How many swaps in a set of size n will ensure that the set is shuffled reasonably well?

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I'm implementing my own version of a shuffle method for shuffling a set of objects in a list. My implementation generates two (pseudo)random numbers and swaps the elements at these two indexes. Currently these swaps occur 1000 times, but this obviously isn't great for large lists.

My question, is there a way to find how many swaps should occur so that my list (of some size n) is shuffled reasonably well?

Thanks