67s on the button, 8 to the flop, i flop top pair

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Our equity against 7 completely random hands is ~18.2%. The random hands equity is ~11.7%. A 'fair share' would be 12.5%. Notice that we are actually likely to improve and still lose, our showdown equity is significantly lower than our chance to improve.

If we are sure that 6 people will call our bet we can treat a bet like pumping a draw, actually we want to be fairly certain all 7 will call as atleast 4 of them hold a non-random hand.

If for some bizarre reason we were sure our opponents were so tight that a bet would cut it down to 1-2 villains we could bet for that reason. The problem is that we are going to end up somewhere between those extremities.

Betting to avoid giving infinite odds is a good point though. (And I retract the likeness to 2OP hands) It's pretty much the only point really.

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Our opponents won't have random hands when they call our bets. Randomness is weighting the odds of AA and 82o equally likely as calling bets on this board and that's bad from what I can see.

As I said to a friend, you're not going to win this pot as often as you'd like, but you'll win it more than often enough to justify putting bets -- be it one or multiple -- in on the flop.

Rob