Winning involves two variables. Time remaining (minimum possible) and bid amount (maximum possible).
I've been an active buyer for many years. My aggregate total in purchases well exceeds $10,000. This is an expensive hobby. In all those years I've never lost an auction. Not once. I've only twice been forced to pay anywhere near my actual maximum bid amount. And I was happy to do so (see below).
I've never used sniping software.
The key is to just manually place your bid 3-5 seconds before the auction closes. That's plenty close enough. As Truzi says, that help hold down bidding wars that get out of hand. Then make sure you have already considered well and decided in advance what your maximum comfortable bid amount will be.
You must be realistic. You must ask and answer with brutal honestly the two related questions, "If I win at this amount, will I still be happy? If I lose at this amount plus one dollar more, will I still be happy?"
If your answers to these two questions are honestly and truly yes, you're good to go. You will walk away happy regardless of what happens. And if, like me, you only bid on items that you really, really want and can really, really justify buying and will really, really use to solve real problems, your bid will almost always be the highest. And if someone else wanted it more, it won't matter. If it does, you didn't honestly answer those two questions.
I have yet to encounter that second outcome.