This is a very common spot and I always have a hard time to find a best play in this kind of spot. I feel both betting and checking are make sense, I guess its depends on how we construct our whole range with other hands. But without software like CREV, its very hard to analyze hands on range vs range perspective. So Im gonna get some numbers with PokerJuice first and start by hand vs. range analysis, and see how things going.

I'm curious to know things like
a) Whats the immediate FE by betting on the flop? (I guess its pretty low)
b) Whats our EQ vs. his calling range?
c) Whats our EQ vs. his stack off range? Can I stack off profitable here? How about with diff stack size?
d) Whats villain's range distribution on the flop?
e) How many good/bad turn cards for our hand?

According to this assumption, we can start to do some EV calculation.

pot size = 16.2bb
eff stack = 90.9bb (SPR=5.6)
cbet size = 11bb

EV(bet) = %villain folds * payoff1 + %villain calls * payoff2 + %villain raises * payoff3

1) Assume villain always/only potting with his top range

2) I don't know whats the right way to estimate "payoff2", I made a sheet and use R factor to estimate it but I think its not a very good way.

By adjusting those parameters back and forth(assume villain's freq keep the same), I found

1) EV(bet-fold) is usually greater than EV(bet-call) with SPR=5.6. Except that if we just pot it, then BC is greater than BF due to the odds, but the EV of smaller cbet size is greater than with big size.

2) If we have a shallower stack, let SPR<4.4, then bet-call is always better than bet-fold.

3) with SPR=5.6 and cbet size=11bb, we need R>0.31 to make a profitable bet.

And then I wanna compare the EV between betting and checking, but its even harder to estimate the EV of checking cuz there are too many decision point on later streets and I dont feel using R factor to estimate would be accurate enough. I still make a sheet to estimate the EV though.

This is the sheet to calculate EV of XC, again I adjust the parameters back and forth and found EV of betting are usually greater than EV of XCing.

Thoughts
1) I believe that the R of betting is usually greater than checking in this spot, cuz this board is dynamic and I dont expect we could have a good R vs. good betting strategy.

2) I usually check on this kind of spot before cuz I think there are too many bad turn for my hand, but I found actually there are ~50% turn card are good for my hand, and by betting we can let him fold his bottom 30% range which had 25% equity and with position.

I know I still havnt find any solid conclusion here... will update this thread after I find more interesting things. This is my first post at PLO forum. Any suggestion/thoughts is appreciate!

Thanks