[pete fabrizio]

well if you know your opponent is drawing with one card to come you would rather have a blocker than a third pair. but that's just one of many ways that another card could have more value, so it's not that interesting. you could be bluffing in a spot where you would prefer the person had some kind of set or two pair hand rather than the straight or flush showing, so not having the third pair card would make it slightly more likely that they had a pair or set of that rank. or conversely, if you're playing someone who will pay you off light, you might prefer to only have top two so that it's more likely they have top and bottom, allowing you to bet for value. are those the kinds of spots you're thinking of?

generally i could care less about the 3rd pair. although it makes it slightly less likely that someone has bottom set, and it gives you redraws if someone hits a made hand, it's kind of redundant and usually i'd rather have a card that gives me a gutshot or something. also it depends somewhat on rank, e.g. a third pair of deuces is not particularly useful since the person is unlikely to have a set of them anyway.

as for the hand i posted, i'm not so sure about it. it feels like maybe i'm overplaying it, especially when i run into a weirdly played top set, but looking over my hand histories i c/c, c/r with much worse and it works pretty well. people fold a large amount of the time, and frequently when they call i'm ahead anyway. in this particular hand i'd rather it were stacks were shorter or the pot were raised so that i wouldn't be leaving that awkward 8k to call, since op is in control of that money. but i'm pretty sure it's my standard line, and in a cash game i probably wouldn't have given it much thought.