When our semi-bluff doesn't improve and we face a large river bet, we must fold our high card and wait for better spots.
Checking is the preferred play here. While we have a slight range advantage on this Ace-high board, our specific hand lacks any direct draw or pair, making it a poor candidate for a c-bet.
Note: Betting here is unnecessary; checking allows us to realize equity or bluff later streets with better board coverage.
After betting the flop, we should follow through with an overbet on the Ten. We now have a nut gutshot and our range contains many strong Ax and Tx hands that want to put maximum pressure on the Big Blind.
Note: Checking misses a high-EV opportunity to overbet and polarize our range with a nut gutshot semi-bluff.
Checking is the only play. Our hand has zero showdown value and we have no reason to turn it into a bluff after the turn went check-check.
Folding is mandatory. We are at the absolute bottom of our range and Villain is representing a polarized range with a large overbet.