The South Wales Police released video of the February 5 incident on Tuesday.
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According to police, the victim had just used an ATM outside a Sainsbury's grocery store in Cardiff when a man with a backpack approached him.
The video shows the suspect grabbing the victim, but the 77-year-old broke free and began throwing boxing jabs.
The suspect made a few more attempts to steal the money, but the senior citizen kept punching.
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"The victim bravely fought off the suspect who made off empty-handed," police said in a Facebook post.
Police said 77-year-old man was left shaken. The suspect remained on the loose.