Dominion Strategy Forum
Dominion => Puzzles and Challenges => Topic started by: JW on November 30, 2016, 03:01:59 pm
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What board would you design to give P1 the highest chance of victory? Let's assume that there is a 2 event/landmark limit.
I'll start off with Ferry, Travelling Fair, Squire, Gardens, 8 villages. Hope for a 3-4 split so you can Ferry Squire turn 1, topdeck 3 squires on turn 2, and gain all the remaining Squires on turn 3! All credit to gamesou for this discovery.
IRL game with Gardens, Squire, Travelling Fair & Ferry. Gain all the Squires by turn 3 and you feel like Celestial Chameleon.
(perhaps the most favourable board for P1 I've ever seen).
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This one? (http://forum.dominionstrategy.com/index.php?topic=15851.0)
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This one? (http://forum.dominionstrategy.com/index.php?topic=15851.0)
First, it has more than 2 events/landmarks. Also, if you don't draw the turn 1 win (only a 42% chance you'll draw it), can you do anything to stop your opponent from pulling it off (if they have the 42% hand themselves)?
A game where you're almost certain to win a key split by being first player may offer substantially better odds. I'm not sure if the Squire-Gardens example above qualifies, it depends how many Squires Player 1 can assure themselves of on a start beside 3/4.
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Courtyard, Fool's Gold, Village, City, Fortress, Mining Village, Port, Walled Village, Worker's Village, Border Village
Donate, Travelling Fair
Now you see what I am saying.
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I'll start off with Ferry, Travelling Fair, Squire, Gardens, 8 villages. Hope for a 3-4 split so you can Ferry Squire turn 1, topdeck 3 squires on turn 2, and gain all the remaining Squires on turn 3! All credit to gamesou for this discovery.
A game where you're almost certain to win a key split by being first player may offer substantially better odds. I'm not sure if the Squire-Gardens example above qualifies, it depends how many Squires Player 1 can assure themselves of on a start beside 3/4.
If Player 2 didn't buy any, Player 1 could gain a total of 9-10 Squires by the end of T3 with a 3/4 or 5/2 start, and 6-7 Squires with 4/3 or 2/5. But player 2 can also buy 2-4 Squires on their first two turns (2.6 on average). So player 1 will always win the split at least 6:4, but usually 7:3 and occasionally (P=25%) 8:2.
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I get 5 Squires after two turns with a 5/2:
Turn 1: Travelling Fair, Ferry, Squire (top deck)
Turn 2: Play Squire (+2 Buys), Travelling Fair, Squire x4
Still, that's a 11/12 chance of winning the split, usually 7:3 or better. Of course, you still have to prove a win with this advantage, though I'd be surprised if there weren't a way to do that, given the slots available; and if you can win these about 83% of the time you're already better off than the turn 1 solution (even ignoring the Event restriction).
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Still, that's a 11/12 chance of winning the split, usually 7:3 or better. Of course, you still have to prove a win with this advantage, though I'd be surprised if there weren't a way to do that, given the slots available; and if you can win these about 83% of the time you're already better off than the turn 1 solution (even ignoring the Event restriction).
Where do you get the 83% number from? To approximate the turn 1 kingdom, a kingdom where we alternate having 41.7% chances of winning on our turns, and I go first, only yields a 63.2% chance of victory for the first player. For those interested, the formula is 1 / (2-p), where p is the chance each of us wins on each turn.
In the 11/12 (91.7%) of the time the first player wins the Squire split, they won't need anything close to an 83% average win % to have an overall chance of winning above 63%. On the assumption that P2 wins half of games when they get 5-2 and can tie the split, the required percentage to equal the turn 1 solution is only 64.4%.
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I had started to write something about this earlier, and then forgot I didn't post it, so it does look like I pulled that number out of nowhere.
In the turn 1 kingdom, I'm pretty sure the first player can always win on turn 2 if neither player wins on turn 1; the setup of the Mission turn is simply a topdecked Fortress, which can be done for $2 with Travelling Fair + Alms (so, always). The one potential hangup I see is that the second player gain multiple Villas somehow and keep you from having enough Buys, but on the other hand turn 2 has the advantage of being able to buy cards normally, so you can likely get around that somehow.
So the probability of winning is 5/12 + 7/12*7/12 (win first turn + don't win first turn and neither does P2) = 109/144 > 75%. (And then divide by 11/12, 109/132 is about 82.6%.)
The 83% is still too high though; I didn't account for the 1/12 case of P2 having a 5/2 and splitting the Squires evenly. P2 might have a slight advantage here (except in the case where P1 also got a 5/2), but it's certainly not a lost cause for P1. So, somewhere between 78% (if 5/2 is 50-50) and 83% (if it were always a P2 win), but closer to the lower end of that.
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What about donate, delve, masterpiece, feodum, baker. Strategy there should be exact minor. 2 silvers in t1/2 with masterpiece for 6 and delve on 5/2. p2 could likely win with lucky 5/2 hand mostly reversing player order.
Then donate on t3 keep 4 silvers, pay debt on turns 4, from turn 5 overpay masterpieces. On turn 6 p1 does final overpay and win silver split which likely wins a game.
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What about donate, delve, masterpiece, feodum, baker. Strategy there should be exact minor. 2 silvers in t1/2 with masterpiece for 6 and delve on 5/2. p2 could likely win with lucky 5/2 hand mostly reversing player order.
Then donate on t3 keep 4 silvers, pay debt on turns 4, from turn 5 overpay masterpieces. On turn 6 p1 does final overpay and win silver split which likely wins a game.
Why would you Masterpiece for 6 when you could Delve 3 times instead? Your average $ with 4 Silver is above 1, so you're diluting it by getting a Masterpiece Copper, which means your Debt might be 1 higher.
Also, T3 you can Delve + Donate for that extra Silver to keep and guarantee $10 on the next hand. Not sure if Delving 2+ times before Donate is worth doing though. Possibly equivalent to doing it the next turn, though there's something with Masterpiece and Debt totals where there's an optimal play at each amount.
Feels like this should go into a simulator.
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<player name="Delve/Donate"
author="Ephesos"
description="Delve -> Donate -> Masterpiece -> Feodum">
<type name="Province"/>
<type name="UserCreated"/>
<type name="Bot"/>
<type name="TwoPlayer"/>
<board contents="Baker, Masterpiece, Feodum, Donate, Delve" bane="" Mountain_Pass_Bid="0" Obelisk_Choice=""/>
<buy name="Delve">
<condition>
<left type="countTurns"/>
<operator type="smallerOrEqualThan" />
<right type="constant" attribute="2.0"/>
</condition>
</buy>
<buy name="Delve">
<condition>
<left type="countTurns"/>
<operator type="equalTo" />
<right type="constant" attribute="3.0"/>
</condition>
<condition>
<left type="countCardsInDeck" attribute="Silver"/>
<operator type="equalTo" />
<right type="constant" attribute="4.0"/>
</condition>
</buy>
<buy name="Donate">
<condition>
<left type="countTurns"/>
<operator type="equalTo" />
<right type="constant" attribute="3.0"/>
</condition>
</buy>
<buy name="Masterpiece">
<condition>
<left type="countAvailableMoney"/>
<operator type="greaterOrEqualThan" />
<right type="constant" attribute="6.0"/>
</condition>
<condition>
<left type="countCardsInSupply" attribute="Silver"/>
<operator type="greaterThan" />
<right type="constant" attribute="0.0"/>
</condition>
</buy>
<buy name="Delve">
<condition>
<left type="countCardsInSupply" attribute="Silver"/>
<operator type="greaterThan" />
<right type="constant" attribute="0.0"/>
</condition>
</buy>
<buy name="Feodum"/>
<buy name="Province"/>
</player>
And it is done. 79.45% P1 win, 12.88% P2 win, 7.67% ties
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I believe there is a way to turn the turn 1 solution into a turn 2 solution by adding Death Cart and removing Shelters. Death Cart gets around the possibility of opponent buying a Villa on turn 1 (only need 5 buys to empty the Ruins, instead of 10 for Patrician/Emporium; the remaining buys can gain Border Village/Duchy for points), and also gives you a way to be sure your turn 2 hand gets to 5.
With 2 or 3 on turn 1, just buy Travelling Fair + Ruin - this sets up turn 2 to have at least the Ruin and 3 Coppers, and then the turn 1 solution follows.
With 4 or 5 on turn 1, buy Borrow + Travelling Fair + Death Cart (use Baker token if needed) - this gives you a Ruin in hand and $5 from Death Cart (trashes itself or the other Ruin, either way), so you don't need the Baker token.
Unless I'm missing something, this is 100% for player 1, though of course we are still well over the Event limit.
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What about donate, delve, masterpiece, feodum, baker. Strategy there should be exact minor. 2 silvers in t1/2 with masterpiece for 6 and delve on 5/2. p2 could likely win with lucky 5/2 hand mostly reversing player order.
Then donate on t3 keep 4 silvers, pay debt on turns 4, from turn 5 overpay masterpieces. On turn 6 p1 does final overpay and win silver split which likely wins a game.
Why would you Masterpiece for 6 when you could Delve 3 times instead? Your average $ with 4 Silver is above 1, so you're diluting it by getting a Masterpiece Copper, which means your Debt might be 1 higher.
Also, T3 you can Delve + Donate for that extra Silver to keep and guarantee $10 on the next hand. Not sure if Delving 2+ times before Donate is worth doing though. Possibly equivalent to doing it the next turn, though there's something with Masterpiece and Debt totals where there's an optimal play at each amount.
Feels like this should go into a simulator.
Even better you could delve+donate on turn 2 which with baker token leads to 4 silver deck for both 5/2 and 3/4. Not sure if p2 3 delve+donate on turn 1 helps.
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I think using Raid instead of Masterpiece is better in most cases, too - best case is SSSSS which is 7 Silver with Masterpiece and 7 Silver with Delve+Delve+Raid (plus the -1 Card effect). If both players are buying Raid every turn, both max out at $9 for Borrow+Delve+Delve+Raid (so 6 Silvers per turn); might as well Borrow as long as the Raids are happening.
5/2 might look like:
T1: Delve+Delve+Delve+Donate (keep two Coppers)
T2: $8 - Pay debt
T3: $8 - Borrow+Delve+Delve+Raid (and you have a deck of 9 Silver, 2 Copper; so you'll only get 5 Silvers per turn sometimes from this point)
That seems awfully strong, I don't see an obvious way to prevent P2 having an advantage if he gets 5/2 and P1 doesn't.
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Even better you could delve+donate on turn 2 which with baker token leads to 4 silver deck for both 5/2 and 3/4. Not sure if p2 3 delve+donate on turn 1 helps.
Redid the sim with T2 donate, leads to 98.07% P1 win, 1.93% P2 win, 0% ties, and ever so slightly beats out T3 Donate in both start orders.
I think the next best thing would have to be 100% at this point.
EDIT: With the P2 3 delve+donate, it's back down to 96.92% P1 win, 2.86% P2 win, 0.22% ties.
Slight nuance I just noticed though; the sim doesn't keep any Copper from Donate, and goes down to 4 Silver every time.
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Even better you could delve+donate on turn 2 which with baker token leads to 4 silver deck for both 5/2 and 3/4. Not sure if p2 3 delve+donate on turn 1 helps.
Redid the sim with T2 donate, leads to 98.07% P1 win, 1.93% P2 win, 0% ties, and ever so slightly beats out T3 Donate in both start orders.
I think the next best thing would have to be 100% at this point.
EDIT: With the P2 3 delve+donate, it's back down to 96.92% P1 win, 2.86% P2 win, 0.22% ties.
Slight nuance I just noticed though; the sim doesn't keep any Copper from Donate, and goes down to 4 Silver every time.
If you will Donate on turn 2, then except on a 2-5 start shouldn't you buy Feodum on turn 1? You keep a coin token on 5-2 while still having 4 Silvers after turn 2 and on a 3-4 or 4-3 start you end up with 5 Silvers after turn 2.
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Even better you could delve+donate on turn 2 which with baker token leads to 4 silver deck for both 5/2 and 3/4. Not sure if p2 3 delve+donate on turn 1 helps.
Redid the sim with T2 donate, leads to 98.07% P1 win, 1.93% P2 win, 0% ties, and ever so slightly beats out T3 Donate in both start orders.
I think the next best thing would have to be 100% at this point.
EDIT: With the P2 3 delve+donate, it's back down to 96.92% P1 win, 2.86% P2 win, 0.22% ties.
Slight nuance I just noticed though; the sim doesn't keep any Copper from Donate, and goes down to 4 Silver every time.
If you will Donate on turn 2, then except on a 2-5 start shouldn't you buy Feodum on turn 1? You keep a coin token on 5-2 while still having 4 Silvers after turn 2 and on a 3-4 or 4-3 start you end up with 5 Silvers after turn 2.
Thats a problem. It gives counter to second player. If he buys it when first player doesn't then at end p1 must choose between winning silver split but losing feodum one 4-3 or winning feodum split and losing silver one which gives smaller advantage. Then there could be problem that silver will split evenly instead p1 winning split if they get more silver in turn 1/2, one must check that or invoke rule that you could play with any number of silver. Second possibility to fix this would be 3 player game, but I didn't analyze that yet.
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Some math on Feodum/Silver
Losing the split means you need to earn more Silver, but how much more? With 3/4 of the Feodums, you need to have 4/3 as many Silvers, approximately.
So that's 4/7*40, which rounds up to 24 Silvers.
And we can see that at 24 Silvers, you get 8*3=24 points, and your opponent gets 5*4=20 points.
At 23 Silvers, you get 7*3=21 points, and your opponent still gets 20 points. But at 22 Silvers, your opponent's Feodums go up, so you lose 21 to 24.
So to give up the Feodum split, you need to win Silver split by 6 or more
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Sadly the simulator is stupid and doesn't trash Feodum. Maybe after the quarter is over, I'll make a fork and see if I can get it running.
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Some math on Feodum/Silver
Losing the split means you need to earn more Silver, but how much more? With 3/4 of the Feodums, you need to have 4/3 as many Silvers, approximately.
So that's 4/7*40, which rounds up to 24 Silvers.
And we can see that at 24 Silvers, you get 8*3=24 points, and your opponent gets 5*4=20 points.
At 23 Silvers, you get 7*3=21 points, and your opponent still gets 20 points. But at 22 Silvers, your opponent's Feodums go up, so you lose 21 to 24.
So to give up the Feodum split, you need to win Silver split by 6 or more
Additionally, if one player has more Feoda and less Silver and the other player has more Silver and fewer Feoda, but both have equal points from their Feoda, the player with more Silver has the advantage because they have better money density.
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True, I didn't actually account for the post-Feodum game. If you're even close to tied, I think Silver lead wins just by getting more Provinces.
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Not 100% win though; Silver leader could have worse draws (SSSFF only buys Duchy) while the other player's Feodum's spread out.
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One of possible fixes of my strategy would be add alms, trav.fair and borrow so you could on turn 1 get buy from baker+borrow using tfair. With first buy alms a feodum, with second donate. Opponent would need to mirror it or be turn behind. I hope that silver would split unevenly here.
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One of possible fixes of my strategy would be add alms, trav.fair and borrow so you could on turn 1 get buy from baker+borrow using tfair. With first buy alms a feodum, with second donate. Opponent would need to mirror it or be turn behind. I hope that silver would split unevenly here.
That's more than 2 events though.
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Even better you could delve+donate on turn 2 which with baker token leads to 4 silver deck for both 5/2 and 3/4. Not sure if p2 3 delve+donate on turn 1 helps.
Redid the sim with T2 donate, leads to 98.07% P1 win, 1.93% P2 win, 0% ties, and ever so slightly beats out T3 Donate in both start orders.
I think the next best thing would have to be 100% at this point.
EDIT: With the P2 3 delve+donate, it's back down to 96.92% P1 win, 2.86% P2 win, 0.22% ties.
Slight nuance I just noticed though; the sim doesn't keep any Copper from Donate, and goes down to 4 Silver every time.
If you will Donate on turn 2, then except on a 2-5 start shouldn't you buy Feodum on turn 1? You keep a coin token on 5-2 while still having 4 Silvers after turn 2 and on a 3-4 or 4-3 start you end up with 5 Silvers after turn 2.
Agreed. You can also use the token to have 5 Silvers after turn 2 with 5-2.
I really don't see how you get a 90+% win for P1 on this board. If both players Donate T2 for a 5 Silver deck, they'll usually split the Silvers 20-20 on T5 and then also split Feoda and Provinces evenly, resulting in a perfect tie.
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Agreed. You can use the token to always have 5 Silvers after turn 2, also with 5-2.
I really don't see how you get a 90+% win for P1 on this board. If both players Donate T2 for a 5 Silver deck, they'll usually split the Silvers 20-20 on T5 and then also split Feoda and Provinces evenly, resulting in a perfect tie.
T2: Both have 5 Silvers and 8 Debt
T3: Both have $2 and Delve, 6 Silvers
T4: Both Masterpiece overpay 7, 13 Silvers
T5: If both hit 5 Silvers, split 20-20. Otherwise, on the next turn, P1 can win the split 21-19 or 22-18. The odds of not getting the 1 Masterpiece is 2/3, so ties are 4/9 of the time, P1 wins 5/9 of the time.
But also, you can factor in endgame: if P2 misses a Province, P1 can pick it up. Whereas if P1 misses a Province, P2 is just back to even. So I could see the odds getting to 70+% off that alone.
EDIT: Considering it again, if you trash Feoda, the extra Silver is only worth 3 points or so. But it adds to money density and breaks ties. Not an instant win though.
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Agreed. You can use the token to always have 5 Silvers after turn 2, also with 5-2.
I really don't see how you get a 90+% win for P1 on this board. If both players Donate T2 for a 5 Silver deck, they'll usually split the Silvers 20-20 on T5 and then also split Feoda and Provinces evenly, resulting in a perfect tie.
T2: Both have 5 Silvers and 8 Debt
T3: Both have $2 and Delve, 6 Silvers
T4: Both Masterpiece overpay 7, 13 Silvers
T5: If both hit 5 Silvers, split 20-20. Otherwise, on the next turn, P1 can win the split 21-19 or 22-18. The odds of not getting the 1 Masterpiece is 2/3, so ties are 4/9 of the time, P1 wins 5/9 of the time.
I was also considering this state of play, but this way P1 can only win the split 21-19 if P2 hits Masterpiece, which has probability ~1/3. P1 hitting Masterpiece doesn't matter.
But I've just found a better strategy for P1: Start buying Feoda T5. Then if P2 follows, P1 wins the Silver split at least 21-19 on T7, and if P2 doesn't, they win the silver split but P1 wins the Feodum split. So either way P1 wins the game unless P2 wins the Province split 5-3 resp. 6-2, which is almost impossible.
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I realized that I could use other combo that I discovered for almost certain p1 win.
donate,alms,ironworks,lurker,baker,hunting grounds. As there isn't nothing better than mirror its quite deterministic.
Turn 1 alms ironworks. Turn 2 donate, keep only ironworks. Turn 3-4 gain two lurkers, Turn 5 trash 4 hg for duchies and gain two estates. It suffices to get one lurker on turn 6 to win on estate points by trashing hg number 9.
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I think there are some weaknesses, but perhaps you can explain it in more detail.
1) What would you do if I don't choose to mirror. After 4 turns, you have the possibility to kill 5-6 cards per turn from the supply. If you go for HG (to increase the number of cards removed), you pollute your deck so that your trashing speed decreases. If you switch for a different plan you need ~4 turns and have very little points, so that I have 8 turns to compete with you.
2) If I choose to mirror, wouldn't gaining a estate with your Ironwork in T5 cause a reshuffle putting all the VP cards on the top of your deck. Perhaps you want to gain another Lurker and gain the estate in T6.
PS: Why do you need Baker in the kingdom?
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I realized that I could use other combo that I discovered for almost certain p1 win.
donate,alms,ironworks,lurker,baker,hunting grounds. As there isn't nothing better than mirror its quite deterministic.
Turn 1 alms ironworks. Turn 2 donate, keep only ironworks. Turn 3-4 gain two lurkers, Turn 5 trash 4 hg for duchies and gain two estates. It suffices to get one lurker on turn 6 to win on estate points by trashing hg number 9.
You can't buy Alms if you have debt, so getting two Lurkers each on turns 3-4 doesn't work.
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ok, that lead me to better board
tfair, donate, baker, lurker, king''s court, hunting grounds
Plan is following
t1 lurker
t2 tfair lurker+donate
t3 gain kc
t4 gain kc and lurker
t5 trash 9 hunting grounds.
If p2 gets lucky 5/2 opening he will win as player roles are reversed, otherwise I don't see any way how he could win.
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Trashing 10 Hunting Grounds results in only two empty piles; you can't end the game the way you described unless someone mirrors you. If they don't bite, you're done.
It's just not that easy to have a "guaranteed win" P1 board.
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ok, that lead me to better board
tfair, donate, baker, lurker, king''s court, hunting grounds
Plan is following
t1 lurker
t2 tfair lurker+donate
t3 gain kc
t4 gain kc and lurker
t5 trash 9 hunting grounds.
If p2 gets lucky 5/2 opening he will win as player roles are reversed, otherwise I don't see any way how he could win.
How is P1 supposed to gain/trash the remaining 5 Estates with a treasureless deck that's 80% green?
To even have a chance at winning in the non-mirror, I think you need to trash all 10 HG's in one turn, which requires at least 2 KC, 4 Lurkers and a Lab to draw them all.
You can get 3 more Estates by playing Lurker again, but you need to build up some economy to pay back the debt and then get the last two Estates. This strategy might not even beat HG-BigMoney without further support (P2 can easily hurt you by buying a HG before you trash them all).
Also, P2 could gain 4 Duchies on turn 4 after mirroring turns 1-3.
What do you mean by "player roles reversed"? P2 can still only play Donate on t2 with a 5/2 start (t1: TF+2Lurkers, t2: Donate). I see: with 5/2 either player can play Donate AND gain 1st KC on t2.
Trashing 10 Hunting Grounds results in only two empty piles; you can't end the game the way you described unless someone mirrors you. If they don't bite, you're done.
It doesn't even work with mirroring since there's only 10 HGs to trash for both players combined (the two remaining Estates would be hard to get rid of with no treasure in either deck).
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you can just trash down another pile with the lurkers.
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you can just trash down another pile with the lurkers.
Presumably the Lurkers themselves, though how long it will take on average is something worth considering. If you match KC with Lurker ever, not very long.
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You can get the last two Estates by trashing Catacombs.
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Yes catacombs will work. You don't have to consider anything nonmirror as if opponent couldn't pileout hg with mirror then you could spend turn 6 by getting 9 bakers and trash 9 hg on turn 6.
As lucky 5/2 opening p2 could with baker token buy tfair+topdeck 2 lurker, then on turn 2 gain kc and donate.
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What about P2 doing
T1: Tfair Lurker
T2: Lurker 1 HG for Duchy, Tfair Lurker + Donate, keeping 2 Estates and the Duchy.
T3: Lurker Lurker for KC
T4: Lurker KC Lurker for 4 Duchies. Shuffle luck is only 50/50, so not too bad.
They now have 5 Duchies, 2 Estates for 17 points, and if P1 trashed all their Estates, there's only 3 Duchies and 8 Estates left which is also 17 points. So P1 doesn't have enough points to win without being able to get a Province, and if they wait too long P2 can just 3 pile.
If P1 keeps an Estate when Donating T2, then P2 can keep 3 Estates instead. Odds of combo success go down for both, but if P2 misses on T4 but still gets KC/Lurker or Lurker/Lurker, they can grab another KC and increase their odds of winning next turn if P1 misses the combo T5.
And if P1 keeps 2 Estates, then P2 can just trash completely and gamble that P1 misses the combo.
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What about P2 doing
T1: Tfair Lurker
T2: Lurker 1 HG for Duchy, Tfair Lurker + Donate, keeping 2 Estates and the Duchy.
T3: Lurker Lurker for KC
T4: Lurker KC Lurker for 4 Duchies. Shuffle luck is only 50/50, so not too bad.
They now have 5 Duchies, 2 Estates for 17 points, and if P1 trashed all their Estates, there's only 3 Duchies and 8 Estates left which is also 17 points. So P1 doesn't have enough points to win without being able to get a Province, and if they wait too long P2 can just 3 pile.
If P1 keeps an Estate when Donating T2, then P2 can keep 3 Estates instead. Odds of combo success go down for both, but if P2 misses on T4 but still gets KC/Lurker or Lurker/Lurker, they can grab another KC and increase their odds of winning next turn if P1 misses the combo T5.
And if P1 keeps 2 Estates, then P2 can just trash completely and gamble that P1 misses the combo.
Make it a Shelters board ;)
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that or add rebuild for kc-kc-lurker-lurker-rebuild. Or add catacombs add silk roads
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Here is the best non-mirror strategy that I could come up with
1 Lurker
2 TF Lurker + Donate
3 L,L -> KC
4 KC-L,L -> KC,L
5 KC-KC-L-L-L -> trash remaining L
6 KC-KC-L-L-L -> trash remaining KC
7 KC-KC-L-L-L -> trash 9 HG -> 8D, 3E = 27vp
game ends on empty D, L, and KC. If the other player helps you by getting a single HG, you can end it in 6 turns.
Make it a Shelters board ;)
ephesos' strategy would still work to achieve at least a tie
5 duchy = 3 duchy + 6 estate
that or add rebuild for kc-kc-lurker-lurker-rebuild. Or add catacombs add silk roads
You have to be careful with adding cards. It may also help the other player. I guess catacombs + silk road would work, but it also opens up space to try a different strategy.
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Here is the best non-mirror strategy that I could come up with
1 Lurker
2 TF Lurker + Donate
3 L,L -> KC
4 KC-L,L -> KC,L
5 KC-KC-L-L-L -> trash remaining L
6 KC-KC-L-L-L -> trash remaining KC
7 KC-KC-L-L-L -> trash 9 HG -> 8D, 3E = 27vp
game ends on empty D, L, and KC. If the other player helps you by getting a single HG, you can end it in 6 turns.
That's neat. I retract my HG-BM claim :-[. This certainly beats any non-mirror strategy, I think. especially since there's no +Buy available.
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...
(Edited out stupidity, there's TF, of course...)
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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.
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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.
Will be interesting to see how quickly you can end the game from here. Assuming worst possible shuffle luck:
5: KC + 4*Duchy, nothing.
6: Duchy *2, Lurker*3 -> empty Duchies.
7: KC + 4*Duchy
8: 4*Duchy+Lurker.
Okay, so P2 should be able to buy the last 2 HG by turn 8. That means that P1 has to empty another pile without HG help. That will be difficult. I think there will be a non-zero chance for P2 to win.
You could use Landmakrs to improve P1's chances even further. Battefield seems like a good idea, and probably Tomb.
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I got idea that we could with modified kingdom three pile on turn 6 for win. I am tired for complete plan now but it should be possible from kc-kc-lurker-lurker-ironwork hand get kc, upgrade,fortress,remodel, draw them by trashing cultist, then do kc-upgrade, gain rats for another pile and somewhere get stonemason and trash squire for alchemist to change it into 10+ point vineyards.
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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.
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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.
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.
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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.
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.
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.
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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...
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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.