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This was a loss for the American armies which left the British troops with a victory. This war caused a lot of casualties on the American side. Although it is called the Battle of Bunker Hill most of the battle was actually held on a nearby at Breed's Hill (History.com).
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George Washington and what he had left for troops crossed the Delaware River where they surprise attacked the British army at Trenton and after ten days they claimed a victory after a long losing streak this was to be found as a turning point in the war finally in Americas favor (History.com).