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Rincewind was trained (if unsuccessfully) at the Unseen University. One thing he failed to learn was how to spell 'wizard', a fact made obvious by the 'wizzard' logo on his hat. He spent most of his time in the (then) Broken Drum. All that changed when he met Twoflower (the Discworld's first (and last) tourist) in the Drum.
Together, along with Twoflower's luggage (on thousands of legs) they travelled the Disc, met Cohen the Barbarian's tribe, died, saved the world and got chased by a personification of Death. They were allowed to survive by Death, because after Rincewind's failed magical exploits and dimensional shifts, his life timer looked like it had been created by a 'glassblower with the hiccups'. Thus, as even Death didn't know when Rincewind's time would come, and he was needed to save the world, he was allowed to live.
Rincewind's lack of magical ability is compensated for by the fact that he can run away from whatever circumstances arise. It's said that he has the spirit of a wizard and the body of a long distance runner. Rincewind has the ability to solve any minor problem by turning it into a major disaster. Rincewind has said that to balance out the karma of the universe, there must be someone, somewhere who has all the luck in the world. He says he would like to meet him sometime, preferably whilst carrying a large weapon. Despite his lack of courage, it has been suggested that he is one of the few people on the Disc with any common sense.