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In the battle of Cowpens, British Commander Banastre Tarleton lost his cavalry scouts early in the battle and then was fooled by a fake retreat.

Let's suppose that didn't happen. The battle happens during a fog, which is variable. Sometimes one can see 100 meters and sometimes it gets denser and limits vision. The rebel sharpshooters miss their mark. His scouts spot the trap. the infantry advance in line formation instead of pursuit formation. This should be Morgan's cue to run away to fight another day (just as OTL's sniping of Tarleton's cavalry officers should have been his cue to either halt pursuit or only use line formation), but he doesn't

Both sides exchange some fire and then the Regulars prepare themselves for an English Gallop. Meanwhile, 30 cavalry or dragoons (whichever would work better) sneak themselves over on the right flank (Patriot left), confusing it for the rear. By luck (since with the fog it's kind of hard to time things), just as the infantry drive in, the cavalry smashes into the flank.

Victory is undeniable. The casualties suffered for the Patriots are 52 wounded, 83 killed, and 375 captured. The breakdown of this is 40 Continentals, 120 state infantry, and 350 militia (Babbits claim roughly 1260 militia were present, let's assume he's right). The Conteintels retreat, some militia withdraw, and the rest scatter (running away as individuals instead of with the group). British casualties are much lighter, 14 regulars and 3 loyalists (when no one can see very far, battles can be surprisingly lopsided, see some of the minor skirmishes involving 1000 ish on each side in the war of Austrian Succession, also more casualties tend to be suffered routing than actually fighting).

Well... what now?

On one hand, the British Legion was a well drilled by its commander into a great fighting force of cavalry and infantry. There were many rebel nests of resistance post Charleston. According to historian Thomas Fleming, at one point they traversed 210 miles (337 km) (gross distance in travel, not point to point which was a bit less thanks to turning and looping) in seven days, destroying 3 of these nests (he called them "pickup bands") and hauling 3 6-punders taken from the nests back to a British camp. That sortie carried with them seven day's worth of food, ammunition, and money (I guess to requisition food). The military value of this brigade is pretty good.

On the other hand Tarleton could be a liability. His presence inflamed Patriot passion, claiming he killed surrendering foes. It seems his horse was shot in a battle and when the Patriots tried to surrender, they were trying to do so not to Tarleton (again, off his horse and on his bottom) but to a mob of soldiers who thought the Patriots just killed their commander. Point being, he's great propaganda for the Patriots with every battle he fights, he's known as "The Butcher." Also, I think he's a lousy commander. in OTL Cowpens, he ignored the way his cavalry officer's were being picked off. On top of that he fell for a fake retreat. There is no shame in being fooled by Alexander the Great, Caesar, Eugene of Savoy, Maréchal de Saxe, or Napoleon. But... to fall for "fake retreat" just sounds like someone isn't taking his time to think.

And then there is the fact that Tarleton might not influence the campaign at all even if he was a great tactician. After winning a victory at Cowpens (more by luck, the quality of his troops, and the weather than tactical outthinking in TTL), Tarleton would likely follow the standing orders given by Cornwallis. He would go around South Carolina and stamp out any rebels who don't flee North. this is the last time he'll be in contact with Cornwallis for awhile. Then he would go through NC, with the prime target being Virginia. So now he has a rebel controlled state between him and Cornwallis, but that's OK, he's going to secure a port and they have enough money to requisition food. Once the base is secure, they will go around Virginia, crushing resistance like they did in SC and ignoring rebel fortifications (the unit built for speed and melee probably can't crack anyways), and trying to win loyalists on the rural areas east in the state. Cornwallis isn't contacting him, well he thinks nothing is wrong since communications are expected to be patchy with Cornwallis in the still rebel held NC. His scouts are only going to look around Virginia, following his original instructions unless the situation changes. And he's blissfully unaware Cornwallis is trapped in Yorktown and can't get a single horseman through to contact him.
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