Gary, did you listen to the episode?
Sorry for being late on the reply -- had other things going. Yes, I did watch and listen to the episode.
Of course, Kirk didn't realize it was a duel to the death initially... but even still after he learned of this, he was now aware that there would have to be a death in the outcome. Why even continue, knowing how Spock has the Vulcan strength advantage? He should have declined and appealed to T'PAU because he was NOT informed of the death requirement.
So Kirk took a huge risk going forward, as Spock would've killed him due to his mental state. In my interpretation, I believe Kirk was going for the angle of hoping to disable Spock in some way and then not go through with the killing, call it a draw.
Bones took a calculated risk, but he was against the wall, should he stand and do nothing? So he actually allowed Kirk to "quit" by drugging him. Honor was satisfied and no one died. The dialogue is quite clear.
I never suggested otherwise--of course it was prudent for Bones to try something. He did take a huge gamble. Spock was strangling Kirk and then Kirk goes limp due to the neural paralyzer injection. But Spock could've easily snapped Kirk's neck once his resistance went slack. Thankfully Spock didn't keep applying pressure and stopped once Kirk had passed out.
Anyway, I probably came across a bit more harsh than I intended.