It IS possible to win by less than a full increment, but this happens only when your snipe comes in first and nearly its entire amount is needed to make you the top bidder, then someone else comes along in the final seconds and his bid is high enough (in terms of increment) to be accepted, but not enough to beat yours, but is a few cents shy of it.
To use your example: Let us say that the full amount of the winning bid is actually $3.68, though it still shows as $3.14. You come along with eight seconds remaining and bid $4.17, so if you could see the auction screen during those fleeting final seconds, you would appear as top bidder at $3.93, which is one .25¢ increment above the now-second place bid of $3.68. (Of course, you probably will not see the screen like that, as this all happens in a matter of seconds.)
Then, with five seconds remaining, another bidder (a sniper, like yourself) places a bid of $4.16. His bid is enough to be accepted by eBay, as it is at least one .25¢ increment above the current high bid of $3.93, and his max amount is posted in the bid history, because it is still lower than your top bid and is entirely used up in his attempt to win.
BUT, since your bid had already been accepted by eBay, and his came after yours (but still met the .25¢ increment he needed to have his bid accepted), his full $4.16 bid appears, but your slightly earlier $4.17 bid prevails, leading you to win the auction by one cent!
It is a tad confusing and happens very, very rarely, and depends on precise amounts being bid at precise times. This should not change one's sniping strategy, because there is no way to anticipate it. Just bid your max ath the last second through AS, and you will be happy.
