While we have a range advantage, our specific hand is too weak to bluff on a board that connects so well with the caller's range.
Checking is the preferred play here. While we have a range advantage, this low, connected board hits the Button's calling range quite well, making a check-call or check-fold strategy more robust than a c-bet.
Note: C-betting with high card air on a board that favors the caller's range is low EV; checking allows us to realize equity or bluff-catch.
Checking is mandatory. The board is becoming increasingly connected, and our hand has zero showdown value and no direct draws to improve.
Bluffing here is a significant error. Although we have a range advantage, our specific hand lacks the necessary blockers to make this a profitable bluff against a range that contains many pairs and straights. **Ranges:** We have more sets and overpairs (AA-JJ), but the Button has many hands like 98s, 78s, and Tx that are not folding to a single river bet after the turn went check-check. **Board:** The 9s is a very dynamic card that completes several straights (78, 37, 23). This makes the Button's range much stickier as their draws have either realized or turned into bluff-catchers. **Math:** We are betting roughly 75% of the pot, meaning we need the Button to fold more than 43% of the time. Given how well this board connects with a flatting range, we rarely generate that much fold equity. --- > **Takeaway:** Don't turn high-card hands into bluffs on boards where the opponent has a high concentration of realized straights and pairs.
Note: River bluff is over-ambitious; we don't block the calling range (pairs/straights) and the Button is unlikely to fold enough to make this profitable.