Re: Low pair, High board, and an LP
Your odds of picking up the pot on the flop are virtually nil, so if you don't think your opponent will fold to a turn bet, you shouldn't have bet the flop in the first place.
There are two consistent lines here:
1. Bet the flop, then bet the turn no matter what hits.
2. Give up and go on to the next hand.
Given that its a very small pot and you've got an opponent who will call down with anything (LP), line (2) seems far preferable.
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