We should use our range advantage to pressure the BB on dry boards, even when our specific hand has low showdown value.
We should lean toward betting here. As the UTG raiser, we have a massive range advantage on King-high dry boards, and T9s functions well as a mixed-frequency bluff.
Note: Checking is acceptable but betting small (33% pot) is preferred to leverage our range advantage and deny equity to BB's air.
The Jack is a great card for our range, but with our specific hand picking up a gutshot, we should be betting at a high frequency to maximize fold equity. **Ranges:** We have all the sets (KK, JJ, 66) and strong Kx that BB lacks. BB's range is very condensed to marginal pairs and draws after checking twice. **Sizing:** Solver prefers a large sizing or overbet here. This puts maximum pressure on BB's weak pairs (6x, 3x) and high-card hands that are struggling to continue. **Plan:** By betting large, we set up a river shove on many runouts. Our T9s is a perfect candidate because it blocks some of BB's potential Jx and straight draws. --- > **Takeaway:** When the turn improves your range advantage and gives you additional equity (like a gutshot), lean into aggression with large sizing.
Note: Checking back the turn misses a high-EV opportunity to overbet and polarize against a capped BB range.
After checking twice, we have no showdown value and must bet to win the pot. A small sizing is sufficient to fold out the bottom of BB's range. **Ranges:** BB is extremely capped after checking three streets. While we also checked, our range still contains more Kx and Jx that decided to pot-control, giving us the 'permission' to bluff. **Math:** We need very little fold equity for a 1/3 pot bet to be profitable. Since we lose 100% of the time at showdown, any fold we induce is a pure EV gain. **Blockers:** Our Ten and Nine are decent blockers, slightly reducing the combinations of T9 or Q9 that BB might have floated with, though BB's range is mostly weak pairs here. --- > **Takeaway:** On the river, if you have zero showdown value and the opponent has shown extreme weakness, a small 'probe' bluff is often mandatory.