There's no doubt that Prince William is eager to welcome his first child with wife Kate Middleton. But until the royal baby decides to make an appearance, the Duke of Cambridge still has duties and obligations to fulfill as a member of the royal family. On Saturday, July 13, he and his younger brother, Prince Harry, competed against each other in the Kent & Curwen Royal Polo Cup in Sydmonton, England. 

PHOTOS: Kate Middleton's royal pregnancy style

The 31-year-old first-time father-to-be was playing on behalf of the Tusk Trust and Sentebale charities. At halftime, his team led Harry's two goals to one. By the end of the match, however, the tables had turned. Uncle-to-be Harry and his teammates pulled ahead, beating Prince William four goals to three.

PHOTOS: Brush up on the royal family tree

The Duke of Cambridge didn't stick around long after losing, but only because he wanted to get home to his nine-months-pregnant wife. William has been at Kensington Palace in London since Wednesday, July 10, after a long shift with the Royal Air Force in Anglesey. He is expected to return to work on Monday, July 15 -- assuming the Duchess doesn't give birth before then, of course. (Barring any surprise deliveries, he'll also compete in a polo match on Sunday, July 14, in aid of WellChild, Centrepoint, and Child Bereavement UK.)

PHOTOS: Princess Diana's pregnancy with William

It's been a busy few days for the royal family. Amid the increasing royal baby mania, Queen Elizabeth II opened up Buckingham Palace this week to host the Coronation Festival. On Thursday, July 11, the Middleton family -- Pippa, James, Michael, and Carole -- joined the Queen, Prince Charles, Camilla, Duchess of Cornwall, and others at the Coronation Festival Concert in celebration of the 60th anniversary of the Queen's coronation.

PHOTOS: The Duke and Duchess as kids

Aunt-to-be Pippa also had an out-of-town obligation on Saturday, July 13. She flew to Vienna for the day to attend the wedding of Caroline Sieber and Fritz Von Westonholtz.

The Duchess, meanwhile, is nesting at Nottingham Cottage as she awaits her baby's birth. "Catherine and William are very much looking forward to the arrival of their son or daughter," a palace aide told Us. "It's a very exciting time for the couple and their families."

This article originally appeared on Prince William, Prince Harry Play Polo as Kate Middleton Awaits Royal Baby's Birth