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Had King George III been as willing to shed blood as Lincoln, George Washington would have been ultimately beaten.

Not really. Tarleton and other British commanders could be quite brutal. What changed was the nature of war. 19th century war became mass war with much greater firepower.

[DiogenesLamp]

My point is that King George had the forces at his disposal to grind Washington down until he was defeated. He chose not to use them.

Had King George III decided to keep sending armies against Washington, he could have done so. He relented.