Dominion > Puzzles and Challenges
Design the board with the largest P1 advantage
Holger:
--- Quote from: ephesos on February 20, 2017, 06:59:00 pm ---
--- Quote from: Holger on February 20, 2017, 01:19:09 pm ---
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...
--- End quote ---
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.
--- End quote ---
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.
Holger:
--- Quote from: Holger on February 20, 2017, 01:19:09 pm ---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.
--- End quote ---
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.
ephesos:
--- Quote from: Holger on February 21, 2017, 03:30:55 pm ---
--- Quote from: ephesos on February 20, 2017, 06:59:00 pm ---
--- Quote from: Holger on February 20, 2017, 01:19:09 pm ---
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...
--- End quote ---
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.
--- End quote ---
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.
--- End quote ---
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.
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.
--- Quote from: Holger on February 21, 2017, 04:24:41 pm ---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.
--- End quote ---
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.
Holger:
--- Quote from: ephesos on February 24, 2017, 12:35:24 am ---
--- Quote from: Holger on February 21, 2017, 03:30:55 pm ---
--- Quote from: ephesos on February 20, 2017, 06:59:00 pm ---
--- Quote from: Holger on February 20, 2017, 01:19:09 pm ---
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...
--- End quote ---
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.
--- End quote ---
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.
--- End quote ---
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.
--- End quote ---
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.
--- Quote ---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.
--- End quote ---
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.
--- Quote ---
--- Quote from: Holger on February 21, 2017, 04:24:41 pm ---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.
--- End quote ---
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.
--- End quote ---
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...
luser:
If we could add landmark I could modify my board for deterministic three piling. Instead hunting grounds use
kc, lurker, tfair, donate, fortress, upgrade, rats, magpie, university, cultist, catacombs tomb.
When p1 gets kc-kc-lurker-lurker-ironworks he gets magpie/upgrade/rats with kc-upgrade, then draws by trashing cultist with lurker and trash catacombs to setup rest of deck. Then he empties magpie, rats and upgrade piles and gets lot of points from tomb. Without tomb it could be possible to get points from getting gardens from trashing catacombs but I didn't think about details.
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