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...or if you are playing someone correct
I like to look at this from a purely mathematical perspective, let's play perfectly as villain, what combos of hands can we reach the river with that can call a bet that does not beat nut two pair? Zero
but if we get here with a flush draw, which will be naked most of the time on this board, we will have lost the hand, we didn't extract enough odds in a heads up pot, so to make up the ev we have to bluff the river, c/r bluff the river in fact, some % of the time in order to make up our odds
we can in fact calculate the amount of times we need to bluff to make it a zero ev play
the vast majority of players are not thinking at this level, so sure, go ahead and b/f, but the only 2 plays here that are correct are check and b/c
It's more complicated than that. In order to sometimes c/r bluff the river, the opponent would need to show up with an appropriately large c/r value range. Here, this would require having some AA/KK combos that flat pre and c/c flop and turn. In order to construct an appropriately-balanced polarized river c/r range, the opponent will have to have made significant adjustments to standard pre flop flop and turn value ranges. On the other part of the equation, the opponents range will be chock full of bluff catching hands and our range have a reasonable amount of total air.
Without making the requisite amount of PF/flop/turn slow plays, our opponent can only bluff at frequency ~25% as often as he actually backs into the straight. This clearly puts him on the other side of the polarized vs. bluffcatcher game. He needs to not fold the river 60% of the time here. Pretty much impossible to do using a strategy that never calls worse than AK and doesn't slow play AA/KK AND play raise or fold on flop/turn a preposterously high percentage of the time.
As a practical matter, the blind defender's river c/r range will be SO out of whack here that I want to punch myself in the nuts when I get c/r'd holding AA77.