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[gamesou]

Hello everybody,

Here is a puzzle that I hope challenging and fun (I also hope my solution is correct ...)

You play a 2-player Dominion game against an opponent that chooses to go for a Chancellor Big Money strategy. He opens Chancellor/Silver and then buys Province if he can, otherwise Gold, otherwise Silver, otherwise nothing. He always uses the Chancellor ability.

If he is very very very very lucky (or an illusionist), this strategy is powerful. However it's not unbeatable !!!!

The puzzle is to find a Kingdom set (including Chancellor) and a strategy that always wins. No matter how lucky is your opponent, and how unlucky you are, you win.

Ah, something important: you start.

Enjoy !

--
Guillaume

[WanderingWinder]

I'm pretty sure that with perfect luck for him and against you, it's impossible. I mean, he's going to open chancellor/silver, buy a gold on turn 3, and then buy a province every turn from then on. The best you can do is delay him one single turn by somehow reducing his handsize. You can also pump him full of all 10 curses, but a) you need to be quite lucky to do that this fast, and b) it doesn't really matter, as he's miles ahead of you. I mean, at worst he'll have every province at the end of turn 11. Beating that is just not happening, at least with worst-case luck.

[gamesou]

I agree that it LOOKS impossible. Indeed he will buy the last province on turn 11 (or 12 if you reduced his hand once). So you have to stop him before.

[play2draw]

Well, Chancellor/BM, with the best of luck, will end as such:

1: Chancellor
2: Silver
3: Gold
4: Province (Ch/S/G/C/C)
5: Province
...
11: Province

Curses will do nothing except lower the VP count (as with perfect luck, they will never be drawn in hand), and handsize-reduction will only delay one or two turns, taking extra time to buy either gold or silver depending on when you use, say, militia.

Can you get Goons/King'sCourt/Masquerade set up before turn 11?

Now that I think about it, if you can get your deck down to just WorkersVillage/WorkersVillage/Monument/Militia/Masquerade/Curse, the most he'll ever be able to buy are Dutchies (assuming he never gives you the Chancellor). Just keep playing the Monuments and buy a curse every turn until you have enough VP to overtake 8 provinces.

Probably you can open Ironworks/Chapel, Chapel all coins/cash, and use the Ironworks to get the necessary cards, and "Island" away the Chapel at the end... but can this be done quickly enough?

[HockeyHippo]

EDIT:

Just re-read the OP

No matter how lucky is your opponent, and how unlucky you are, you win.

Well that rules out my solution because I used perfect shuffling. Sigh

I believe you can get it set up, with perfect shuffling. Check my solution though please.

Turn 1: C/C/C/C/E -> Buy Quarry       
Turn 2: C/C/C/E/E -> Buy Chapel   Deck: (7xCopper, 3 Estates, 1Q, 1Ch)
Reshuffle
Turn 3: C/C/C/C/Q -> Buy KC
Turn 4: E/E/E/C/Ch -> Chapel 3xEstate, 1xCopper     Deck:(2xC) Discard:(KC/Chapel/Q/4xCopper)
Turn5: C/C/(reshuffle)C/Ch/KC -> Chapel 3x Copper      Deck: (C/C/C/Q) Discard:(KC/Chapel)
Turn 6: C/C/C/Q/(reshuffle)Ch -> Buy Goons  Deck: (KC) Discard: (C/C/C/Q/Ch/Goons)
Turn 7: KC(reshuffle)/Goons/Q/Copper/Copper: KC-Goons +3 from Q +2C = 9$ Buy KC + Masq Deck: (Chapel/Copper) Discard: (KC/Goons/Q/2xC/KC/Masq)
Turn 8: Chapel/Copper/KC/KC/Masq: KC->KC->Masqx3(picking up deck)->Goonsx3 Give Chapel/Copper/Copper Trash incoming cards and Buy Monument
Deck:() Discard: (KC/KC/Goons/Monument/Masq/C/Q)
Turn 9: KC/KC/Goons/Monument/Masq Picking up and passing C/Q Trash incoming cards
Turn 10: Implement KC/KC/Goons/Monument/Masq strategy and trash opponent's deck. Once they have nothing left buy remaining provinces to win the game.

I think that works, but I definitely need to check it over. 1 pair of eyes is not enough!

[WanderingWinder]

Well of course you can beat it with perfect shuffling. You can get all the colonies by the end of your 5th turn with perfect shuffling.

[guided]

"No matter how bad your luck is" is a nasty constraint. You could bury your 2 opening cards at turn 5, which effectively means you don't start your game until your opponent has a guaranteed province every turn. And then every time you buy a key card (at least until you get an engine running) it could miss a shuffle.

I'm not aware of any pin (like KC/Masquerade) with 100% chance of success (given no interference from attacks) by turn 11. If you've found one I'm interested to see it.

There are probably various KC-based approaches that are likely to succeed, but none I can think of off the top of my head that are guaranteed to succeed.

[A_S00]

Does his "perfect shuffle luck" mean he always draws Chancellor along with his biggest treasures, regardless of circumstance, or does it mean he draws whatever would be worst for you given whatever strategy you're pursuing?

[WanderingWinder]

Does his "perfect shuffle luck" mean he always draws Chancellor along with his biggest treasures, regardless of circumstance, or does it mean he draws whatever would be worst for you given whatever strategy you're pursuing?

I'm assuming perfect means perfect, which means whatever is worst for you/gives him the best chance of winning.

[guided]

"no matter how lucky" is pretty clear (unless that isn't actually what he meant?): No matter what you do, your opponent will always have the best possible hand when it becomes their (un-Possessed) turn.

[Deadlock39]

I think the solution would have to be pretty simple, because anything that buys a reasonable amount of cards, it is going to be exceedingly difficult to determine what the "worst possible luck" is. 

It appears it is too slow, but I was curious what the maximum number of turns is that it could take to reduce your deck to Chapel, Treasure Map, Treasure Map.  If it can be done quickly enough, you would then have Chapel + 4 Golds.  This deck could then buy Two King's Courts, a Goons and a Masquerade in 4 turns, and probably activate the combo pretty shortly there after.  Unfortunately, it would then take a couple more turns before the pin even really succeeds since you will be passing the Chancellor Golds.

Now... possibly a more likely solution could be.  How many turns does it take to get down to a deck of: Village, Village, Militia, Monument, Masquerade.  This would knock your opponent down to 2 cards every turn which prevents them from buying Provinces, and will destroy one of their cards each turn.  It can be done without the Monument as long as the Chancellor player is not allowed to buy anything other than Silver, Gold and Province.

As I stated above, it is extremely complicated to determine worst case shuffle order for a Chapel strategy trying to get those cards and trash everything.

[gamesou]

"no matter how lucky" is pretty clear (unless that isn't actually what he meant?): No matter what you do, your opponent will always have the best possible hand when it becomes their (un-Possessed) turn.

Yes, that's what I mean. Except for a few exceptions (minion, possession, ... ), the best for the oppenent is to draw Chancellor+4 highest treasures.

The probability of success of your strategy should be 100%.

Actually it's already not easy to find a strategy that has a reasonable probability of success against the Lucky Chancellor. You can try using the cards, it's fun since you don't have to handle the opponent's shuffles. If you succeed in defeating the Lucky Chancellor, I guess you will have essentially found the strategy (I would be surprised if there was another solution), and then there are a few tricks to ensure the 100%.

[DG]

I wouldn't be surprised if there was some way to get a big vineyards score using a selection from chapel, ironworks, great halls, islands, hamlets, havens, scrying pools, university, throne, vineyards etc that became bulletproof to bad draws. There would be no need to attack the chancellor, just amass a lot of non terminal actions and a few vineyards.

[play2draw]

Now... possibly a more likely solution could be.  How many turns does it take to get down to a deck of: Village, Village, Militia, Monument, Masquerade.  This would knock your opponent down to 2 cards every turn which prevents them from buying Provinces, and will destroy one of their cards each turn.  It can be done without the Monument as long as the Chancellor player is not allowed to buy anything other than Silver, Gold and Province.

Well, I was able to get my method up by about turns 9 through 11 (where you use an Ironworks to draw all the necessary cards, trash the Ironworks with Chapel, and Island the Chapel away) It seems possible that the worst possible luck might be too slow, but it's fairly reliably set-up (ignoring the whole "island the chapel" is unnecessary, since I could have just passed the chapel and trashed whatever the opponent sent me).

If you have the chance to open 5/2, you can probably mess around with mint/secret chamber, get a remake, and acquire the villages and masquerade by trashing the estates.

[Deadlock39]

I didn't think about using Ironworks and that eliminates the biggest issue I found which was figuring out how to get the cards you need with the worst luck possible.  (and even figure out what "worst luck" is.)

Can we get clarification on whether the Chancellor player can buy Duchies and or other cards to 3 pile the game, or if he will only buy Gold, Silver and Province?  I guess you did say Big Money, so I assume that excludes any kingdom cards, but if he can drain Duchy, Estate, and Gold, using the pin and only trashing one card a turn won't be good enough because he can 3 pile the game with all his VP intact.

[Tahtweasel]

Do you get to choose whether you start 5-2 or 4-3?

[Tahtweasel]

A possible set people haven't tried yet: Chapel, Goons, Wharf, Village, Bridge, Iron Works, Nobles, Watchtower, King's Court, Chancellor. You need 52 points, which will mostly come from copper, purchased and trashed through watchtower. You have to reliably draw your whole deck, otherwise bad things can happen.

[gamesou]

Do you get to choose whether you start 5-2 or 4-3?

No. Your strategy should work 100% of the time.

Can we get clarification on whether the Chancellor player can buy Duchies and or other cards to 3 pile the game, or if he will only buy Gold, Silver and Province? 

For simplicity, I asked the question when the Lucky Chancellor applies the most basic Big Money strategy (see my OP). However I guess it can be adapted to work 100% of the time against any Big Money strategy (i.e. any strategy that buys only Victory and Treasure cards, besides the initial Chancellor), though I didn't doublecheck.

Well, I was able to get my method up by about turns 9 through 11 (where you use an Ironworks to draw all the necessary cards, trash the Ironworks with Chapel, and Island the Chapel away) It seems possible that the worst possible luck might be too slow, but it's fairly reliably set-up (ignoring the whole "island the chapel" is unnecessary, since I could have just passed the chapel and trashed whatever the opponent sent me).

This goes in the correct direction ! However it is too slow to achieve a 100% success (check the case when Estates and Coppers are on the top at every reshuffle).

[Deadlock39]

Okay, I think I beat the Lucky Chancellor, but others will need to check the "worst luck possible" on my end of the scenario.

This is going to be a little long, just to be thorough.


Turn 1 and 2:
You open: Ironworks, Chapel (available for either start)
Lucky Chancellor opens Silver, Chancellor

I am pretty sure, the worst possible luck delays the Chapel and Ironworks both to hand 5 so the conflict and miss the shuffle.

Turns 3 and 4:
You do nothing
Lucky Chancellor buys a Gold, and then a Province(1)

Turn 5:
You draw Ironworks, Chapel, and 3 starting cards (Coppers and Estates are the same because we will never use the Coppers to buy)
You Ironworks for a Great Hall, Gaining an Action and Drawing a card.
You Chapel 4 starting cards.
Your draw pile Contains 6 starting Cards.
Your discard Contains Ironworks, Chapel, and Great Hall
The Lucky Chancellor Buys a Province(2)

Turn 6:
You Draw 5 starting cards and do nothing
Your draw pile contains 1 starting card.
Your discard contains Ironworks, Chapel, Great Hall, and 5 starting cards
The Lucky Chancellor Buys a Province(3)

Turn 7:
You draw 1 starting card, Reshuffle and then draw 4 more.
You do nothing.
Your draw pile contains Ironworks, Chapel, Great Hall, and 1 starting card.
Your discard contains 5 starting cards
The Lucky Chancellor Buys a Province(4)

Turn 8:
You draw Ironworks, Chapel, Great Hall, and 1 starting card.  You Reshuffle and draw another starting card.
You play Great Hall and draw a starting card.
You play Ironworks and gain a Great Hall, Drawing another starting card
You Chapel 4 starting Cards
Your draw contains 2 starting cards.
Your discard contains Ironworks, Chapel, and 2 Great Halls.
The Lucky Chancellor buys a Province(5)

Turn 9:
You draw 2 starting cards.  You reshuffle and draw 2 Great halls and an Ironworks.
You play a Great Hall, Drawing your Chapel.
You Ironworks and gain a Throne Room.
You Chapel 2 starting cards and a Great Hall.
Your draw pile is empty.
Your discard contains Ironworks, Chapel, Throne Room, and Great Hall
The Lucky Chancellor Buys a Province(6)

Turn 10:
You reshuffle and Draw Ironworks, Chapel, Throne Rome, and Great Hall.
You Throne Room Ironworks, and gain a Village and a Militia.
You Chapel a Great Hall.
Your draw pile is empty
Your discard contains Ironworks, Chapel, Throne Room, Village, and Militia
The Lucky Chancellor buys a Province(7)

Turn 11:
You reshuffle and draw Ironworks, Chapel, Throne Room, Village, and Militia.
You Throne Room Ironworks.
You gain an Island and Draw it.
You gain a Masquerade.
You play Village and Draw Masquerade.
You play Island and set aside your Chapel.
You play Militia and the Lucky Chancellor Discards 2 Coppers.
You play Masquerade.
You receive a Copper from the Lucky Chancellor and trash it. (Yeah, that lucky bastard drew 3 this turn and protected his Silver).
Your draw pile is empty.
Your discard contains Ironworks, Throne Room, Village, Militia, and Masquerade.
The (un)Lucky Chancellor only has his Chancellor and Gold left this hand, so he buys a Silver.

Turn 12:
You reshuffle and draw Ironworks, Throne Room, Village, Militia, and Masquerade.
You play Village.
You play Militia and the (un)Lucky Chancellor discards 2 Coppers.
You play Throne Room and...
You play Masquerade and pass your Ironworks to the Lucky Chancellor.
You receive a Copper from the (un)Lucky Chancellor and trash it.
You play Masquerade again.
You get your Ironworks back from the (un)Lucky Chancellor and trash it.
Your draw pile is empty.
Your discard contains Throne Room, Village, Militia, and Masquerade.
The (un)Lucky Chancellor again only has his Chancellor and his Gold left and buys a Silver.

Turn 13-??
You reshuffle and draw Throne Room, Village, Militia, and Masquerade.
Every turn you play Village, Militia, Throne Room->Masquerade, trashing 2 of the (un)Lucky Chancellor's cards, and leaving him with only one card in his hand.
The (un)Lucky Chancellor can buy only one card a turn, but he is losing two, so eventually you will trash his entire deck.
The best he can do is have is Gold remaining in hand one hand, and his Chancellor in hand the next.  He can buy Silvers and Estates, and Copper, but soon he will have no cards and nothing he can do.  He might be able to run out the Estates and Copper, but he can do no harm, and cannot end the game.

Once you have destroyed the (un)Lucky Chancellor's entire Deck, you can do the following:
Throne Room->Militia, buy a Silver.
Throne Room->Militia, play Silver, Buy a Gold (or a Silver).
Play Village if you drew it (you have 6 cards), Throne Room->Militia, play Silver and Gold, buy the final Province and WIN!

The Kingdom contains:
Chancellor
Chapel
Ironworks
Great Hall
Throne Room
Village
Militia
Island
Masquerade
and one free spot...

The Free spot could be used for a Monument which could be grabbed once the Chancellors deck is gone, and you can continue the pin while generating infinite VP.

[michaeljb]

Looks good, just tested it on Isotropic and with that shuffling, I got to your turn 13 on turn 9.

Of course, in this case when you go and buy that Province it won't be the last one, since you'll be able to stop him before he gets to 7, though I suppose you could decide to just wait until the right time.

edit: link

[A_S00]

This goes in the correct direction ! However it is too slow to achieve a 100% success (check the case when Estates and Coppers are on the top at every reshuffle).

I'm not done testing it yet, but I'm pretty sure that play2draw's solution only needs Great Hall added to it and it works, even with the worst possible shuffle luck.

*edit* Yep.  I'm pretty sure the following is the worst possible shuffle luck (note the delay of both opening buys until turn 5, followed by every shuffle putting as many terminals into the hand as possible):

1 - 4c1e - buy IW
2 - 3c2e - buy Chapel

(reshuffle)

3 - 3e2c - do nothing
4 - 5c - buy Village

   DISCARD = Village, 7c3e; DECK = Chapel, IW

(draw IW, Chapel, reshuffle)

5 - Chapel, IW, 3c - IW (Great Hall, draw 1c), chapel 4c, no buy
6 - village, 1c3e - village (reshuffle, draw 1c), no buy

   DISCARD = Village, 2c3e; DECK = Chapel, IW, Great Hall, 1c3e

7 - Chapel, IW, 1c2e - IW (Island, draw 1e), Chapel (1c3e)

   DISCARD = Chapel, Village, IW, Island, 2c; DECK = Great Hall

(draw Great Hall, reshuffle)

8 - Great Hall, Island, IW, Village, Chapel - IW (Village), Village (draw 1c), Great Hall (draw 1c), Chapel (2c)

   DISCARD = Village, Island, Chapel, Great Hall, Great Hall, IW; DECK = Village

(draw Village, reshuffle)

9 - Village, Village, Island, Great Hall, Great Hall - Village (draw Chapel), Village (draw IW), Island (Chapel), IW (Militia), Great Hall (draw Militia), Militia

   DISCARD = Village, Village, Great Hall, Great Hall, IW, Militia

(reshuffle)

10 - IW, Militia, Great Hall, Great Hall, Village = Village (draw Village), IW (Masquerade), Great Hall (draw Masquerade), Great Hall (nothing to draw), Militia, Masquerade (nothing to draw, nothing to pass, trash incoming card)

(reshuffle - at this point, the pin is complete)

11 - IW, Militia, Masquerade, Great Hall, Great Hall - Great Hall (draw Village), Great Hall (draw Village), Village (nothing to draw), IW (Monument), Village (draw Monument), Monument, Militia, Masquerade (nothing to draw, nothing to pass, trash incoming card)

...etc.

(Technically, on subsequent turns you'll have to IW yourself another village, then IW yourself another Island, then Island away your IW, so that you don't have to keep picking up an action card with IW every turn in order to avoid having it in your hand when you play Masquerade...but this won't be a problem.  Picking up extra villages and extra Monuments before you get rid of IW will help you pick up VP faster, which might actually be necessary, since at 1VP/turn, the silver pile might actually empty before you rack up enough VP to beat your opponent.)

[gamesou]

Congratulations to Deadlock39 who found essentially the same solution as mine (they diverge from turn 9, see below) ! The strategy suggested by play2draw and AS_00 looks also nice (I didn't take time to convince myself that it works).

I find it crazy that a key card seems to be the innocent-looking Great Hall.

Now, a puzzle for which I don't know the answer. The Lucky Chancellor wants a rematch. Now, he starts (as stated in the rulebook). Can you still always beat him ?

Below is my solution for the initial problem. It uses only cards from base and intrigue.

Turns 1-2 : open Ironworks/Chapel

Turns 3-8 : do the following: buy nothing and ironwork Great Halls until
you chapel 4 starting cards twice. By the end of turn 8 (possibly
before) you have

Chapel, Ironworks, 2 or 3 Great Halls, 2 starting cards

Turn 9 : play Great Hall, ironwork a Throne Room, and chapel the 3 or 4
remaining cards. You have now

Chapel, Ironworks, Throne Room, Great Hall

Turn 10 : Play Throne Room->Ironwoks to gain Militia/Throne Room, and chapel
the remaining Great Hall. You have now

Chapel, Ironworks, 2 Throne Rooms, Militia

On turn 10 the Lucky Chancellor buys his 7th Province

Turn 11 : Play Throne Room, Throne Room, Militia, Chapel (to trash the
Ironworks). Buy a Masquerade.

You have : Chapel, 2 Throne Rooms, Militia, Masquerade

The attacked Lucky Chancellor buys Gold on his 11th turn.

Turn 12 : Play Throne Room, Throne Room, Militia, Masquerade. You pass a
Chapel to the opponent, and trash the 2 cards he gives you.

For the subsequent turns you apply the pin and trash 2 cards from the
Lucky Chancellor's deck, while he can buy only a Silver. Once his deck
is destroyed, you just collect the remaining Victory cards.

[A_S00]

Checked again; play2draw's solution actually works in the case where you go first without Great Hall.  Here's the worst-case scenario (I stopped when the pin is complete at the end of turn 11; getting yourself set up to pick up VPs works the same as before):

1 - 4c1e - buy IW
2 - 3c2e - buy Chapel

(reshuffle)

3 - 3e2c - do nothing
4 - 5c - buy Village

   DISCARD = Village, 7c3e; DECK = Chapel, IW

(draw IW, Chapel, reshuffle)

5 - Chapel, IW, 3c - IW (Island, draw 1c), chapel 4c
6 - village, 1c3e - village (reshuffle, draw 1c)

   DISCARD = Village, 2c3e; DECK = IW, Island, Chapel, 1c

7 - Chapel, Island, IW, 1c1e - IW (Village), Chapel (1c1e)

   DISCARD = Chapel, Island, IW; DECK = Village, Village, 2c2e

8 - Village, 2c2e - Village (draw Village), Village (draw Island)

   DISCARD = Village, Village, Island, 2c2e; DECK = Chapel, IW

9 - Chapel, IW, Island, Village, Village - Village (draw 1c), Village (draw 1c), Chapel (2c)

   DISCARD = Chapel, IW, Island, Village, Village; DECK = 2e

10 - IW, Village, Island, 2e - Village (draw Chapel), Chapel (2e), IW (Militia)

   DISCARD = IW, Village, Island, Chapel; DECK = Village, Militia

11 - Village, Militia, Chapel, Island, IW - IW (Masquerade), Village (draw Village), Village (draw Masquerade), Island (Chapel), Militia, Masquerade (nothing to draw, nothing to pass, trash incoming card)

-----

For the case where the Chancellor player goes first, the solution I posted above works (pin complete at the end of turn 10).

*edit* Actually, I'm wrong.  The solution from my previous post doesn't quite work, because of the VP stuff at the end.

Specifically, once you IW yourself a second Island, it becomes possible to draw (IW, Militia, Monument, Masquerade, Island) on any given turn.  With that hand, you can IW yourself a Great Hall to make it possible to draw your entire deck and continue the pin, but doing so makes it impossible to Island away your IW (since it's in play).

However, the addition of Peddler to the kingdom makes the solution work.  Play the same game up through completing the pin on turn 10.  On turn 11, instead of IW (Monument), you IW (Peddler).  You do this four times, on turns 11-14 (you are guaranteed to be able to play your entire deck on these turns, so Peddler will always cost $0).  Then you IW (Island) on turn 15.  On 16, your turn is:

IW, Militia, Masquerade, Island, Great Hall - Great Hall (draw Great Hall), Great Hall (draw Village), Village (draw Village), Village (draw Peddler), Peddler (draw Peddler), Peddler (draw Peddler), Peddler (draw Peddler), Peddler (nothing to draw), Island (IW), Militia, Masquerade (nothing to draw, nothing to pass, trash incoming card), buy Monument

Your deck now consists of (Masquerade, Militia, Monument, Great Hall x2, Village x2, Peddler x4).  With only 3 terminals, you are guaranteed to be able to play your entire deck without gaining any cards every turn.  You can even pick up a second Monument to double your VP income rate without risking letting up the pin.

With that revision, the Kingdom becomes (Chapel, Chancellor, Village, Great Hall, Masquerade, Ironworks, Militia, Island, Monument, Peddler) for a total of 10 cards - just fits!

[WanderingWinder]

You can't ironworks peddler without having 2 quarries play via black market or 4 bridges in play, because peddler doesn't get cheaper until the buy phase. So it doesn't work.

[Thisisnotasmile]

Peddler will only cost $0 in the buy phase. Ironworks does not operate in the buy phase.

Ninja'd. I expected it.