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To me, the answer is pretty clear.
I would bet big!!
– if they fold, who cares, they likely would have folded to a smaller bet also. Bluff catchers are rare with 4 to a straight on the board. They need showdown value to call. Make them pay if they think they have the best hand.
– if I’m bluffing, I don’t want to offer a good price for them to get curious and call. My plan is to bluff big and value bet slightly bigger. DNegs made this comment on the RecPoker podcast.
– when value betting the river, your goal should not be to catch BOTH fish. Thats unrealistic. Plan on getting only one caller. If both call and you have the nuts, sweet….but don’t plan on it happening. Ideally, I want to get called or raised by a worse straight, a set, or an inferior two pair. If these hands will call a 50% bet, they will likely call 75% bet just as often. Especially if these hands think you’re bluffing or they think they have you beat.
If it’s a tournament, my bet size will depend on stack size. In a cash game, I’m likely betting 75% of the pot or larger.