Preflop:
I think it is ok to coldcall 88 there in general. It is w/o set hard to play postflop so one should check in his DB if he really turns a profit but i think on average it is still possible.
Some things that would work in our favour are:
- BB does not squeeze much but overcalls a lot.
- CO has a tight range CO-range and is SD-bound
- BB barrels a lot with air (better payoff with Sets).
Flop: If villain tends to cbet a lot 80% or more in HU-spots then i still prefer the checkraise here. C-betting too much is a quite common leak and craising a lot on boards he misses a lot of the time is a nice exploitive line. However if we think that villain checks back a lot on such boardstructures as he misses them a lot then a donk is the better alternative. Since the most likely coldcalling-Range from SB is PPs + Facecards + Ax it is actually not such a bad spot for villain to cbet a lot since we rarely ever have a Set and might fold OCs right away leaving us with a very weak calling-Range. But on average i think this board is perceived as to hit the SB more often than not so i do not expect too much cbetting.
Check-Calling is not an option in my opinion as there are plenty of cards that can kill the action even if he does not improve.
Hence i prefer the donkbet.
Considering the size I would argue that we should make it close to potsize. I personally dont expect random Floats so his most likely holdings that will call us are Pair+Draw, Overpair, 2pair or better. So he is likely to call us no matter what betsize we use (static callingrange).
If we want to balance this spot at least a little i suggest c-raising/donking JTs (if we have it) or other Tx type hands. We still have some outs and we cannot call with those anyway and become less readable.
Facing the raise i think we actually should be glad to get it in. if he is on a bluff he is not likely to continue on T+R so we dont miss out value. But he can very well have a lot worse hands that would like to get it in here but are less prone to do son once the Turn brings a scarecard.
Turn: I think check-calling here is only warranted in very special cases with very good reads. More often than not we encounter a negative freeroll. As the opponent appears to be straight forward i think bet/fold is the way to go. He can still call with a lot of worse hands but he is unlikely to raise anything but the 9. If he does so too small we can actually call for Quad/FHouts. As we have those and our line looks kind of weird i think he can actually valuebet worse hands so he have to call.
River: Since i do not expect him to fold any 9x on the flop it mainly depends on his preflop-Range how many 9x he can actually have. I am not so much afraid of the BD-Flush as hands like Th9h or 9h7h had us beat anyway. Only possible FD that now has us beat is 7h6h but i kind of doubt it would bet the Turn.
Opening from CO he can have 99,A9s,J9s,T9s,98s. And 97s A9o K9s Q9s are all possible too.
So he has at least 15 combos (99,A9s,T9s,98s) that beat us and he may have up to 55 combos (99, A9s-97s, A9o T9o, 7h6h).
In my opinion he is not likely to valuebet worse hands than ours. As we need 28% he must habe at least 4 combos to bluff with but we may need him to bluff 10+ combos. Since he does not have missed draws we need him to turn hands into a bluff. While he has enough weak made hands in his range i highly doubt that on this limit it is realistic.
Hence the River is an easy fold.