You dont need to bring your own ball. I saw people there all the time, so I dont think it closes except for when there are tournaments.
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Past Cruises-
Sovereign of the Seas 2/03
Navigator of the Seas 2/04
Adventure of the Seas 2/05
Serenade of the Seas 2/06
Monarch of the Seas 7/06
Liberty of the Seas 8/07
Majesty of the Seas 5/08
I was on the Navigator in Oct. I was always able to checkout a ball to play. The balls, rims, and court are high quality too. My guess is that it is open during daylight hours. I never tried to get a ball at night.