By all counts the odds were stacked against the United States winning their independence, so why did the American Revolution succeed?

There are several factors that made the triumph of American Revolution possible.

In the first place, after initial defeats and mistakes, the patriots of the Continental Army and the militias fought bravely and with determination to have a free homeland. Secondly, the support of France was fundamental to beat the British: supplies, weapons, ammunitions, the engagement of the French navy and troops. Thirdly, the British had the disadvantage of having long lines of supply, it was hard and costly to send more troops and supplies from Britain, and particularly after the French and Spanish blockade. And we can safely quote as a fourth reason the great human, moral and intellectual quality of the Founding Fathers who were able to overcome their personal differences in order to reach a common vision with shared values of the future free nation.