Gonna just throw this out there and may not be entirely correct but it may get some things going. First, I think the 3rd reason you mention is basically #2. If you are not betting for value and trying to force your opponent to fold his equity, then essentially that is a bluff.

That being said, I do believe there are times when there is a 3rd reason that people bet and that is for protection. I believe that it is looked at this way because I am pretty sure that I read somewhere, that when you bet for value your are getting to the river and winning more than 50% of the time.

This hand doesn't really meet the value criteria. You very well could have the best hand right now vs a bunch of broadways, SCs, and smaller pocket pairs but by the time you get to the river you more than likely won't. I think a good example of this is with PP like 88-JJ and you have a fairly low dry board on the flop.

Whether or not to bet this I don't really know. I think sometimes I do and sometimes I don't. I think in spots like this, or the one I mentioned, if you opted to bet it could be looked at a lot like a semi bluff. You may opt to cbet this and be happy if you got broadways and such to fold out there equity. If you got called you would know that any 7 or any 9 would more than likely give you the best hand at that point so you could go into value mode. JT and 65 get there with the 9, so in this example maybe the 9 isn't the greatest card, but you get the general thinking. Not to mention cards like a 6 or a T could give you some more equity and outs. You could also continue to bluff on later streets depending on what the turn card is and how that card interacts with the your perceived range and the range of the villian. I think in a lot of cases this is a better cbet then maybe even some of the small pocket pair examples as you have more outs to improve. 5 outs immediately improve you and you have more backdoor possibilities vs a pocket pair that has only 2 direct outs to make a set and maybe some backdoor stuff. Obviously if you get called and any club comes it will make things more difficult, so in some cases this could just be fire once and then try and get to showdown. Others may say this is just a check and fold when bet to and just hope villains have nothing and check down, but I don't know that this will happen very often.

Nice post @fawltyfelix

Betting or checking in those spots mostly depend on how clean or good your outs are. If your twopair-outs are good and clean, like 86s on A82, I tend to bet, if the outs are not so great like in your example, I often check but if there are some backdoorouts possible it is often good/okay to bet. The backdoor outs should be nut-outs in terms of straights, flushouts to backdoorflush is often nice.

@Stats: If someone folds to much, I'll bet these hands, if someone raises often I'll check. Against unknown and good players I'll play and select hands like I write above.

@eroticjesus Thanks man. Nice to know my thinking is headed in a good direction. Actually just nice to know I am thinking in general.

I guess some of your advice and posts must be rubbing off on me