The bet between Eisenhower and Montgomery is a fitting memento of their turbulent relationship.
They disagreed about when the war would come to an end, just as they argued about almost everything else.
It would be hard to imagine two more contrasting characters. The American general: likeable, diplomatic, balanced and gregarious. The British general: egotistical, prickly, brilliant and caustic.
Yet despite their very different personalities, and frequent disagreements, they managed to work together, and won a war together.
Relations were tricky from the start: at their first meeting in 1942, Monty reprimanded Ike for smoking. They were mutually wary ever after.
Montgomery could be fabulously rude about his commander, telling one colleague: "He knows nothing whatever about how to make war or to fight battles. He should be kept away from all that business if we want to win this war."
Although he conceded that only Ike had the personality needed to maintain Allied co-operation, the sniping continued after the war. In his memoirs, Monty observed loftily: "I would not class Ike as a great soldier in the true sense of the word."
To his credit, Eisenhower showed remarkable patience in dealing with the sniping. Eisenhower and Montgomery had already disagreed over plans for invading Sicily in July 1943.
They would subsequently argue over Monty's tactics in Normandy after D-Day, and over Monty's claim to credit for victory at the Battle Of The Bulge.
In the final chapter of the war, Monty argued for a single, swift thrust into Germany, while Ike, he complained, was in favour of "bulling ahead on all fronts".
During a one-on-one planning session in September 1944, Montgomery is said to have launched into a patronising lecture, until Eisenhower interrupted: "Steady Monty," he said. "You cannot talk to me like this. I am your boss."
Montgomery mumbled: "Sorry, Ike." Yet this unlikely combination of a great soldier and great politician played an important part in bringing about victory.
In 1943, the end was in sight, but the odds on Ike and Monty ending the war still on speaking terms were very long indeed.