I think that cbet is bad because he only call with K and the board is dry.
Check/call is fine?

Don't think you can go wrong with check/call and giving him the opportunity to bluff would tip this to a better play I assume. No way you can fold with the odds though.

Was going to say ofc he will only call if you pot c-bet but then realised villain only has $2.90 behind. If he is only calling with a K but is going to bluff a decent amount when checked to - then sure, it's better to check. But betting still has value in denying equity from hands with 15-20% equity.

Not only that, but I'm sure you will get calls from QQ, JJ and even some 8x if villain doesn't believe you and/or is a bad player.

With this particular hand, I do quite like a check - because we hold 2 back door draws ourself. But with a bare AA with no BD draws then it's better to deny hands from villain that might turn a flush + straight draw that have enough equity to then GII.

My default would have been to c-bet, too, but I do like the check/get it in line.

If he has a K then we're in bad shape irrespective of how we get it in, and, well, hard luck for us. We do have a couple of back door flush draws and a back door straight draw, which means we do have some equity if he doesn't already have a boat.

So the question about checking and risking a free card would be how many turn cards we don't want to see, and there are almost no real scare cards. If he has an 8 he can't make a better two pair than us with his side cards. Almost half the deck give us a flush draw. The only really awkward cards would be the remaining three 8s, and these are only bad if villain has an 8, in which case there are only two of them left in the deck and so less likely to hit when it is a problem.

So unless villain is super passive (won't bluff) and a calling station, likely calling with any 8 or high pocket pair (e.g. QQ-TT), I think checking has some merit.

The down side, which is not a concern at lower stakes, but which may become problematic at higher stakes, is that if you always check AAxx on boards like this in a 4-bet pot, you will become easy to read, and you'll surrender the possibility of bluffing when you have, say, QJT9.

There are probably some other alternatives we could take with bet-sizing. EDIT: But not when villain only has half pot behind.

All of the above assumes villain believes you're 4-betting wider than AAxx. If you are only 4-betting AAxx and villain knows this, then it doesn't much matter which line you take, because villain can play almost perfectly.

It might sound good in theory to check but in practice I think there is no other play than betting. I think you bet your air here almost 100% of the time because you have so much fold equity, so you also bet your AA. I bet this board like 1/4 pot size with my whole range, even less given that SPR. With this SPR I think there is not a lot more value in either of the plays.