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As eBay is using proxy bidding, legitimate question is - why snipe at all? If you submit your bid at eBay early, and if your maximum bid is higher than that of a sniping user, you will win regardless. While this fact is true, user experience and even some scientific research conducted says that sniping does pay. Here are some reasons why.
It's almost always good for you to use sniping. In the worst case, you may end up paying a tiny fraction more, because early bidder has a small advantage in fact that your bid has to be a bit higher (search for "Bidding increments" in eBay help), however situations 1-4 above by far outweigh this. Generally, less known the fair value of an item, it's more beneficial to use sniping.
There are three main ways to do this:
There is a number of paid software and online services you can use for sniping. Make an online search and you will find plenty. Here I will only list free ones:
Free sniping software: JBidWatcher.
Good luck with your sniping!