"Could you explain this (assuming a relatively dry board). Especially rethink the part where we get value from weaker aces when we hold A5."

A dry board would suggest checking is better. On this board texture though we have a lot more fold equity in general firing two barrels, especially with a backdoor straight draw out there. However, heads up against this type of player I generally like to lead a lot with most of my range dry or not. The more you bet at aces, weak or not, the more you set up for him to fold when you have KQ, KJ, and other misses, while extending the impression that you have a lot of aces and weak ones in your range. Sometimes you will face raises though that will keep you honest while leading, which often will require an accurate play as well and may take a few thin calls or 4bets to slant play in your favor again for your range.

Every now and then heads up I will check/raise weak aces on the flop even, because doing so keeps a player who likes to bet a lot with air honest or making unprofitable drawing hand calls. He is either shoving over the top because he has the nuts (sets or top two pair) or he is going to usually fold to a check/raise. If he calls, he probably has an ace or strong draw so you can evaluate turn from there, but trips are also an option for smooth calling rather than shoving. Most of the play I have suggested is more generally a set up to lead with other hands in your range, because this player will give you a lot of value when you hit a set or straight by calling with things like two pair rather than raising on the flop.

How much of his range is a2, a3, a4? I don't think it's enough to justify checking the flop too often with the intention of calling rather than raising. A lot of times the correct play here with a weak ace can be to c/r the flop because a lot of times you'll be dealing with jacks or tens or even kq from utg and the button that will fire out a standard cbet to see if he is good. This sort of play will also allow for the occasional C/R with air, so it's a decent balance here even with as weak of a hand as TPLK.

Another line that is good for this particular type of hand in your range is bet, check turn, check/call river if you feel that will keep more draws in and improve your showdown value. I agree that raising pre-flop is the right play with the weak ace, btw, to take initiative as well as take the more aggressive line in general. Against this type of player, I recommend checking your weak draws and if they look decent on the flop, playing an aggressive line, while with your weak aces and pairs and strong draws (910s, j10s, qj/qjs), etc.. you can raise pre-flop and play the line aggro that way. He is not actually investing much equity in your blind. Raising p-f also will help define whether or not you're dealing with pocket pairs, kq, or aq or something like that from the UTG player in this particular situation, if they cap or re-raise pre-flop, they've made a positional play and you can easily fold.

"If he's raising alot of those (which I saw him do a few hands ago) I'm better of with a c/C."

Still bet flop, he isn't raising pre-flop so you have to define the range by this, otherwise you're at his range's mercy. If he does raise with air + weak draws, you may want to call his raise, check turn and call river bet if you reasonably think you're ahead, or you can fold to a semibluff if you are scared of it / it's not profitable.

You can catch bluffs this way and him inflating a pot with missed hands is also good for you.

Obviously if we know he will never continue with draws after a second barrel, then our showdown value is hurt, which is why we check/fold river and hope he stays in through two barrels a certain percentage of the time. If we know with certainty that his draws don't stay in on the river enough, we can check the turn and call a decent river bet to keep them in. It really depends on how he'll react to the turn check... I submit though that it hurts your range if you give up too much on the turn here against this player who will likely sense weakness (though that is obviously a set-up for a later play if you want).

The reason I like bet/folding the turn is simply because we set up future plays for huge amounts of value if he thinks that we are aggro and will bet into him. We want to reward him for this type of play against us, because when you make a stronger hand you will extract maximum value from out of position (which is another reason to raise pre-flop, make the pot worth drawing for / betting at).

We make him show the strength of his hand by checking the river and seeing if he wants more value or if he checks behind that is fine too because we've controlled our investment based upon reasonable equity estimates.

"89,67,K8,Q8,J8,7T. That's what I'm asking myself."

Considering he is connecting two pair on the flop 1/49 times, and he is connecting a pair about 25% of the time that is not a pair on the board, I think it is reasonable based on his Aggression Factor (which includes 25% calls) that he is likely calling a lot more with pairs that hit at all than exclusively two pair. That sounds obvious, but my guess is that he is raising the flop more with air than anything else. You also have to take into account that we are leading here, so his calling range in position is going to be different than his bet/raise range out of position or if everything gets checked to him on the flop. Does that make sense? Take note of what he is calling with when you see showdowns against him, but don't assume he has two pair every time he is calling in position, I'm including a lot of pairs, medium pairs, etc. for that reason.

Like I said though, I do not think it is likely though that he is floating two streets on you. He is calling 25% of the time, so if we think of the likeliness of him calling two streets it is about 1/16. So we are dealing on the river with a range that is fairly defined and your read from earlier about two pair suggests you can reasonable check/fold this if a big enough bet comes out on the river, but he may check behind still with smaller aces. His range does not have more small aces than medium pairs, simply in combination possibilities alone.

Remember that he is probably not showing up with two pair at this river from the flop too often here, he could be showing up with a pair often enough to make betting the turn worthwhile until proved otherwise or exploited (which we have a plan for if he begins doing). Besides which, when we bet this turn we really are setting up a play for us using the odds of us hitting our draws and getting paid off by him due to this play for our ENTIRE range.

For example, you have 910s from the big blind, so you raise it over his limp from the button to 4 BB, he calls so the pot is 8.5 BB now. You hit the same board and he has the same type of hand. You have 30% equity in this situation vs. the top pair range. So you bet the pot because more often than not he is missing the flop and you've been raising from the big blind with weak aces and strong aces, so a good portion of his range folds. He probably folds to a continuation bet here enough to make this play alone profitable or break-even when you lead.

If he calls, we may say he has an ace, a middle pair or a draw. You are drawing to the nuts though, so we want to keep his draws in really because it's unlikely that much of his range is blocking your draw after the flop bet (see why this is good for your draws also to bet here? Also, consider your aces / weak aces as drawing hands with showdown for kicker battles in the high card game and you can see why leading this flop is a pretty good idea to block out a lot of other aces that miss the flop like in this particular situation (i.e. a king and three had come rather than an ace and seven, does that make sense?).

Back to our situation, IF he calls the flop, we now have 24.5 BB in the pot. On this turn, you bet 16 BB here whether or not you've hit, because your range consists of aces that are usually ahead of his drawing hands, so you want to charge him when you have each have those respective holdings. I suggested you also bluff occasionally here, because for him to break-even on the river, he simply will HAVE to fold some of those medium pairs once in awhile, otherwise you get way too much value from even your weak aces for him to stick around for two barrels every time.

If we check here, we give him a free card if he's drawing, we allow him to bet if he has the nuts and he can still check behind planning to bet the river with two pair the size of the pot where we'll be priced in to call. If he folds this turn, you've invested 20 BB to win 24.5 BB, a 4.5 BB ROI. What percentage is he folding this turn? Well, he probably has to fold out about half of his draws that blank on the turn, so I'd guess this second barrel is working pretty well here against his range.

If he calls the turn the pot is now 40.5 BB. We generally have an ace, so we check/fold the river with the weaker aces if we're pretty sure in his line that he has a big hand and check/call with things like a10, aj, etc. (we may call a small bet perceived to be a bluff with a5o to encourage his value betting this river as you will see why...), and our range is likely to win anywhere from 40% of the time to 60% of the time if we consistently make a play like this against a loose player at showdown alone. So based on showdown alone I think we're probably coming in against his likely range with our FULL range, not this specific hand, about a coin-flip.

So if he doesn't fold out to two barrels, I suggest that ~50% of the time on the river, we are going to win a showdown if he lets us get there. Investing 20 BB to win 20.5 BB about half the time, so that is even if we get to showdown and we have put together his range accurately. If he is folding out 33% of his turns / range, we may be 33%/66% to win at showdown, so make your check/calls + check/folds based on this and other river reads. Either way, betting the turn will be profitable here simply because of the fact that he needs to fold certain turns and you save money on his river bets because of a more defined range.

But we assume that he will not let us just check every river and get to showdown, so we set up a play by either planning on check/raising nut hands here, or by betting the river depending on how we think we'll get most value.

He knows that he can not fold that often on the river or we will be getting the best of him in this play too often, so he will be compelled to call or raise... but he will also be compelled to value-bet the river for the same reason so since we are leading, we can force him to make a mistake here because of his weaker range and our stronger range.

Back to our example of 910s, let's say we hit our draw on the turn with the straight so we bet 66% pot as we have been doing, he calls so now the pot is 40.5 BB. We get to the river and depending on how we want to vary our play, we can bet here or check depending on how scary the board might look for his holdings. With a hit draw, I'd tend to bet here a lot, because he's calling three streets with hands we get a lot of value from, two pair, sets, etc. We can also check/raise our own sets / two pair on the river to balance our range and set up a slew of profitable river plays. But against this opponent, I tend to just bet/bet/bet/raise to get as much money in when I have a monster, and follow similar lines when I have showdown value because if he doesn't want a coin-flip at river against most of my range at showdown then he has to value-bet on a checked river more often than not, which I can profitably c/call, check/fold or check/raise depending on my holdings and the situation + certain metrics like my perceived bluff frequency, etc..

Also, my bets will very likely be overbets at the river. For example, on our straight example, I am going to lead that third barrel because MOST of his range (I think I stated 75% if he is folding his mediocre holdings on the turn) as discussed earlier can call most bets and often has to if he wants to remain competitive on the river and not get pushed around by my aggressiveness. So I may want to really make him indifferent to calling or folding here so I can also incorporate bluffs here as well. I may bet on that straight 60 BB into the 40.5 pot. If he calls, I've invested 60 BB to make 105. BB which is equal to a 56.8% ROI out of our 32% of flop equity. Not a bad margin. (Keep in mind also that we are actually hedging pre-flop 4BB to win 8.5 and have 48% equity, so that is also a winning play, but notice the exponential amount our margin has increased here.)

Betting the turn allows us to hit our straight MORE OFTEN than checking, because some bets we will not have equity to call, which is why he needs to be raising more turns and flops, I doubt he will adjust at this level. If he is folding on the river to our overbet frequently, then we simply do it EVERY NOW AND THEN with our more TPTK sort of hands run as bluffs because if he is trying to bluff catch with a7 for example you still outkick him, but they can also profitably be checked, so depending on your more specific hand reading, you can make the most accurate decision in your estimation. I would tend to bet hard on made hands the river (trips, top two pair, straights, flushes) really often, given that he called your river bet with a two pair holding on this particular hand. So the reason I've suggested the line I did is not simply for this hand, but for your entire range against this particular villain if he is calling bets in this spot like he is.

Does all of this make sense to anybody else? It's not so much about this particular hand's result as it is about how to play against a villain that sponges and won't raise the flop when he has, "le nuts." (Which he doesn't really have here...)