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SAN FRANCISCO — The tourists arrived by the dozens carrying cameras and wearing sun hats only to be told that there would be no boats to the historic prison on Alcatraz Island.

“The government is shut down, and so Alcatraz is shut down until further notice,” shouted Nick Estrada, a security worker whose announcement prompted furrowed brows and confusion on the faces of visitors from across the world.

“What is the reason for this?” asked Brigit Roth, 29. “This would never happen in Austria.”

Ms. Roth and a friend had bought their Alcatraz tickets more than two months ago, only to be turned away because of a political impasse they did not understand. Back home in Austria, the two women had watched all the movies about the former prison in preparation for their visit.

About 5,000 people visit Alcatraz Island every day, and tickets tend to sell out far in advance. Between 1934 and 1963, the prison there held some of the nation’s most notorious criminals, including Al Capone, Machine Gun Kelly and the mob boss James (Whitey) Bulger.

More than a dozen people at the departure pier milled forlornly around a large-scale model of Alcatraz Island, among them Marie Fredlund, 49, and her two sons, ages 9 and 11.

“The boys are so sad,” said Ms. Fredlund, a Swede who lives in Beijing. “They know about Al Capone and all the attempted escapes. For them, going to Alcatraz was like being in an adventure movie.”