There isn't a ton going on here from a big picture strategic view. Some form of engine is going to clearly take the game down, with Horn of Plenty as a payload really shoring things up. There is definitely a question of which engine to go for (or perhaps you prefer the phrasing of how to build the engine), but the general principles will be the same.
As the game turns out, my opponent gets one Envoy and then sticks mostly to Hunting Parties with a few Stables, whereas I focus on getting lots of Envoys and supplementing them with Inn, fueling this strategy with a Workshop to up the number of Envoys. The question of when to go for Counterfeit and HoP amongst the 5s you want is a quite interesting one. My gut reaction, looking at things now, is that I would like to build the draw based on Stables, with a few HP sprinkled in. There are a few concerns with this plan, though - first of all, you are trashing treasures out from under yourself, which hurts Stables, and second, Stables, HP, Copper, Silver, Gold, Counterfeit, and Horn of Plenty only bring you up to a total of 7 unique cards. So things are a bit tricky - however, I don't think this is too much of a concern, and I believe that a Workshop to gobble up more silvers once the deck is getting closer to being under control can actually provide a solution to both problems.
Regardless of this, that's not the real reason I want to talk about this game. Instead, I want to jump to my eleventh turn . I dud out here, which is pretty unlikely, but not crazily so, and this plus my opponent's first-player advantage allows him to go up to six Horns of Plenty on his twelfth turn. We reach a first interesting positioning question here: should he have taken the seventh Horn? The main factor for is actually a denial plan - with only three, I can't fire off to end the game all that easily. The main call against are that getting another component makes his own deck far more reliable. In general, I am not a big fan of denial plans, but in this case, I think it was the right way to go. It was, however, a reasonably close call, and on an axis which can be difficult to see during the midst of the game - and I am not even certain which way is correct now - so this decision cannot be hugely faulted.
On my opponent's turn 13, he duds out. This helps me a lot. Still, on my own 13th turn, I am in a weird spot. Despite having picked up the 4th horn... 4 simply aren't enough. If I Counterfeit a Horn, I will have $7, can gain 5 Provinces, and... really not be able to quite put the game away. It's very tempting to go for this in a situation like this, because it looks really hard for my opponent to overtake and win in his next turn. He can't draw everything, and even if he could, he has 7 gains plus $10 and 2 buys, which is only enough to tie. On the other hand, if he just chooses to not go for it - as a good player should - then I am not doing much in the mean-time, and he would be able to pick up a bit more draw and another counterfeit or two and have his turn get quite a bit bigger. It's not entirely hopeless for me, but if he is merely patient, I'm going to need very good luck. So I build up my draw and bide my time. Almost certainly, this is a mistake from me, in the very least by not picking up another Counterfeit for more pile control. And probably I should actually have gone for it at this point, anyways, because I have some chances of stringing together enough to try to limp over the finish line, whereas this way, once again, with correct play I am probably lost.
Then we come to the pivotal turn, turn 14. My opponent draws his deck, sans a Horn of Plenty I am able to deny on the last Envoy play, and he goes for it. He cashes all of his Horns of Plenty in for provinces, buys another province, and an estate to top it off. It's actually a pretty clear mistake for him to not counterfeit Horn, though I had kept in mind that he couldn't double-gain Province that way, as the Horn was his 8th unique card. Still, the extra Duchy would have been pretty good for him. Of course, the big weakness of this plan is that his deck becomes substantially worse, particularly in his ability to control the game. And the biggest problem is that he just doesn't need to do this - since I didn't pick up any more economic components, my best possible next turn is going to be more or less the same as last turn, and that's probably not enough. In the mean-time, he can continue to grab more draw, along with another counterfeit or two, and an Inn, which will not only let him kick off his next turn reliably, but also lets him counterfeit HoP for 2 provinces. This would essentially guarantee him the ability to get 8 provinces his next turn, forcing me to go for it. And then he would have a relatively sure thing of mopping up afterwards.
Certainly, on my own 14th turn, I can't come back - it's just WAY too many points. But I do know that I don't have just tons of time - he has enough decent treasures that he will lock me out within the next few turns, at least. But there is no point in cashing the Horns in until the last possible moment, and so I continue to build, while gaining points where I need to - most notably, Silk Road off of Workshops.
On Turn 15, my opponent can even pick up Province number 7 as well as a duchy. But Silk Roads are not to be underestimated! I draw my deck, do some calculations... and win rather cleanly. Certainly it was good to be able to win then, as with a good draw, my opponent could have grabbed Counterfeit+Gold+either of his other treasures, and finished off the provinces, though as things fell, I could have had another turn.
The thing I want to highlight here is not panicking. I got behind by a HUGE amount, but I didn't turn in for points. So often, I see people do this - they get behind, they feel pressure, and the knee-jerk reaction is to catch up ASAP, feeling that the opponent is likely to close out the game if they don't. The problem is, you actually need to have a plan to win the game. If you massively close the gap, but you're still behind, then where did you get yourself? Generally, you want to wait more or less as long as you can to pull the trigger on your mega-turn. If your opponent is liable to go off, in a way that will lock you out, then you have to think about going for it. But if they're going to be able to win the long game after by being patient themselves... you pretty much need to hope for them to have a dud. And when behind, going for it in a way that won't bring you the lead does no good. Either way, you need to have a plan for being able to finish the game out, and think in terms of "What gives me the best chance to win by the time the game ends?" rather than "What gets me the best points gap?"
