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Yes, you are correct. On the turn card (2/47), you have a 4.255% chance of hitting the set, and on the river (2/46) you have a 4.347% chance. While the odds are slightly better on the river because there is one less card in the deck, it's not really enough to ever make a difference.
As a practical matter, if you are in a game with a lot of callers, and you have a pair of Aces, Kings, Queens, and even Jacks, the fact that there are other callers may indicate that there's a slightly smaller chance that you are going to hit your set.
The reasoning: More players will play hands like AT, JT, QT, than hands like 3-6, or 4-7. For the same reason, let's say you have AA, and the flop comes 10-3-3. In this case, there's probably a smaller chance that someone is out there with three 3's, than if the flop was 10-J-J. However, this assumes people play fairly well pre-flop (ie. they aren't going to play something like 4-8 in early, or middle position). If you have really loose players who will play Ace-anything or King-anything (which is very frequent online), all this is irrelevant.
Again, this shouldn't really enter into your thinking much at all, as it doesn't really affect strategic play. Without proper odds (which basically never happens in No Limit, unless you have a very passive and loose table), you should never chase a set past the flop. There have been several times in No Limit tournaments where I've folded small pairs when there has been a big raise to my right - it's just too costly to play.
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