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The single biggest factor when holding a big pair or 2 overs is how many other players saw the flop. If it's more than 2 and you don't even have a pair, seriously consider check & fold. AK gets around a 1 in 3 shot at hitting something, with more than 2 callers you paid your money, saw your flop and the odds of someone else hitting (and maybe even needing 2 cards to catch up) aren't with you today.
This is precisely why you raise these hands to limit the field. They play so much better against a small number of opponents.
The rest of my answers will assume 1 or 2 opponents
Flush draw comes up (2 cards or more suited), no high cards
Be careful, but don't assume you're beat if 3 suited cards come up. If an opponent has 2 suited cards (figure it can't be pairs, so maybe 1 in 5 shot?) they have a slightly less than 1 in 4 shot of matching the potential flush on the board, so that puts my back of the envelope guess at 1 in 20? Odds of them having the flush are even slightly lower if you have one of that suit in your pocket. Bet it if you otherwise got the best of it. If there are 3 suited cards on the flop or the turn and you don't have one of that suit however you should be a little more concerned.
Low pair shows up (7,7,2)
Probably safe to disregard, handle it pretty much like a miss. If you're really lucky a 7 will come up on the turn and the river giving you the nut! A lot of new players don't understand that any Ace is the nut when 4 of a kind are on the board, so go all in and see if they chase thinking it's a split pot.
Straight draw appears ( 10,9, 8 )
If it leads into a Jack or Queen and you have neither, be really concerned. Probably a good check & fold. One of the worst flops you can get with Big Slick.
Other high card appears (rainbow K/Q/J,2,5 but they don't match your A/K or A/Q).
More dangerous than a flat out miss. Play the other player, but check + fold is a looking pretty attractive.
I know position matters as well. I'm stuck on whether to bet high or not. If I have late position and everyone checks, I would try and take the pot I guess, possibly folding on a check raise.
This is why I like to show a lot of consistent moderate aggression and use pre-flop raises on hands like these to keep down the size of the field. I also play strong pairs from early position (unless I get a shot at re-raising) and moderate pairs the same way.
If I have early position, I get kind of stuck. I don't want to check (sign of weakness), but I don't want to bet into trips or the straight or flush with only Ace high. Then again, if I check, someone in late position most likely will just try to take the pot.
Start check-raising pot stealers more often. I've also come to learn to love beting the flop and check-raising the turn from early position.
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