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There's no set time for it - it really depends on how you use them! The clearest sign is when the tread is worn down so much that you see smooth rubber, or when you start getting flats constantly. If you don't ride much, the tires might age before they wear out - after a few years check if the material is brittle or if there are cracks. A good rule is to inspect them once in a while: if they're worn down to the casing or you notice they're not holding pressure well, it's time to change them!
Besides worn tread, a simple trick is to press your fingernail into the tire: if you can make a deep mark easily, it's time to change them. Another sign a lot of people overlook is when tires start to "age" even if you don't use them much - after a couple of years the material gets brittle and loses grip, especially if you leave them in the sun. If you notice flats or punctures becoming frequent even on normal surfaces, or if the tire has cracks and splits on the sidewalls, that's the final wake-up call they're not waiting any longer.
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