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Jack: You've accidentally doubled the likelihood of catching your set, it's about 4.3% on the turn (and another 4.3% on the river).
I hate to say, "It all depends", but it really does (I'm talking about $10NL). If I raise, it's 4xbb+1bb per caller, and the c-bet (or call) depends on the flop and what I have. If I'm TT/JJ the only way I won't bet is if the flop is a dissaster (say straight/monotone flop) and there are multiple callers. The other ones are very flop dependent. What's also important is whether or not I want to hit my set. (For instance, if there are already two hearts down, then I'm not sure I want my 8h to hit. Or, if the board is JTx and if I have 99/88 I really don't want my set to hit).
Finally, I'm always surprised how often a mid-ish pp winds up holding up and winning the pot. This doesn't mean I'll call a raise/reraise post-flop, but if the bets are low in proportion to the pot I may call where I would otherwise fold.
Good luck.
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