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[Powerman]

So, you are playing a 2 player game.  Your opponent plays Chancellor - Big Money.  He opens Chancellor - Silver, then has the following buy rules:
Province: $8+
Gold: $6-7
Silver $3-5
He always draws the luckiest hand, plays his Chancellor with it's cycling ability, and sets his deck in the order he wants.  This is all the same as Part 1.

Now, the solutions to that puzzle revolved around a Masquerade pin.  Masquerade is banned from this puzzle.  Can you design a strategy that beats the lucky Chancellor player every time, regardless of how he sets his deck and how unlucky your draws are?

Easy Mode:  You go first.
Hard Mode:  Your opponent goes first.
Harder Mode:  Your opponent goes first, and changes his strategy by adding in a single Moat.
Hardest Mode:  Your opponent goes first, changes his strategy by adding in a single Moat, and Scheme is banned from the kingdom.

[Note:  I do not know if Harder or Hardest Mode is possible]

[Edit: You choose if your split is 5/2, 4/3, 3/4, or 2/5.  And if you have Baker in the kingdom, well add the coin where you want.]

[DG]

You might want to rule out the baker, shelters, and colonies as well.

[Asper]

Nothing can beat Chancellor. Nothing.

On a more serious note, i assume "the luckiest hand" means his hand is terrible if i possess him?

[liopoil]

idea:get a pillage and discard his chancellor. that should slow him down a bit

[Powerman]

You might want to rule out the baker, shelters, and colonies as well.

Why?

[achmed_sender]

Plan for playing this IRL: Pointing out of the window, if your Chancellor-player looks away: act fastly and gain the entire province pile (and for experts also some Golds and +Buy cards, so you can legitimate your win )

Unfortunately, it doesn't win 100% (opponent might be clever and not fall in trap again )

[scott_pilgrim]

Plan for playing this IRL: Pointing out of the window, if your Chancellor-player looks away: act fastly and gain the entire province pile (and for experts also some Golds and +Buy cards, so you can legitimate your win )

Unfortunately, it doesn't win 100% (opponent might be clever and not fall in trap again )

This sounds like a good response to your opponent's "shuffling".

[florrat]

I think that the two harder modes are also possible. I have some promising strategies, although they do not work completely yet.

My idea is to open Chapel + Doctor (overpaying 1). This will almost always results in having chapel on turn 4. In this case, you can get a thin deck by turn 7, having grabbed some $2-cost cards on the way and start grabbing peddlers.

The only case which can go wrong is when you get $5 on turn 1, buying doctor, trash 2 coppers, and then drawing E,E,E,Do,C on turn 2. But then you can trash 5 lot of coppers by the end of turn 2 and buy a poor house (or you can trash 1 less copper in turn 1, and buy a chapel on turn 3).

In all cases I think you have a reasonable chance to beat lucky chancellor + moat, by getting 46VP from goons and buying a last province in turn 11.

[jonts26]

I think that the two harder modes are also possible. I have some promising strategies, although they do not work completely yet.

My idea is to open Chapel + Doctor (overpaying 1). This will almost always results in having chapel on turn 4. In this case, you can get a thin deck by turn 7, having grabbed some $2-cost cards on the way and start grabbing peddlers.

The only case which can go wrong is when you get $5 on turn 1, buying doctor, trash 2 coppers, and then drawing E,E,E,Do,C on turn 2. But then you can trash 5 lot of coppers by the end of turn 2 and buy a poor house (or you can trash 1 less copper in turn 1, and buy a chapel on turn 3).

In all cases I think you have a reasonable chance to beat lucky chancellor + moat, by getting 46VP from goons and buying a last province in turn 11.

Reasonable chance isn't what were looking for. You have to assume worst case scenario for your draws and guarantee a win. 100%

[florrat]

Reasonable chance isn't what were looking for. You have to assume worst case scenario for your draws and guarantee a win. 100%

Okay, I worded that wrong. I think that in all cases you can guarantee a win, but I haven't found the way to do it yet

[liopoil]

is buying chapel worth it? I understand that we need trashing, but we aren't gonna draw it until turn 5 and then not again until like turn 8. I think doctor's on buy trashing will be better.

[eHalcyon]

is buying chapel worth it? I understand that we need trashing, but we aren't gonna draw it until turn 5 and then not again until like turn 8. I think doctor's on buy trashing will be better.

But in the worst case, how much can you really expect to overpay, and how early?  Baker guarantees $5 only, which is only an overpay of 2.  Not that great.  And you would get it in the second hand, which makes Doctor miss the shuffle you just caused.

[Grujah]

I think that the two harder modes are also possible. I have some promising strategies, although they do not work completely yet.

My idea is to open Chapel + Doctor (overpaying 1). This will almost always results in having chapel on turn 4. In this case, you can get a thin deck by turn 7, having grabbed some $2-cost cards on the way and start grabbing peddlers.

The only case which can go wrong is when you get $5 on turn 1, buying doctor, trash 2 coppers, and then drawing E,E,E,Do,C on turn 2. But then you can trash 5 lot of coppers by the end of turn 2 and buy a poor house (or you can trash 1 less copper in turn 1, and buy a chapel on turn 3).

In all cases I think you have a reasonable chance to beat lucky chancellor + moat, by getting 46VP from goons and buying a last province in turn 11.

Reasonable chance isn't what were looking for. You have to assume worst case scenario for your draws and guarantee a win. 100%

But Baker in kingdom, you can always open Doctor+2/Chapel, so you can guarantee chapel turn 4?

[Kirian]

Doctor on buy doesn't work well.  The worst case is that you buy Chapel first, then Doctor.  When you shuffle, the top card is Chapel... which you can either discard and not see until T6, or leave alone and end up with a worthless Doctor.

[florrat]

Doctor on buy doesn't work well.  The worst case is that you buy Chapel first, then Doctor.  When you shuffle, the top card is Chapel... which you can either discard and not see until T6, or leave alone and end up with a worthless Doctor.

But making sure that you get chapel on turn 3 is worth 1 worthless card in your deck. I don't know if it's also worth the opportunity cost of buying a doctor, but I think it is. You lose ~2 turns when chapel misses the reshuffle.

[Powerman]

Edited the OP.  I do want this to be where you control your first hand. (So you can include [or not include] shelters)

[Kirian]

Edited the OP.  I do want this to be where you control your first hand. (So you can include [or not include] shelters)

Oh man, being able to control the split is likely to make this a lot easier, I think.

[gamesou]

Now, the solutions to that puzzle revolved around a Masquerade pin. 

That's not true. DG had a solution that defeated the lucky Chancellor using only VP tokens.

[florrat]

That's not true. DG had a solution that defeated the lucky Chancellor using only VP tokens.

You're mostly right, but there are some complications with that solution. First, the solution solves only the easy part of this puzzle, and second, this part of his solution shows that the solution he wrote there is not complete.

On turn 5 there's a different continuation if you immediately draw the cellar. You get to cycle the cards and use the ironworks more often but only trash 3 cards on turn 5. The worst draws puzzle is pretty bad to prove since I should really exhaust all possible draws and exhaust everyone's patience.

[Davio]

I don't think it's doable from a mathematical proof point of view, just because we might like to use cards that lets P2 make some decisions which aren't immediately clear whether they were right or wrong, say trashing with Bishop or discarding to Vault. And every decision creates a new branch for our ever growing tree.

So if we're going to do something with a tree of which we can explore every branch, the easiest thing to do is just to use simple, interchangeable cards. 1 Gold is the same as another Gold. Anything else just makes it explode I'm afraid.

[scott_pilgrim]

I can do hardest mode without Chancellor/Moat in the kingdom.  I'm not sure if that counts.

Kingdom: Chapel, Black Market, Doctor (Bane), Watchtower, Great Hall, Procession, Ironworks, Catacombs, Highway, Border Village, King's Court

On turns 1-9, you use Chapel and Doctor to trash your deck down to just 2 Ironworks, 2 Processions, and a Chapel.  This is always possible; the proof is left as an exercise for the reader (which is a fancy way of saying I don't want to list every possible case in this post).  Someone should probably verify this though, because it is quite possible that I made a mistake.

Notational warning: I letter each card so that generally, the first one you get is A, then B, etc. (i.e. the first Procession I get is Procession A, the next one is Procession B, then Procession C, etc.)  However, I think a few of the cards mixed up the letterings and I was too lazy to fix them.  For example, I think you get Catacombs G before Catacombs D-F.  Since the labels are arbitrary, it doesn't affect the solution, but it might look funny.  Similarly, Great Halls A and B don't exist because of herp derp.  You can get some Great Halls where I say to get Estates at the end, but it doesn't matter.

Notational warning #2: Upon previewing my post, I see that typing three ?'s comes up as , (when I first typed it up I had three ?'s) so I guess that will be the symbol that I use when you draw cards that can't be determined because of the shuffle.  Usually when this happens, you draw the rest of your deck shortly after so that I know what is in your hand again.  This happens a lot at the end when it doesn't matter because you're ending the game anyway.

On turn 10, you have this megaturn:
Your hand is Procession A, Procession B, Ironworks A, Ironworks B, Chapel A
   Play Procession A:                  
      Play Procession B twice:            
         Play Ironworks A twice:         
            Gain Watchtower A         
            Gain Great Hall C, re-shuffling and drawing either Great Hall C or Watchtower A
         Trash Ironworks A            
         Gain Catacombs A            
         Play Ironworks B twice:         
            Gain Procession C         
            Gain Procession D         
         Trash Ironworks B            
         Gain Highway A            
      Trash Procession B               
      Gain Catacombs B               
   (If Great Hall C is in hand, play it to draw Watchtower A)      
   Play Watchtower A:                  
      Draw Catacombs A, Catacombs B, Procession C, Procession D, Highway A
   Play Highway A                  
   Play Procession C:                  
      Play Procession D twice:            
         Play Catacombs A twice         
         Trash Catacombs A            
            Gain Procession E         
         Gain Border Village A         
            Gain Catacombs C         
         Play Catacombs B twice         
            Draw Procession E, Border Village A, Catacombs C
         Trash Catacombs B            
            Gain Procession F         
         Gain Border Village B         
            Gain Procession G         
      Trash Procession D               
      Gain Catacombs G               
   Play Procession E:                  
      Play Catacombs C twice:            
         Draw Procession F, Procession G, Border Village B, Catacombs G
      Trash Catacombs C               
         Gain Procession H            
      Gain Border Village C            
         Gain Catacombs D            
   Play Procession F:                  
      Play Procession G twice:            
         Play Border Village A twice:         
            Draw ,          
         Trash Border Village A         
         Gain King's Court A            
         Play Border Village B twice:         
            Draw , King's Court A      
         Trash Border Village B         
         Gain King's Court B            
      Trash Procession G               
      Gain Catacombs E               
   Play King's Court A:                  
      Play Procession H three times:            
         Play Border Village C twice:         
            Draw King's Court B, Catacombs E   
         Trash Border Village C         
         Gain King's Court C            
         Play Catacombs D twice:         
            Draw King's Court C         
         Trash Catacombs C            
            Gain Ironworks C         
         Gain Border Village D         
            Gain Procession I         
         Play Catacombs E twice:         
            Draw Ironworks C, Border Village D, Procession I
         Trash Catacombs E            
            Gain Procession J         
         Gain Border Village E         
            Gain Catacombs F         
   Play King's Court B:                  
      Play King's Court C three times:         
         Play Procession I three times:         
            Play Border Village D twice:      
               Draw ,       
            Trash Border Village D      
            Gain King's Court D         
            Play Catacombs G twice:      
               Draw ,       
            Trash Catacombs G         
               Gain Ironworks D      
            Gain Border Village F      
               Gain Highway B      
            Play Border Village E twice:      
               Draw ,       
            Trash Border Village E      
            Gain King's Court E         
         Play King's Court D three times:      
            Play Procession J three times:      
               Play Catacombs F twice:   
                  Draw ,    
               Trash Catacombs F      
                  Gain Ironworks E   
               Gain Border Village G   
                  Gain Black Market A   
               Play Border Village F twice:   
                  Draw ,    
               Trash Border Village F   
               Gain King's Court F      
               Play Highway B twice:   
                  Draw ,    
               Gain Border Village H   
                  Gain Ironworks F   
            Play King's Court E three times:   
               Play King's Court F three times:
                  Play Ironworks C three times:
                     Gain Border Village I
                        Gain Ironworks G
                     Gain Border Village J
                        Gain Ironworks H
                     Gain Ironworks I
                  Play Ironworks D three times:
                     Gain Ironworks J
                     Gain Duchy A
                        (worst case) Draw Duchy A
                     Gain Duchy B
                        Draw (not Duchy B, because of re-shuffle)
                  Play Ironworks E three times:
                     Gain Duchy C
                        Draw
                     Gain Duchy D
                        Draw
                     Gain Duchy E
                        Draw
               Play Black Market A three times:
                  Buy Silk Road   
                  Buy Tunnel   
                  Buy Duke      
               There is at least one Ironworks in your hand; play it three times:
                  Gain Duchy F   
                     Draw    
                  Gain Duchy G   
                     Draw    
                  Gain Duchy H   
                     Draw    
            There is at least one Ironworks in your hand; play it three times:
               Gain Great Hall D      
                  Draw       
               Gain Great Hall E      
                  Draw       
               Gain Great Hall F      
                  Draw       
         There are three Ironworks in your hand; play one of them three times:
            Gain Great Hall G (if you run out of Great Halls to gain, just gain Estates)
               Draw          
            Gain Great Hall H         
               Draw          
            Gain Estate D         
               Draw          
      There are two Ironworks in your hand; play one of them three times:
         Gain Estate E            
            Draw             
         Gain Estate F            
            Draw             
         Gain Estate G            
            Draw             
      Play the last Ironworks in your hand three times:      
         Gain Estate H            
            Draw             
         Gain Estate I            
            Draw             
         Gain Estate J            
            Draw             
You should have around 53 points, which is enough to beat the Lucky Chancellor.  Silk Road should be worth at least 6, Duke should be worth 8.

Someone who has cards on Goko should verify my solution, I don't trust myself to get through a megaturn like that by hand without any mistakes.  I would imagine though that even if there are mistakes, it can easily be adjusted.

This gets me wondering, with worst case shuffle luck, what is the fastest you could empty the supply?

[eHalcyon]

@scott I'm not checking it, but I can see that your strategy doesn't fully work.  First note that Black Market isn't yet available on Goko, so it can't be verified there.  Searching your solution, it looks like BM is there only for this:

Play Black Market A three times:
                  Buy Silk Road   
                  Buy Tunnel   
                  Buy Duke   

This breaks the constraints of the problem of worst shuffle luck, because you have assumed that you will be able to buy those three VP cards when you play BM.  In the worst case, none of them will appear in the BM.  The only real way you can guarantee getting those three cards out of the BM is to make the BM deck a maximum of size 5 (in which case you will always draw at least one of the three VP cards you have specified).  But most people will consider that to be an unreasonable BM size.

[scott_pilgrim]

That is a good point, I had not thought about that.  I assumed that setting the BM deck is kind of like choosing the kingdom, so I assumed control over it.  That makes a big difference though.  I might try to work out a way to do it without Black Market later.

[dondon151]

I would love it if were an official Dominion icon.

[Kirian]

That is a good point, I had not thought about that.  I assumed that setting the BM deck is kind of like choosing the kingdom, so I assumed control over it.  That makes a big difference though.  I might try to work out a way to do it without Black Market later.

This seems easy enough to work around... replace Black Market with Duke, and gain 8 Dukes in those last few plays of IW.  Bam, 64 points.

However, not having Chancellor in the kingdom does kinda make this problematic.  Neat how this builds from CC's T4 solution, though.