In the mirror case, P1 should usually trash the HG on turn 5, but even with Shelters, ephesos' P2 strategy has a 40% (for 4/3) resp. 20% (for 3/4) chance to have a Lurker and $4 on T2, and can thus gain 5 Duchies and tie (or win on tiebreak) with 15 vp each.

To prevent this, I think you need to add Catacombs, allowing P1 to still gain 3D and 8E on turn 5 in this case and winning 17-15 by 3-piling. Is there anything P2 can do then to still have a chance at winning/tieing if he doesn't draw $5 on T1? I don't think so...

But if you add Catacombs, P2 can T2 Lurker a Catacombs to gain a Lurker, which means they have an extra Lurker turns 3 and 4 to get two Duchies instead of 1.

So it's:

1: TF Lurker

2: Lurker trashing Catacombs gaining Lurker, TF Lurker + Donate

3: Lurkerx3, gaining KC and trashing 1 HG for Duchy

4: KC Lurker, Lurker, Lurker for 5 more Duchies and 18 points total, while only 2 Duchies and 8 Estates are left in the game for 14 points.

Good point. This P2 strategy has still the same 40% (for 4/3) resp. 20% (for 3/4) chance of success. But P1 can try to "steal" this strategy as well, with no real risk: At best, he has an extra Lurker after the first two turns and the chance to gain 6 Duchies on T3/4 if P2's first two turns were equally successful. At worst, he gains only 1 Lurker on T2 and can still follow the original "9 HG on T5" strategy.

I thought about P1 using this strategy, but if the timeline works out the same for both players, then P1 gets 6 Duchies for 18 points and P2 gets 2 Duchies 8 Estates for 18 points, a tied game. And P2 can match that every time: 1 Duchy from the first HG, 1 Duchy 6 Estates from the last 3 HG's, and 2 more trashed Catacombs.

2 Duchies + 8 Estates only give 14 VP, not 18. There's only 32 VP available in total from Duchies and Estates, so 17+ VP win the game.

Also I thought we were still talking about Baker being in the game, and thus a 4/4 split. If it does go 4/4, this has a 100% success rate i.e. if you wanted, you could perform the exact sequence and end up with 6 Duchies every time, since until the end you never have more than 5 cards in your deck.

Yes, it's technically a 4/4 split due to Baker (unless you're unlucky to have a 2/5 start). But since you draw a topdecked Lurker on T2, you don't draw the bottommost (10th) card of your deck. And if it's the 7th Copper you're missing (which is very likely), you only have $3 available on T2 even with the Baker token (either $3+1/$3 or $4/$2+1). In this case you should buy the 3rd Lurker on T2 instead of Donate, and with a lot of luck you'll still draw all 3 of your Lurkers on T3 to gain a KC, Duchy and then Donate, which still gives you 6 Duchies by T4. But if you're unlucky again, you do lose.

I've done the detailed calculations and got a ~40% win chance for P2 on the board without Catacombs, and a ~20% win chance for P2 on the board with Catacombs (if you like, I can post the calculations later). So adding Catacombs is a clear improvement, but still far from perfect.

Another way to achieve a higher win rate for P1 is to add some Action-Victory card instead of Catacombs. E.g. Great Hall or Mill should be harmless enough, and allows P1 to gain 2 extra VP on T5 if P2 was lucky to gain 5 Duchies before (P1 can use its first 5 Lurkers to trash the remaining Hunting Grounds, and use the last 4 Lurkers to trash and then gain two Great Halls), leading 17-15 and having a reasonable chance to win the Great Hall split and thus the game.

Haven't thought about this much yet, but I think P2 also has reasonable chances to win that split. And if P1 trashed for 3 Estates per HG their deck will be noticeably worse than P2's.

Also I think P2 gets 6 Duchies with the new strategy, so you would have to be leading 20-18.

No, this is without Catacombs, so P2 can only reach 15 VP by T4.

It's not clear to me which player has the better chance to win the GH split - P1 does have more green cards, but he also has 2 KC and 3 Lurkers while P2 only has 1 KC and 2 Lurkers. In this situation, you don't want to play a single Lurker any more (which only helps the opponent), and P1 may well have better chances to draw 2 Lurkers or KC-Lurker within one hand. And P1 only needs to tie the remaining 6 GHs to win...