Failed to represent an A OTR

you have showdown value. so you should think twice about bluffing.

if you still want to bluff, you could count the Ax combos you have in your range and bluff accordingly.

repping an A and expecting to get all the folds, is not how it works.

Why would you bet turn with A high ? Or why would you bet so small with DP river ? So Vilain has easy odds bluff catch..

I don’t see why would you represent an A when he could have so many straights, sets and 2 pairs. I think you’re actually representing some of those hands + missed 1 card flush draws and missed straights, so A is really a blank for your ranges. If you actually had Ac here I think you should X back and take a showdown.
That said I think your hand is missplayed all over the place. For start it’s maybe better to X preflop. It’s borderline, but if you are raising then raise to 5-6BB. You have 2 limpers and could be out of position vs BU, so you don’t want to give them such a good odds to call. Flop is very coordinated so you want to either bet big or check back. Vs unknown limpers I would usually bet big once and then give up, but that big bet would usually fold out hands like KTo.

Hmm you bet all the streets, why would the villain think you are representing an A?

I can see the point of your question because, against me, you could have represented any of the following:

Value: AdXd, KdXd, Ad,Xo (49 combos)
Bluff: KdXo (32 combos).

This is the betting range (after the river) that I would have put you on.

If I were you, I would have checked because your hole cards had showdown value; but, if I had felt that I was losing and I had wanted to win, I would have made a polarized bet, probably a bit more than pot size. With your bet size, villain only needed 33% equity. Using my range, he had 40%.

edit: Probably, much fewer bluff combos because I wouldn't really think you'd raise preflop with K9o or worse.

ore he can not let par go away many people like that

On the river, when opp bets 1/2 pot, and hero calls, hero only needs 25% equity. That's why your bluff would fail so often.

To make it simple, if the pot is $200, and opp bets $100, and hero calls $100. If hero loses 3 times, lose $300. If win once, wins $300. So it's not 33%, but 25%.

If your hand was the top pair or over pair till the turn, and opp bets on river ace, you call even a pot bet. You need only 33% in this case.

** I have been wondering for a long while why the micro regulars call down my pot bet bluff with just a 8-pair, when they need 50% of equity. I was wrong in the equity assumption, it costed me so much.

extra advice: dont get creative on monotone boards. they are VERY different to anything else, and are beyond your tier capacity. and thats okay, you dont need to know that stuff in nl2. they arent a priority on your "to study" list; they arent that common. on those boards, just bet when you have value.

LeMahdi
I would recommend to you to google:
free ebook theory of poker
You should to find David Sklansky's full classic book and read that. It seems to be a great start for all NL2 players.