The customer can be seen in the video sneaking up behind the suspect before hitting him with a bar stool. He also fought off the man using a potted plant, video shows.
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The man, 29, then chased the robber out of the bar. The man tackled him outside and the robber dropped the money before fleeing. He remains at large.
"I think it was very much a spur of the moment (thing), a reflex action by him. It's very courageous," Detective Acting Senior Sgt. Dane Sheraton told the Australian Associated Press.
The patron and bartender were not injured in the skirmish, police said.