Schooling is not the same thing as what you're talking about. Schooling is when a made hand goes from being a favorite shorthanded to being an underdog (as in winning less than its share) in a multiway pot because there are so many ways for it to lose. A good example would be 22, it's a favorite against most non-pairs heads up but put it against 3 non-pairs that don't share cards and it's less (against AKo, QJo, and T9o it's only 22% or so to win even though it's a slight favorite against each hand individually)
About not raising the favorite: one thing to realize is that any time you don't bet or raise the best hand, you are giving up EV on
that round. So the question is, is it worth it to push an equity edge on an earlier round if that edge mitigates mistakes on later rounds?
Actually even that statement isn't entirely accurate. You make money when called as the favorite, even if your opponents are correct to call. However, there is a specific situation where you can consider not raising:
-Your equity edge is small
-Your opponents call too much
-Raising may bloat the pot to the point where you are forced to call on the next street, where not raising would allow you to fold your weaker hands
In this circumstance you can limp and then make up for it by folding as an underdog if you hit a mostly unfavorable flop.
With all the above in mind,
don't talk yourself out of raising big pairs. The first requirement, that your edge be
small, is not met. Generally the requirement about making you more likely to call isn't met either because PPs don't tend to flop draws.
However, you can do this preflop with big offsuit cards (other than AKo and AQo, again your edge is just too much to give up). Your edge is usually like 2% so you're not giving up much by just calling so you can fold a gutshot draw.
On the flop, in your example it could be correct to not raise. But notice I just said don't
raise, not don't
bet. A free card won't make a difference for open-straights and four-flushes. It will make a difference if someone has the naked A [img]/images/graemlins/club.gif[/img], or small pocket pairs, or other random cards that can catch a backdoor straight. Even though you can't protect your hand from some hands, you can protect it from enough hands that betting is necessary.
As far as whether to raise, depends on where the bet comes from. If it comes from my right I raise since certain hands like a gutshot are now getting correct odds to call if I just call. If UTG bets then I call hoping for a safe turn planning to raise there.
Another note: this concept is not a reason not to raise a set on a two-flush board (there might be other reasons, just this isn't it. [img]/images/graemlins/smile.gif[/img] ). You're calling the turn no matter what it is so you might as well get the money in as a favorite.