Six-high on the river: shove or give up?

What is said

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1. 0:00River. The big blind checks to you.
2. 0:02You have six-four suited, on seven, king, ace, three, deuce. Six-high: complete air. Shove, or check?
3. 0:09Three-bet pot.
4. 0:10They bet the flop. You call.
5. 0:11They check the turn. You bet, they call.
6. 0:14The river: a deuce. They check to you.
7. 0:16Your shove needs folds fifty-eight percent of the time.
8. 0:19The solver shoves this hand every time. Checking can never win, and they fold sixty-six percent.