What are the most decisive battles of the revolutionary war under George Washington and the outcome

1 - Saratoga

Yes, even over Yorktown, because Saratoga brought decisive French support to the American cause.

#2 - Chesapeake Bay

Without the defeat of the British fleet, Yorktown never occurs.

#3 - Yorktown

Yorktown effectively ended the war.

#4 - Trenton

Trenton kept the Continental Army alive and kicking.

#5 - Boston

Kicking the British out of the center of the revolution gave the patriots legitimacy, ensuring that the revolution would not just peter out through lack of activity.