Just to clarify, a 3 bet would be him betting, you raising, him re raising, you calling, but that's just semantics. Pre flop, the blinds are considered the first bet, therefore, you raising him would be a 3 bet.
OTF, remember, you bet for 3 reasons, value, info, or a bluff. In this case, a raise would be warranted for information. If he flats, it's likely just a C bet and maybe a draw, if he 3 bets you, you're probably beat and can exit stage left minimizing your loses. When you flat call, he probably puts you on a draw or Ax.
The turn is a blank, he's betting here assuming it missed you entirely, i.e.; didn't complete your draw or improve your A. A call from you is about all you can do, a raise won't make any sense.
OTR, he's checking here because the club most likely scared him, or because he has you on something completely different and is banking on you bluffing at the pot. On your end, think about what you beat. AK, AJ, QT. Otherwise, you're only getting called by what beats you. Without being sure you have the nuts here, it's smarter just to check it down and show. When he raises you, he either thinks he has you beat (in which case he probably does), or he's spewing as a last ditch effort. Tough call.
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