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As posted by the other users, I think the things you need to consider are:
a) Know your opponent
b) Position
c) Have you defined your hand?
d) Flop texture
e) Strength in the face of high scare cards
a) Know your opponent: Level of skill, how they play with premium holdings, whether they stack off with Top Pair on the flop, or whether its 2 pairs+. Do they tend to slowplay their monster holdings like made straights, flushes or sets.
b) Position: being last to act and seeing which players limp or raise preflop is an advantage. limp callers probably have low to middle pairs, and raisers probably have big cards. If you have position against someone who slowplays a set, bet reasonable on the flop and turn, then check the river.
c) Defining your hand: Defining your hand could be dangerous for you here when the opponent has a set. Since you raised preflop, they would put you on a premium holding: big pair like AA, KK or big cards like AK. On the flop, if you alert them by defining your hand as unimproved AA - you run a higher chance of losing your stack to implied odds. Since by way of your action (a re-raise preflop and a re-raise on the flop), they know you have AA, and they know they have you beat. This makes the overpair laydown very difficult. However, if they believe you have AK and missed, they know they will not be paid.
d) Flop texture: This can give you clues, especially if the flop contains no draws. However on a drawing flop, the opponent could pretend to be pushing a semi-bluff flush draw into you - in the hope of disgusting the Set. Again you need to know your opponent.
e) When a high scare card lands on the Turn, that could have helped the preflop raiser: For example a Queen high flop followed by a King on the turn with no completed draws, and they still come out firing strongly. This could indicate a set or 2 pairs not afraid of a lone king.
If all else fails, just put it ALL IN on the flop. You might second guess yourself otherwise and make a bad laydown. Especially if the flop comes low, making alot of overpairs possible. The odds are well in your favour with you being ahead 87% of the time. Like in Super Systems by Doyle Brunson, if you get them cracked - you get them cracked.
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