Never C-betting with air.

[RiversAreBad]

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not Cbetting is 0EV.

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No, folding is worth 0. Checking does not mean you lose the pot. Comparing a continuation bet with folding will strongly bias your analysis in favor of making continuation bets, even when they are less profitable than the alternatives.

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Folding is deffinatly worth 0EV, however checking is a different story. Checking could actually be close to -EV. If you will miss the flop 2/3 of the time with AK/AQ/KQ etc and your opponent will also miss the flop with two unpaired cards 2/3 of the time then checking when both have missed may be -EV. If you can expect your opponent to fold 2 out of 3 flops and you only bet when you hit (1/3) and check the rest you will be missing opportunities to pick up the pot. Say it is a 1-2 NL game and you raise to 10 out of the SB and the BB calls so the pot is 20. You will both miss the flop 2/3 times and you will both hit 1/3 of the time, so the pot is really split up like this: $13 is what you will be fighting for when you both miss and $7 is what you fight for when you both hit. If you both miss and it goes check check(assuming you are not going for a check-raise) then the bigger pot($13) will go to whichever one of your hands holds up or improves in the end. Essentially you are giving your opponent a chance to catch up, or perhaps to win with a better A high or something. If you give up the pot by checking it could be a -$13 EV rather than a 0EV. This is of course assuming your opponent folds when he misses and is a pretty simplified version but in this case checking could actually be worth -EV sometimes. And times that is could be worth +EV would be checking to induce a bluff or checking to as a slowplay.