[Macquarie]

Hey,
it's getting pretty heated.

Two conclusions I think.

EV of a line through a hand is defined as expected profit from this decision forward relative to folding. Folding has 0EV. A line that starts with a check can have a negative EV if we make bad decisions afterwards; saying the check itself has -EV is meaningless without stating what your line is for the rest of the hand.

Folding the flop has 0EV by definition. If we decide to check the flop and fold any turn, that line has 0EV. If we check the flop and push a non-club turn, that line is +EV. If we decide to check the flop and fold any non-club and push any club turn, that line is -EV.

Whenever we talk about the EV of a decision we are actually also assuming how we will play out the rest of the hand and are really talking about the EV of a complete line to the end of the hand. Whenever we talk about the EV of calling a turn bet on a draw, we are assuming that we will not put in more money if we miss, and make a guess that villain will put in $x when we hit. In this case we are estimating how the hand will play out after the turn decision in order to make the EV calculation.

Other conclusion is, checking the flop and giving the villain "infinite odds" to draw to his hand is a better play than the push that gives villain better than correct odds. But this applies only in this case where we cannot protect with two cards to come on the flop, but can protect with one card to come on the turn.