1713--Treaty of Aix left France and Prussia against Austria and England. By 1756 it was England and Prussia against France and Austria. How? Frederick liked to believe his insults to Mme Pompadour and Czarina Elizabeth--nonsense. Old reasons for French/Austrian hatred largely dead, and Kaunitz had sounded out France as early as 1748. Also France and Austria saw each other as the surviving Catholic champions of Europe. Clincher was English deal with Elizabeth to guarantee Hanover. Frederick offered himself instead, England agreed. Russia angry, France again stabbed in the back--thus Treaty of Versailles 1756. Russia also joins France.
Marriage to Marie Antoinette sealed the deal--very unpopular. Frederick got English gold, Maria Theresa got French troops to fight Prussia, England got security of Hanover--France got nothing.
Maria Theresa had 130,000 men--good officers and men, but too slow and raditional. Frederick raised army to 147,000 and trained them with brutal discipline. Russia had 360,000 men on paper, really only 130,000 in field--stubborn serfs with bad officers, little cavalry, and a huge baggage train. France 180,000 men with incompetent noble officers.
Frederick fought on inner lines, but needed quick movement to keep his enemies apart. Bottled up French in Hanover and turned east, but eventually driven out of Bohemia. Had to take defensive in 2nd half of war (1758-1759). Defeated by Russians at Kumersdorf near Frankfurt, almost committed suicide. But neither Russia nor Austria followed up on their victories, and Frederick regrouped. Then Elizabeth died and was followed by Peter III, a fan of Frederick, who went over to his side. Austria had to sign peace treaty of Hubertsburg in 1763. Frederick took Silesia and won the war.
Frederick's tactics brilliant--famous advance en échelon at Leuthen against Austria. England gave him a subsudy of £670,000 a year and maintained its "army of observation" in the west--worth another £1,000,000. England forgot Silesia and turned "Old Fritz" into Frederick the Great, the Protestant hero. Prussia greater than Austria in Germany, and greater than France in Europe. And it was this successful, militarized Prussia that would unite Germany in the next century.
William Pitt the Elder became Secretary of State in 1757 and directed the war effort. But besides bankrolling Frederick, he wanted all of America east of the Mississippi. 1759 The Plains of Abraham. 1757 Robert Dlive at Plassey. In West Indies British seized the sugar and slave trade. Deal sealed in Treaty of Paris, 1763 by Pitt's successor the Earl of Bute. Results of expenses ultimately the American and French Revolutions.