As a hold em player who cut his teeth on the 1-5 stud games in the local cardroom, I am always aware of the probability that my cards might be live.
I mostly find this valuable with position preflop and in deciding how to proceed with drawing hands postflop.
Preflop with position, I am more likely to come into the pot (even a raised pot) with small pockets or medium suited connectors if there are callers. This is not only because I'm getting good pot odds to take a shot at hitting my hand, but also because I think the probability of hitting might be good. Say I'm in the cutoff with 44. I know that UTG didnt raise w a 4 in his hand and I can reasonably assume that the two middle poistion callers don't hold a 4 either. Actually - with all of the usual caveats about texture of the game, size of the raise and so on, I might sooner call with 44 here than with 88, since I could put middle position callers on a hand like 8-9 suited. The same reasoning allows a player to easily muck nice overs, even suited ones, in the same situation.
Postflop, I'll factor the liveness of cards into decisions; a four-flush or OESD
does not have the chance of hitting if I can reasonably put others on a similar draw based on their actions. Even if I think I'm drawing to a better hand, I can lay these draws down if the chances are that the outs are in other player's hands.

Any insights?