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For example, if you have AK on a QTx flop and bet half the pot into 2 opponents, they will both have to fold roughly 33% of the time [adjusted for the times JT just calls/would have bet if you checked, and the turn card is an ace, so it's actually around 30%] for the bet to make any sense. If you bet the pot, they must both fold slightly under 50% of the time.

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I'm not following you.

You bet so as to offer opponents 3:1 and they both have to fold 1/3 of the time to make the bet profitable.

You bet so as to offer opponents 2:1 and they both have to fold 1/2 of the time to make the bet profitable.

Yet not accounting for other factors, this event will only happen roughly 1/6 of the time (2 players each with 3 possible decisions {call, raise, fold}, 6 possible outcomes one of which is both fold).

On this basis alone, are either of the bets rational?

I have to believe that players are more inclined to fold if one bets the pot (or better still overbets the pot) rather than half the pot. But facing two opponents one would have to have some combination of factors working in his or her favor (e.g., much bigger stack, proven ability to knock people out with semi-bluffs, or simply being in the outright lead at that point).

A lot would seem to depend on the preflop action and subjective probabilities of their likelihood of folding versus caling or raising.

In other words, using your example with AK, presumably you raised and were called by two players preflop. The flop more or less completely missed you.

So what is the probability that flop hit one of the others? Or what is the probability that you were behind from the start (eg., one or both opponents is on a medium pair) and are now down to perhaps 10 outs at best with the QT flop.

Under these circumstances, wouldn't you need a higher probability of both opponents folding in order to make your bet profitable?

I guess what I'm getting at is that this is a much more complicated situation facing two opponents, one of whom presumably cold called and the other overcalled preflop. Head-up is a whole different and probably simpler story.

I tend to be thick in the head on theory, so maybe I'm not looking at this in the right way. Hence my response in an effort to exchange dialog and learn.