In studying the campaigns of American generals such as Nathaniel Greene in various campaigns, George McClellan at Antietam,* George Meade at Gettysburg, and others, I was struck by the reluctance of them (and others) to follow up battles where they did major damage to their enemies, because of their own losses,even though a "second round" might have destroyed the enemy army, winning the war "right away." (The other side is weaker, so losing "half your army" does not mean losing the war.)
The probable exception to the rule that I can think of is Ulysses S. Grant,.
A Pyrrhic victory was defined by a winning general, Pyrrhus, who said something like, "if I win a another battle like the last one, I will lose the war, because my army would be destroyed." The converse of that would be something like "If I fight another battle like the last one, and lose half my army, I will win the war because the enemy will be totally destroyed."
Apart from Grant (and possibly his protege, William T. Sherman), are there any generals in history who made such a claim and went on to win a war in this way? Grant's behavior was so atypical that I was wondering which, if any other generals, at any time, was willing to take such a position.
*Example: At Antietam, an 87,000 man Union army lost 12,000 men against 10,000 from a 38,000 man Confederate army. If you "multiplied" those casualties by 3.8, the Confederates would have lost all 38,000, and the Union would have lost 46,000, a little more than "half" their army of 87,000. That's what I meant by "gambling half the army." That would have been a better result than having the war last two and a half more years.