[dfan]

Mason, while the concept is a useful one and I appreciate you pointing it out to me (I had never thought of it that way) your guestimate as to what it does for your odds is off, at least in your first example. Also (unless I'm missing something) the math is simple and I'm surprised that you didn't recognize this.

The situation was a raise and 3 callers in front of you. You argued that none of these 4 players is likely to have a 3 given that they entered the hand.

Lets assume the best case, that these 4 players never have a 3. That means that instead of their being 50 unknown cards 2 of which are 3's (which gives you the usual 7.5 to 1 odds), in this case there are 42 unknown cards containing 2 3's. Then the prob of hitting a set on the flop is:
1 - (40/42 * 39/41 * 38/40) = 13.9% or odds of 6.1 to 1. While the bunching effect does improve your odds, it does not reach the 5 to 1 number you guestimate.

Also the 6.1 to 1 assumes that those 8 cards in your opponents hands NEVER includes a 3. Since this won't be true your true odds of hitting your set will be slightly worse.