How about some hand ranges here
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Checking behind with outs is good if we're not likely to have the best hand. That's not the case here.
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Actually, I think there is where we disagree. It's fairly likely we don't currently have the best hand if a reasonable BB calls a bet on this flop.
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I agree, which is why Hero should check behind here.
Let's assume that villain has a reasonable blind defense range and for simplicity's sake that he will always call and not re-raise against a perceived steal raise from button. Let's also assume that while he may chase draws with not quite proper odds on the flop, he doesn't get too carried away with it. When villain check-calls this flop and then checks the turn I think a somewhat reasonable (but probably too broad) hand range for him is:
AA-22; AK -- AT; KQ - KT; K9s; QJ-QT; Q9s; JT; J9s; J8s; T9s; T8;; 8c7c; 7c6c;5c6c.
Hero is chopping with 9 combos (one of which is freerolling against him), ahead of 33 combos and behind 141 combos.
Thus, unless you asume a pretty high fold equity on a turn bet it looks like Hero can use the free card more than it can hurt him. And that's the case even if we knew there was no risk of a check-raise (which, of course, we don't).
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