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Thanks. I'd discount Q-Js somewhat, since most players are more likely to knuckle, than raise, preflop with this hand, and the turn ace might slow Q-J down, especially out of position again two opponents, one of whom capped the flop.

When I said "strictly mathematical," I didn't mean to imply that you hadn't considered what hands BB was likely to have given the action. (Your analyses are unfailingly well-thought out and instructive.) A guy keeps betting like this I usually put greater emphasis on him having a great hand rather than a very good one. But no doubt BB wouldn't put either of his opponents on a set, given that neither of them raised pre-flop and he might figure Steve would slow play a set of 2s. And guys just don't put other guys on sets of deuces. He'd have reason to believe A-Q was the best hand, putting Steve on Q-J.

Your point, as usual, is well taken.

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Andy if we eliminate QJs, the hero would then be neutral at 9:9 against the BB's range. In this situation I would still feel compelled to raise the turn to protect my hand the times it is good, but if I somehow had all this information heads up I would just call down, since I would see no use in putting more money in the pot when I'm just even money to have the best hand.