It was my understanding that at the battle of Waterloo, Napolean was out numbered again with 128,000 to 234,000 Allies troops (coalition of British, Dutch, Belgian and Prussian forces.) Plus Napoleon's diplomacy did not go well a couple of years before the battle of Waterloo. In October of 1813, he faced four powers in what was to be known as the Battle of the Nations: Russia, Prussia, Austria and Sweden. It was a 3 days war that Napoleon was outnumbered and suffered heavily from his enemy's 1,400 artillery pieces. Napoleon's army had 38,000 casualties and lost 30,000 as prisoners. Napoleon's total losses for the year were around 400,000. It sent Napoleon retreating back toward France, Napoleon crossing westward over the Rhine River on November 2, 1813. Since 1813, France began to witness more invasion from the Allied and ultimately head Napolean to be exiled to Elba Island.
The battle of Waterloo was the last draw from the great Napolean who I believe was not well prepared for the battle as he had just overthrown Louis XVI in February and marched into Belgium by June of the same year.
Umm, the numbers are not quite as you suggest they were in the 100 Days campaign. In any event, for most of the battle the Prussians were not engaged. They did not arrive at Plancenoit in numbers until around 1700. By this time the French had thrown away most of their cavalry in massed attacks on the Allied centre, although the final straw was the failure of the Guards to break through the Allied line after the fall of La Haye Sainte.
Arguably, the day could have been won by Napoleon if Grouchy had marched to the sound of guns and prevented the Prussians from reaching Plancenoit. Had he done so, Napoleon's left flank would have remained secure, and he would have had an additional ten battalions of Guard to throw at the Allied centre.
In the 100 days campaign, Napoleon set out to pin the Prussians while destroying the Anglo-Belgian army in detail, and then turn to fight the Prussians.
To understand how Napoleon felt so confident in fighting two larger armies, it is important to understand the typical disposition of his army, and tactics. Napoleon typically marched his army in four bodies - an advance guard, a corps or more marching in parallel on each flank, and the vanguard. This diamond formation allowed easier foraging, less congestion on the roads (and hence faster movement), and the ability to change direction of advance by 90 or 180 degrees by changing the designation of each of the four formations. For a fuller explanation see David Chandler's seminal work, Campaigns of Napoleon