First battle of the war: Paul Revere and William Dawes ride to Concord to warn the Patriots that the British were on their way to confiscate their weapons. The redcoats are intercepted by the colonists, and the shot heard round the world is fired. The British win at Lexington, but when they get to Concord they are chased away by Patriots.
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The British try to capture Bunker Hill, in Boston. As they ascend the hill, militia leader William Prescott orders his ragtag army to not fire until they can see the whites of their eyes. In the end the British won, but only on their third attempt, and they lost 40% of their army.
Washington planned an attack on the Hessian soldiers the day after Christmas, when they would be unaware. After crossing the Delaware River, the arrived at the garrison to find everybody inside due to the snowstorm. They were able to capture 800 hessians, and lose only one American. This was their first major victory.
The Battle of Saratoga was the turning point of the war. The Americans beat the British and Hessians, provoking interest in the French. This victory finally proved to them that the Americans had a chance of winning.
George Washington was unable to reclaim Philadelphia, so he instead sets up camp to shelter in for the winter. The camp, Valley Forge, becomes infested with sickness and malnourishment. After many deaths, a man named Baron van Steuben sets up a training program to get them back in shape to fight the British.
In this battle, the French aided the Americans, attacking from the left while the Patriots attacked from the right. The British surrendered, ending the war once and for all.