It's not how often it's charged, it's how low you let it discharge before charging it. If you never let it drop below 40%, it should last for years. If you use it until the phone shuts off every day, it'll be dead in about 6 months.
50% happens to be about the best charging point for longest life. You'll probably get tired of the phone long before the battery shows signs of losing capacity. Considering that it's an S3, you might find that apps are getting too large for it to install the latest ones (and the CPU isn't fast enough to run them well) even before you get tired of the phone. (My 11 year old V-551 original batteries [I always carry a spare] still give me about 95% capacity.)
And even if the battery should go (if it grows a dendrite - something the industry still hasn't figured out how to predict or prevent - it has to be replaced, even if it happens a few months into its life), an Anker battery for the S3 (I like them better than Samsung batteries) is only $10.