What makes a great general? Napoleon, who knew a thing or two about generalship, said he would rather have a lucky general than a good one. Yet he didn't mean a commander who blithely staked the fortunes of war on a roll of the dice, as if combat were a spin at the Vegas roulette wheel. A lucky general was one with a cool head who could take advantage of opportunities.

Some qualities seem universal: perseverance, shrewdness and keeping cool during a crisis. Others are debatable: Some would say a professional military education from institutions such as West Point is a necessity, while Vo Nguyen Giap, the schoolteacher who became the general that defeated professional French and American commanders, might disagree.

Either way, in its nearly 250-year history, America has produced some very good and very bad generals. Each was great in his own way, in the circumstances of his time and in the qualities that America needed.

But greatness they earned, and here are five of the best:

George Washington:

It was Washington's misfortune to end up on the $1 bill. The portrait of what appears to be an effete old man in a wig has caused future generations of Americans to underestimate him.

In reality, he was a physically tough and mentally ruthless commander. He had to be. His successors, like Grant or Eisenhower, might have lost a war for the United States. For Washington, defeat of the American Revolution meant losing the only war that mattered.

Many doubted he could succeed. How could a bunch of ragged, poorly supplied and untrained colonists beat an army of formidable British redcoats backed by the power of the Royal Navy?  But he did succeed, aided by British strategic miscalculations, French logistical and military aid, and the sheer enormity of Britain trying to control an area the size of the eastern United States with an 18th-century army.

Washington may not have been a great battle captain of Napoleonic caliber, as evidenced by his disastrous New York campaign of 1776. Yet by Bonaparte's standards, he could be considered lucky, as when he exploited British mistakes to win the Battle of Trenton and restore flagging American morale.

However, his real genius was strategic insight. He simply realized that as long as he kept the Continental Army intact and able to strike, the British could never consolidate control of their former colonies. He didn't need to destroy the British armies; just occupying their attention while American militia and guerrillas harassed British troops and eliminated Loyalist strongholds would be enough to sustain the Revolution and wear down London's resolve.

Winfield Scott:

Since 1943, America has become accustomed to launching amphibious assaults of overwhelming strength. D-Day and Tarawa were tough battles, but at least the attackers were backed by massive resources.

When Scott landed at Vera Cruz, Mexico in March 1847, he was conducting the largest American amphibious assault until World War II. But where Eisenhower at Normandy could land 150,000 men backed by enormous naval and air support, Scott had just 10,000 men.

Yet he marched 200 miles from his beachhead to Mexico City, fought and won several battles against Mexican forces that were sometimes superior in numbers, and seized the Mexican capital. And he did so on a slender logistical thread while deep in enemy territory.

Granted that Santa Anna's army of the Mexican-American War wasn't exactly Hitler's Wehrmacht. Or, that the U.S. force was a Who's Who of future Civil War stars, including Lee, Grant and Jackson. Nonetheless, Scott made intrepid and skillful use of what he had to win what turned America into a continental power.

Ulysses Grant:

Grant or Lee? Lee or Grant? Trying to decide which general was better will trigger debate and tempers until America itself is but a memory.

But ultimately, Grant gets the nod, because he had a keener sense of the military realities of the War Between the States. Lee was a superb commander who masterfully defeated a series of hapless Union generals, and held his own to the bitter end against Grant. Had he accepted an offer to command the Union army at the beginning of the war, America's bloodiest conflict might have ended in four months instead of four years.

Yet winning battles doesn't equate to winning conflicts, as Germany also learned in two world wars. To win, the Confederacy had to survive in the face of stronger Union military and economic resources, until war-weariness induced the North to accept Southern independence. For this to happen, the South needed strong armies—but only strong enough to parry Union thrusts and convince the Yankees of the futility of their efforts.

Every battle fought by Lee and his Army of Northern Virginia, even if it made fools of McClellan, Hooker and the Army of the Potomac, was one more battle that bled Confederate manpower. Obviously, winning battles is a path to victory. But to what end did Bull Run and Chancellorsville lead? The Army of the Potomac was not destroyed, Washington and other Northern cities were not captured, and the Union fought on.

Grant saw that to win, the Union had to keep a death grip upon the Army of Northern Virginia, engaging the cream of the Confederate armies while Sherman's armies devastated their way through the South. Grant was no more a butcher than Lee—Pickett's Charge was as bloody and futile as Cold Harbor—but he knew that the road to victory could not be won bloodlessly.

George Marshall:

If any one man deserves credit for America's victory in World War II, it is Marshall. When he became U.S. Army Chief of Staff in 1939, he inherited an army smaller than that of Romania and led by decrepit old generals unfit to lead a Boy Scout troop. By 1945, he had built the most formidable fighting machine in the Western world, arguably second only to the Red Army.

Marshall was not a commander of armies, though some thought he might have done better than Eisenhower. But he had a ruthless eye for getting rid of deadwood generals, and an even better eye for picking stars such as Patton and Bradley. Notably, he picked a colonel named Dwight Eisenhower and elevated him to supreme commander in Europe.

He won't go down in history as a legendary battle captain, but he also proves that the battlefield isn't the only way to win the laurels of a great general.

Matthew Ridgway:

Korea was not the U.S. military's finest hour. "The wrong war, at the wrong place, at the wrong time, and with the wrong enemy," was how General Omar Bradley described "The Forgotten War."

The nadir of American fortunes was in the winter of 1950-51, when Douglas MacArthur's arrogant and foolish drive through North Korea to the Chinese border triggered a surprise counteroffensive by 300,000 Chinese soldiers. Surprised, dispersed and unprepared, the UN forces were routed.

Fortunately, President Truman got rid of MacArthur as supreme UN commander and appointed Ridgway, a noted World War II paratroop general, famous for wearing a grenade strapped to his uniform. Appalled by the defeatist "bug out" retreat fever of his forces, Ridgway fired inadequate officers and demanded aggressiveness from his troops. But for all his bellicosity, Ridgway's tactics were methodical, sound and calibrated to the strengths of his troops and the nations from which they came.

He launched carefully prepared and focused offensives that relied on maximum air and artillery firepower to inflict massive Communist casualties at minimum cost to his troops. This may have lacked the elegant operational art of a Rommel or the grandiose goals of a MacArthur. But in the Cold War, where nuclear annihilation meant conflicts had to be restricted, and Western peoples were not willing to accept huge casualties, they were the right tactics at the right time.

Michael Peck is a contributing writer at Foreign Policy and a writer for War Is Boring. Follow him on Twitter:@Mipeck1.

Image: Flickr/Contando Estrelas/CC by-sa 2.0