Hello! So, can you guys tell if my thought process is wrong? Lets say we open raise KK mp and the button calls. the flop is Ah7d9h, we check and he bets, knowing that he has a A on his hand and we have the K of hearts, he bets half pot, giving us 1/4 pot odds, the same that is to get a K or another heart on turn which will give us 1/4 odds to call the a bet on turn, if is guaranteed that he will bet half pot again, the odds we need to follow with a flush and a K draw, plus the implied odds, is this thought wrong?

It is incorrect. Getting correct odds just means that the value of calling is more than 0. If we barely have odds to call it means that the value of our call is a small positive number.

So on the flop we aren't drawing for the whole pot. We are drawing for a situation that will give us a small amount of value. To give some number let's say pot is $100 on the flop, villain bets $50 we call and hit a heart draw. Villain bets $100 into $200. Assuming we have 22% to hit and villain always calls $300 when we do the value of calling is $32, so calling is correct here.

So was our call on the flop also correct? No, because we called $50 for the opportunity to "win" $32, about 20% of the time. Clearly a bad call.

My thought was: calls 50 into 100, 3 times loses 50 (-150)
1 times follow calling 100 into 200, losing 3 times 100 (-300).
If its sure that the villan would call 3/4 bet into 400, winning a pot of 700$, being half the 400 pot my money.
700-200= 500-450= 50 profit.

but anyways, not worth.

Even if we think he has an Ax here, I'm still calling otherwise we would be folding too much.

Yeah, I used something similar, but used 22% chance for hitting not 25% and villain calling a full pot sized bet. Either way it's not very close if you think the only way to win the hand is by hitting your draw.

Even if he showed you his cards?

If we know he has an ace, as supposed in the op, then it's an easy fold.

Yes because we have 2 outs kappa.

There is no guarantee u even get paid if u happen to run the hearts unless he has the ace with the Q of hearts. So I wouldn't even count a river bet as money made because the chances are much too high that he would fold to any bet, unless of course he held the Q of hearts. So basically the only way to get paid accordingly would be to call hoping to turn a set and then have the ace pay u off. Bad spot altogether IMO. I am stating this from a NLHE perspective as I am including implied odds, which u won't get running the hearts and it's too risky drawing to a 2 outer unless u truly believe that the Ace will pay u off handsomely and the bets ur expected to call are in relation to such odds.