Six-high in a 3-bet pot: bet the river?

What is said

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1. 0:00River. The small blind checks to you.
2. 0:02You have six-four suited, on five, seven, nine, deuce, king. Six-high: complete air. Bet, or check?
3. 0:10Three-bet pot.
4. 0:11They check the flop. You bet, they call.
5. 0:13They check the turn. You bet, they call.
6. 0:16The river: a king. They check to you.
7. 0:19Your bet needs folds forty-four percent of the time.
8. 0:21The solver bets this hand every time. Checking can never win, and they fold forty-nine percent.