Flop Analysis
On 7s-4h-4s, we have a small range advantage but BB’s defend range is fairly strong, so mixing between small c-bet and check is fine. Checking here is a reasonable mix, especially OOP with a hand that has no real draw and only A-high.
After calling flop and checking turn, we should shove river on the Ace for value; checking leaves money on the table.
On 7s-4h-4s, we have a small range advantage but BB’s defend range is fairly strong, so mixing between small c-bet and check is fine. Checking here is a reasonable mix, especially OOP with a hand that has no real draw and only A-high.
BB bets 3.5BB into 6.9BB, so we’re getting ~3:1 and need ~25% equity. A8s with A-high and a spade has enough equity to continue—our hand is ahead of a lot of BB’s air and some weaker pairs, and we still have some redraws to better hands.
Turn Js is a bad card for us: BB’s range improves with Jx and we still have no made hand. Our range is now somewhat polarized, but we don’t want to bluff into a range that has picked up more strong hands, so checking again is best.
River Ac gives us top two, but with SPR ~1.5 and BB having a capped range, we should bet for value. Shoving for ~20BB into ~14BB is the highest-EV line—BB can call with worse Ax and some 4x, while checking gives up a very profitable shove.
Note: River should be a value shove; checking top two with SPR ~1.5 leaves money on the table versus a capped BB range.