seceedes from the CSA, Cuba is captured when the CSA declares war on Spain, and Alaska never is purchased from Russia. In this alternate unfolding of history, Sara Palin really can see Russia from her front porch.

Return to sensitivity to initial conditions is not enough.