Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.

1

Puzzles and Challenges / Re: Turn 3

« on: February 25, 2013, 07:12:44 pm »

Well, now that we can empty the supply on Turn 4, that leads to what we can do on Turn 3.  This isn't simply a puzzle of what's possible, but also what is likely.

The question is, can you empty the supply on turn 3 in multiplayer. Six players, you go last, they all open Masq / something and draw both on turn 3, passing down the somethings to you. Your buys are of course still in your deck. So they pass you Procession Procession Procession Fortress Watchtower or some such and well, I'm not figuring that out.

I feel like you should be able to do something crazy on turn 2 with three cards of your choice...

Much of the work has already been done:

With just 2 turns and 6 players, and allowing Outpost, you can empty the Colonies pile. 
http://forum.dominionstrategy.com/index.php?topic=4334.0

With just 3 turns and 3 players, you can probably empty all piles as well, combining CC's ideas with what I had back then. 
http://forum.dominionstrategy.com/index.php?topic=3585.0

2

Puzzles and Challenges / Re: Empty the Supply in 4 Turns

« on: February 25, 2013, 07:09:04 pm »

Well, you got one of those right.

The Kingdom change seems so obvious in retrospect...  But pretty sweet that you can get to that point without Develop at all!  To what extent were the first few Black Market cards really important? 

3

Puzzles and Challenges / Re: Empty the Supply in 4 Turns

« on: February 21, 2013, 09:46:01 pm »

Question for CC: How do you actually go about solving a puzzle like this? pen and paper, some computer sim, real cards?

Over the summer, while I was doing a lot of Dominion puzzles, I imagined having simple software to help work out puzzles (those Procession chains...).  People could potentially share log files easily to prove their solutions, and collaborate/tweak easily.  There are huge classes of puzzles that would be more interesting with this sort of framework, e.g. "Empty provinces as fast you can with this Kingdom", "Gain as many points as you can on this turn, with this hand and deck".  You could also make up new cards and play around with them. 

But the UI seemed pretty tricky to get right, I knew it'd take a while, and I suspect interest levels are low (outside of CC), so it was more just an idea than anything I seriously considered creating.   If I'm wrong and people would indeed like such a thing, and any CS-y people are interested in making it, we could start a separate thread to discuss (I have some ideas for how the design should go).  I may be willing to help out with such a project in my spare time.  If this happens, we can collectively destroy the tricky Guilds puzzles that I'm sure some of us will think up 

I was wondering if you'd show up again.

Your heavenly presence beckons (and your camouflage is not sufficient to evade my attention)

To clarify: getting over 50 points in one buy means that one of my buys increases my score by over 50, not that I only use a single buy in the solution. In fact I use rather more than that (around 100 if you include Black Market buys).

Ah, I see.  Seems very possible now.   But only for the celestial.   

And yes, my current solution does score well over 1000 points. I'll probably post it at the weekend once I've finished tidying it up.

Very excited and curious.  You should share with me in advance, so I don't need to wait, haha.

I predict:

• Same kingdom as before, but with Black Market additionally. 
• Solution is the same up to the playing of Peddler on turn 4. 

If they both are true, it will be a crazy optimization feat. 
But if either is not true, I'm more excited.  The most natural thing to try to do would be to fit in a King's Court instead of Catacombs or Peddler, but I remember this being quite hard

4

Puzzles and Challenges / Re: Empty the Supply in 4 Turns

« on: February 21, 2013, 04:54:45 am »

Challenge: In a solitaire game of Dominion with perfect shuffle luck, empty the Supply by the end of Turn 4. Outpost and Possession turns count towards the turn limit.

Hard Modes:
1. Also gain all the Colonies and Platinums.
2. Also score over 500 points.
3. Solve this puzzle as well by scoring over 50 points with a single buy.
4. Do all of the above at once.


 

Oh, man.  This is back!  This place is boring without you  

Hmm... 900 points with only one buy.  I'm guessing you'll be assuming an infinite silver pile?

I'm too busy these days to try anything this time around, but I'm looking forward to the solution!  Looks like there will be some new ideas!  Perhaps I will try to take some time to contribute after you reveal.  Also, I suspect 1000 points is possible.

5

Puzzles and Challenges / Re: Which is the card that should be in this list but is not?

« on: September 13, 2012, 04:52:46 pm »

The common quality is that all those cards can put a card in your hand that you didn't have before when you play them, regardless of what other cards are in the kingdom.

I would nominate Black Market as an honorable mention. 

It's true that regardless of what the actual Kingdom is, it's possible to gain a new card in hand.  But the "can" is across games, not just turns, because you need the right Black Market deck. 

First, assume Horn of Plenty, Watchtower, and Rats/Cultist are all in the Black Market deck.  Then, we can have the following turn:  Play Black Market, playing Gold and Horn of Plenty.  Horn of Plenty for an Estate, revealing a Watchtower to topdeck.  From Black Market, buy Rats/Cultist.  Trash it to Watchtower, to draw the Estate.

It's also fine if Horn of Plenty or Watchtower was a Kingdom card.  However, it's bad if both Rats and Cultist are in the Kingdom, but Horn of Plenty isn't.  Then we can't draw the new card off the Black Market, so we need to play two Horn of Plenties.  Luckily, Counterfeit comes to the rescue... (from the Black Market deck, if not in supply).  Mandarin + Villages + Draw also works. 

6

Puzzles and Challenges / Re: Most VP in 3 Turns

« on: September 13, 2012, 04:57:49 am »

One improvement I can see is that if you have a watchtower, when you gain a fortress, you can gain it in hand. I don't think that makes too much of a difference though.

Actually, I *want* it on deck.  Otherwise, the Cultist draws a Copper, which gets in the way of the Watchtower drawing.

7

Puzzles and Challenges / Re: Which is the card that should be in this list but is not?

« on: September 13, 2012, 03:30:25 am »

The common quality is that all those cards can put a card in your hand that you didn't have before when you play them, regardless of what other cards are in the kingdom.

I don't think Ironworks fits that bill.  You have to assume that either there is:  a $4 or less Kingdom VP, a cost reduction card, trashing, or a Dark Ages card (so we start with Shelters). 

Edit:  Oops, I was misinterpreting "a card that you didn't have before" as a card differently named than everything in your deck (in which case IGG and Beggar wouldn't work either)

8

Puzzles and Challenges / Re: Most VP in 3 Turns

« on: September 13, 2012, 03:27:47 am »

It'd be interesting to see (I'm guessing you've got some kind of epic megaturn idea).

With 2 players, I couldn't seem to do much.  But it turns out 3 players is enough to get a mega-turn.

So, the state of affairs is:

Turn 2 -	6 players (it's likely 5 is enough)
Turn 3 -	3 players (maybe 2, but highly doubtful)
Turn 4 -	1 player

Unfortunately, turn 3 with 3 players doesn't offer too many new ideas.  You basically get the same set-up as that in the turn 4 puzzle.  You even get to use better cards for the piles, without needing Nomad Camp, Hamlet, Peddler.  I can get over 400 points, and there is clearly room for improvement (including Black Market helps, for example).  The transcript is rather long, but here it is:

Kingdom:  Masquerade (Mq), Procession (Pr), Ironworks (Iw), Watchtower (Wt), Squire (Sq), Cultist (Ct), Band of Misfits (BoM), Develop (Dv), Fortress (Ft), Goons (Gn)

Player 1 opens Mq1 and Pr1
Player 2 opens Mq2 and Pr2.
Player 3 opens Iw1 and Wt1.

On turn 3, Player 1 plays Mq1, passing Pr1.  Player 2 passes Pr2.  Player 3 passes Overgrown Estate.
Player 2 plays Mq2, passing Pr1.  Player 3 passes Hovel.
Player 3 has Necropolis, Pr1, Pr2, Iw1, Wt1 in hand. 
Play Pr1 on Pr2
- First Procession plays Iw1, gaining Ft1 and Dv1 on deck.  Trash Iw1, gaining BoM1 on deck.
- Second Procession plays Necropolis, gaining Sq1, trashing it for Ct1, trashing it to draw BoM1, Ft1, Dv1. 
- Trash Pr2, gaining BoM2 on deck
Play BoM1 as Procession, on Dv1. 
- Play the Develop on Ft1, returning it to hand, and gaining BoM3, Dv2 on deck.
- Play the Develop on Ft1, returning it to hand, and gaining BoM4, Wt2 on deck.
- Trash Dv1, gaining Pr3, on deck.
Play Wt1, drawing BoM3, BoM4, Pr3, Dv2, and Wt2. 

Play Pr3 on BoM3, playing as Procession
- 1st Procession plays BoM4, playing as Procession
-- 1st Procession plays Dv2
--- 1st Develop trashes Ft1, returning it to hand. Gain BoM5 and Dv3 on deck.   
--- 2nd Develop trashes Ft1, returning it to hand. Gain Dv4 on deck, and trash Ct2, drawing BoM5, Dv3, Dv4.
--- Trash Dv2, gain Pr4 on deck
-- 2nd Procession plays Dv3
--- 1st Develop trashes Ft1, returning it to hand. Gain Dv5 on deck, and trash Ct3, drawing BoM2, Pr4, Dv5.   
--- 2nd Develop trashes Ft1, returning it to hand. Gain BoM6 and Dv6.
--- Trash Dv3, gain Pr5 on deck
-- Trash BoM4, gain Gn1 on deck
- 2nd Procession plays BoM2, playing as Procession
-- 1st Procession plays Dv4
--- 1st Develop trashes Ft1, returning it to hand. Gain Dv7 on deck, and trash Ct4, drawing Dv7, Gn1, Pr5
--- 2nd Develop trashes Ft1, returning it to hand. Gain Wt3 on deck, and trash Ct5, drawing Wt3, Dv6, BoM6.
--- Trash Dv4, gain Pr6 on deck
-- 2nd Procession plays Pr4
--- 1st Procession plays Pr5
---- 1st Procession plays BoM5, playing as Procession
----- 1st Procession plays BoM6, playing as Procession
------ 1st Procession plays Dv5
------- 1st Develop trashes Ft1, putting it hand.  Gain Wt4 and BoM7 on deck.
------- 2nd Develop trashes Ft1, putting it hand.  Trash Ct6, drawing BoM7, Wt4, Pr6, and gain Wt5 on deck.
------- Trash Dv5, gain Pr7 on deck
------ 2nd Procession plays Pr6
------- 1st Procession plays Dv6
-------- 1st Develop trashes Ft1, putting it hand.  Gain BoM8 and Dv8 on deck.
-------- 2nd Develop trashes Ft1, putting it hand.  Gain BoM9 and Dv9 on deck.
-------- Trash Dv6, gain Pr8 on deck.
------- 2nd Procession plays Dv7
-------- 1st Develop trashes Wt2.  Gain Iw2 and Sq2 on deck.
-------- 2nd Develop trashes Wt3.  Gain Iw3 and Sq3 on deck.
-------- Trash Dv7, gain Pr9 on deck.
------- Trash Pr6.  Gain and trash Ct7, drawing Pr9, Sq3, Iw3.
------ Trash BoM6.  Gain a Gn2 on deck.
----- 2nd Procession plays Ft1, drawing Gn2, Sq2.  Return Ft1 to hand.  Trash Ct8, drawing Iw2, Pr8, Dv9.
----- Trash BoM5.  Gain a Gn3 on deck.
---- 2nd Procession plays Ft1, drawing Gn3, BoM9.  Return Ft1 to hand.  Trash Ct9, drawing Pr7, BoM8, Dv8
---- Trash Pr5.  Gain BoM10 on deck.
--- 2nd Procession plays Pr7
---- 1st Procession plays Pr8
----- 1st Procession plays Pr9
------ 1st Procession plays BoM7, playing as Procession
------- 1st Procession plays BoM8, playing as Procession
-------- 1st Procession plays BoM9, playing as Procession
--------- 1st Procession plays Ft1, drawing BoM10 and Wt5.  Return Ft1 to hand.  Gain Ct10 on deck.
--------- 2nd Procession plays BoM10, playing as Procession
---------- 1st Procession plays Sq2, taking +2 buys twice.  Gain Dv10 on deck.
---------- 2nd Procession plays Ft1, drawing Dv10 and Ct10.  Return Ft1 to hand.  Gain nothing.
---------- Trash BoM10.  Gain Gn4 on deck.
--------- Trash BoM9.  Gain Gn5 on deck.
-------- 2nd Procession plays Sq3, taking +2 buys twice.  Trash Sq3, gain Wt6 on deck.
-------- Trash BoM8.  Gain Gn6 on deck.
------- 2nd Procession plays Iw2, gaining Sq4 and Sq5 on deck.  Trash Iw2, gaining nothing.
------- Trash BoM7.  Gain Gn7 on deck.
------ 2nd Procession plays Ft1, drawing Gn7 and Sq5.  Return Ft1 to hand.  Gain nothing.
------ Trash Pr9, gaining nothing.
----- 2nd Procession plays Sq5, taking +2 buys twice.  Trash Sq5, gain Wt7 on deck.
----- Trash Pr8, gaining nothing.
---- 2nd Procession plays Dv8.
----- 1st Develop trashes Dv9, gaining Iw4 and Sq6 on deck.
----- 2nd Develop trashes Wt4, gaining Iw5 and Sq7 on deck.
----- Trash Dv8.  Gain Iw6 on deck.
---- Trash Pr7, gaining nothing.
--- Trash Pr4, gaining nothing.
-- Trash BoM2.  Gain Gn8 on deck.
- Trash BoM3.  Gain Gn9 on deck.

We now have 25 actions, more than enough to:
Play Dv10, trashing Ct10.  Draw Gn8, Gn9, Iw6.  Gain Gn10, Iw7 on deck.
Play Ft1, drawing Iw7.
Play Iw3, Iw6, Iw7 for Wt8, Pr10, Sq8.
Play Gn1, Gn2, Gn3, Gn7, Gn8, Gn9.
Play Wt5, drawing Sq8, Pr10, Wt8, Gn10, Iw5, Sq7.
Play Pr10 on Sq7, taking +2 buys twice.  Trash Sq7, gain Wt9 on deck.
Play Iw5, gaining Sq9 on deck.
Play Gn10.
Play Sq8 for +2 buys.
Play Wt8, drawing Sq4, Wt7, Sq6, Iw4, Wt9, Sq9.
Play Iw4, gaining Sq10 on deck.
Play Sq4, Sq6, Sq9 all for +2 buys.
Play Wt7, drawing Gn4, Gn5, Wt6, Gn6, Sq10.
Play Sq10, for +2 buys.
Play Gn4, Gn5, Gn6.
Play Wt6, drawing 5 Coppers.

We have 37 buys and $38 (having played 13 Squires, 10 Goons, 5 Copper), and Wt9 in hand. 
Buying 3 Colonies, a Duchy, and 33 Coppers, we get 403 points.

9

Puzzles and Challenges / Re: KC/TR/Procession/BoM

« on: September 07, 2012, 06:18:14 pm »

For use in future puzzles:

With 10 KCs, 10TRs, 10Processions and 10 BoMs, how many Actions cards can you triple?
How About 10KCs, 10Trs, 9 Proccs, and 9 BoMs (so piles are not empty)?
With

This may not be that useful for future puzzles, since the solution will take up 6 Kingdom piles...
Also, having the piles not be empty will rarely be useful for puzzles, since we're almost always fine with ending the game that turn.
Lastly, presumably only open non-chain plays count?  So playing 10 KC in a chain only counts as 19, and not 28? 

Anyways, here's a way to get 68 plays, using 10 Throne Rooms, Processions, King's Courts, Band of Misfits, and 19 Graverogues:
- Play a Bridge.  Play 10 Processions on 10 King's Courts (20 plays). 
- 9 Throne Rooms on 9 Graverogues, getting 9 Processions and 9 King's Courts back.  Play 9 Processions on 9 King's Courts (18 plays, 38 total). 
- Play 5 Band of Misfits + 5 Graverogues, getting 10 King's Courts back.  5 Band of Misfits as Procession, on 5 King's Courts (10 plays, 48 total). 
- Play 5 Graverogues, getting them back.  Play Throne Room on 10 King's Courts (20 plays, 68 total). 

10

Puzzles and Challenges / Re: Maximum Hand Size Before Turn Start

« on: September 06, 2012, 11:07:59 pm »

A conservative estimate is >300 using the following idea

Nice idea!  Seems likely to be in the optimal solution. 

But unless I'm missing something (which wouldn't surprise me, as you came up with many of the ideas of that thread in the first place), the conservative estimate doesn't obviously hold.  A big problem is that Graverobber/Rogue is used in the solution in that thread.  Although Graverobber/Rogue can in fact be played many times, it's not clear to me how it would fit with the Ambassadoring.  Furthermore, we have to either break the chain or use some KC/Procession plays to draw the Cultists to Ambassador (which we would do with Torturer/Council Room/Governor).  Thirdly, a minor nitpick - most action cards can only be played 98 times, not quite over 100, as far as we know. 

Also, here's a trick which will improve the solution some (whatever it has gone down to), but isn't sustainable:
P1 plays Saboteur, hitting P2's Cultist.  P2 gains Squire, trashing it with Watchtower, gaining Cultist, and trashing it with Watchtower.  This draws 6 cards. 

You can do a similar trick with (5 Bridges played and) Swindler hitting Squire, but this is better since Saboteur will search for Cultists, and this doesn't take up an extra Kingdom space.

11

Puzzles and Challenges / Re: Getting the most out of a kingdom

« on: September 06, 2012, 06:57:42 pm »

I overbid the solution to 1) to 781, though I think even more should be possible. The card that is played this often is Procession.

Awesome chain.  Of course my arguments from the earlier post fail completely when the card X is Procession itself... or Graverobber/Rogue, for that matter.  I agree that more is possible.  I suspect you can play the card drawer earlier, playing the same Processions again.  Eventually, the trash pile grows, and you make up for the loss by King's Courting some Graverobber/Rogues outside of the giant Procession chains.  Then repeat, with decreased n.

Also, updated answer for 2:

We can get at least 173 plays of a single Fortress.

Get 10 Throne Rooms, 10 King's Courts, 20 Graverogues, 9 Processions, some Scrying Pools and Ironworks, and a Fortress in hand (drawing them all with Scrying Pool).

Play a Throne Room on Throne Room. 
The first Throne Room plays 9+10 Processions in series.  This gives 20 open Procession plays, which all play Fortress.  8+10 of the Processions are trashed.
The second Throne Room plays 10 King's Courts, giving 20 King's Courts plays.
King's Court 1-6:  Plays 6 Graverogues, getting back the 8+10 Processions.
King's Court 7:  Plays a Throne Room. 
- 1st Throne Room plays Scrying Pool, drawing 8+10 Processions. 
- 2nd Throne Room plays 8+10 Processions.  This gives 19 open Procession plays, which all play Fortress.  7+10 Processions are trashed.
- 3rd Throne Room plays Graverogue, getting back 2 Processions. 
King's Court 8-12:  Plays 5 Graverogues, getting back 5+10 Processions.
King's Court 13:  Plays a Throne Room.
- 1st Throne Room plays Scrying Pool, drawing 7+10 Processions. 
- 2nd Throne Room plays 7+10 Processions.  This gives 18 open Procession plays, which all play Fortress.  6+10 Processions are trashed.
- 3rd Throne Room plays Graverogues, getting back 2 Processions. 
King's Court 14-17: Plays 4 Graverogues, getting back 2+10 Processions.
King's Court 18: Plays a Throne Room.
- 1st Throne Room plays a Graverogue, getting back 2 Processions.
- 2nd Throne Room plays Scrying Pool, drawing 6+10 Processions.
- 3rd Throne Room plays 6+10 Processions.  This gives 17 open Procession plays, which all play Fortress.  5+10 Processions are trashed.
King's Court 19-20: Plays 2 Graverogues, getting back 6 Processions.
Play Ironworks, for the last Procession.
Play Scrying Pool, drawing 7 Processions.
Play 5 Throne Rooms on 5 Processions, playing Fortress.
Play 2 Processions on Fortress.
Play Fortress.

40 + 38 + 36 + 34 + 20 + 4 + 1 = 173 plays of Fortress

12

Puzzles and Challenges / Re: Strategies that lead to unlimited number of victory points

« on: September 03, 2012, 04:36:30 am »

We know such strategies exist (see below). So the real challenge is to find all such strategies, or to find the strategy with the fastest-growing number of VPs. Also, are there strategies with super-linear VP growth?

This problem was actually touched on in a previous thread:
http://forum.dominionstrategy.com/index.php?topic=3032.msg53119#msg53119
And I asked a similar question a while ago:
http://forum.dominionstrategy.com/index.php?topic=4229

With limited piles, I don't think there are strategies with indefinite super-linear VP growth.  Even with infinite Treasure piles, I don't think it's possible. 

OK, so I think this is all right. With goons we can generate 1430 points per turn without fail.

We can do much better:  over 2000.  Instead of Wharf/Scheme as piles, just have a single Scrying Pool and a Scheme in the Black Market deck.  Include Band of Misfits effectively as an extra 9 Squires.  Black Market buys also work.  This actually simplifies things a lot, but I added a couple more non-essential tricks. 

Kingdom:
Black Market (Chapel, Trader, Scrying Pool, Scheme, Young Witch, Sir Martin, Cultist (9 ruined markets), Bridge, Highway, University, Ironworks, Procession, Graverobber, Rogue, Ambassador, Monument, Bishop, Fortress, X more cards with + buys)
Goons, Squire (Bane), King's Court, Band of Misfits, Throne Room, Market Square, Market, City, Festival, Worker's Village

Notice we replace Grand Market with Festival, since we don't need draw, and we Procession a Band of Misfits without wanting to gain anything.
Our deck has 10 Goons, and 9 of everything else.  Silver is out.

- Play Scrying Pool to draw everything.  Play Scheme.
- Play City.  Play Bridge. 
- Play Ironworks, for (the last) Band of Misfits.  Play Highway to draw it.
- Play University, for (the last) King's Court.  Play Scheme to draw it.
- Play a Throne Room on top of Procession.  The first Procession plays Band of Misfits (as Squire).  The second Procession plays 10 King's Courts, giving 20 plays.  Play them on 9 Squires, 9 Band of Misfits (as Squire), a Sir Martin, and a Goons.
- Play 7 Throne Rooms, on 7 Cities.
- Play Graverobber and Rogue, getting back Band of Misfits and King's Court.  Play a City to draw them.  Play Throne Room on Ambassador, returning both to supply (preventing the game from ending on piles).
- Play 9 of each:  Festival, Market Square, Market, Worker's Village, Ruined Market, Goons
- Play 9 Black Markets.  Keep buying things, but reveal Trader to gain nothing.  (A 2-cost is on top, letting us repeatedly buy it for free.  See http://boardgamegeek.com/thread/773553/black-market-trader)
- Play X cards (from the Black Market deck) which give buys.
- Play Monument.  Bishop a Fortress.
With a Trader in hand, buy at least 3+4+117+1+14+54+9+X=202+X Coppers, revealing Trader each time but gaining nothing.  This gives us 2024+10X points. 
Return Scrying Pool to the top of your deck.

We can double this score, if Outpost counts.  But I guess it doesn't, since Possession doesn't?  It essentially always just doubles the answer anyways, so it's not that interesting. 

13

Puzzles and Challenges / Re: Getting the most out of a kingdom

« on: August 29, 2012, 05:45:23 am »

I think the best card for part b) of this puzzle is Fortress, which I can play at least 63 times

Playing TR and 10xKC allows 21 actions to be played 3x. The first 20 of these will be Processions and BoM played as Processions, so that we can play Fortress 60 times, directly getting it back in the hand. Then we use the last KC to play it thrice

Oh, wow, you're right!  Although you forgot that BoM can't play as Procession if there are one in supply.  We can fix this by playing the BoMs first, and having a Watchtower in hand.  On (the last BoM or) one of the first 8 Processions, gain a Catacombs, trash it, and gaining the last Procession on top, and drawing it with the next played Fortress.  So we still have at least 63!

Also.  It's better for part a) too, and makes the solutions simpler.  But at least we know how many times you can play Coppersmith now...


Updated answers:

1) 138
2) 63
3) 1860 


New solution for 1)

With Scrying Pool, draw your deck of 9 Processions, 9 Fortresses, 10 Band of Misfits, 10 Throne Rooms, 10 King's Courts, 10 Graverobbers, 10 Rogues.  (Use University to gain some stuff beforehand, so that the game didn't end on the previous turn.)

Play a 10 Throne Rooms, and then 10 Band of Misfits as Processions in series underneath.  This gives us 20 Procession plays, which we play on Fortress each time. 

Play 10 Graverobbers, getting back the 10 Band of Misfits. 
Gain the last Procession and draw everything. 

Play 10 Processions, all on Fortress.  Play 9 Rogues, getting 9 back and drawing them. 
Play 9 Processions, all on Fortress.  Play a Rogue, getting 1 back.

Play 10 King's Courts, giving 19 King's Court plays.  Play 9+10 Fortresses.

Gain and draw the final Fortress.  Procession it.
Play the final Fortress.

20 * 2 + 10 * 2 + 9 * 2 + 19 * 3 + 1 * 2 + 1 = 138

14

Puzzles and Challenges / Re: Cards with maximum buying value

« on: August 29, 2012, 02:44:00 am »

On copper
10 king's courted coppersmiths and 10 king's courted bands of misfits acting as coppersmiths bring a coppers value up to 61. Played with a counterfeit that's $122 from the copper play. Where is everyone getting 90 from?

Good point.  I only got up to 30, and can't see better than ~60 with BoM.

I had written up explanations...
Procession, Graverobber, and Rogue let you get higher.  Actually, it's possible to get $99.  I updated the explanation accordingly.

without looking

Nice score!!  Though you did get lucky with some faulty reasoning   Without Graverobber/Rogue, Pirate Ship and Band of Misfits fall to 7th and 8th!  And I'm not convinced you had the Copper figure at $90 for the right reasons... Coppersmith alone is only enough to get it to 60.  And though this turned out not to matter, Band Of Misfits can't act as Tribute.  Also, hehe, everyone forgets Forager's name and function...

15

Puzzles and Challenges / Re: Getting the most out of a kingdom

« on: August 29, 2012, 02:25:48 am »

Before any (non victory) kingdom card could be played at most 30 times (King's court on all 10 cards).

I don't think you can KC a Horde. I could be wrong though.

Pedantic man notices that he said "at most", so your objection is wrong.  But then he also notices that the statement was still wrong - all the Kingdom Treasures are Kingdom Cards which could be played more than 30 times, thanks to Black Market, Horn of Plenty, Mandarin.  Then, he notices your mispelling of Hoard 

Anyways, I have...

Lower bounds for all of your questions:

1) 108
2) 43
3) 1860 

All bounds are tight or close to tight, I think.

Explanations

1)

Let me show how to play 98 Coppersmiths, since Coppersmith is fun.  The actual solution will use Rats and play 10 extra of them...

Kingdom:  Scrying Pool, University, Coppersmith, Scout (or Chapel), Band of Misfits, Procession, Throne Room, King's Court, Graverobber, Rogue

With Scrying Pool, draw your deck of 9 Processions, 9 Coppersmiths, 10 Band of Misfits, 10 Throne Rooms, 10 King's Courts, 10 Graverobbers, 10 Rogues.  (Use University to gain some stuff beforehand, so that the game didn't end on the previous turn.)

Play 9 Throne Rooms in series, and 9 Processions underneath them.  Play these on 9 Coppersmiths and 9 Band of Misfits (playing as Coppersmith).
Play 10 Graverobbers and 8 Rogues to recover the 9 Coppersmiths and 9 Band of Misfits.   
University the last Procession.  Draw everything with Scrying Pool.

Play Throne Room on Procession, playing 2 Coppersmiths.
Play 2 Rogues to get them back.  Draw them with Scrying Pool.

Play 10 King's Courts, giving 19 King's Court plays.  Play 9 Coppersmiths and 10 Band of Misfits playing as Coppersmiths.

Gain and draw the final Coppersmith.  Play it.

18 * 2 + 2 * 2 + 19 * 3 + 1 = 98

A couple arguments convince me that this is reasonably close to optimal.  In all the logic, Band of Misfits can replace Coppersmith.  A Graverogue is a Graverobber or Rogue:
 - It's never good to Graverogue back Graverogues.  Suppose you play Graverogue 2 to get back Graverogue 1.  This means Graverogue 1 was played by a Procession (otherwise, it can't help to have trashed the Graverogue.)  But we're wasting a play of Graverogue 2 (notice I don't assume anything about whether it was played by Procession or King's Court), and we might as well have not played Procession on Graverogue 1, and have an extra Procession play open.  I believe the only reason this argument isn't airtight is that you might've wanted the Graverogued card for playing up to the current chain you're in (which seems implausible to me). 
- It's never good to Graverogue back King's Courts.  This would mean King's Court was played by a Procession.  But if the King's Court were played by a King's Court, we would gain an extra King's Court play, and have an extra Procession open.  Unless we're severely limited by the number of Coppersmiths to play, this seems terrible. 
- It's not better to King's Court Processions, if we have non-chained Coppersmiths at the end, and all Graverogues are played.  Playing King's Court on Procession gives us two extra Procession plays and two less Coppersmiths.  The Processions can give us two extra Coppersmith plays, but nothing more, unless we have extra Graverogues to play.


2) 

For 43 Coppersmiths from the Black Market deck:

Kingdom:  Beggar (bane), Village, Walled Village, Black Market, Talisman, Procession, Band of Misfits, Graverobber, Rogue, Saboteur, Cache
Black Market contains King's Court, Coppersmith, Native Village.

Draw your deck with Native Village.

Do this 10 times: 
- Band of Misfits, playing as Procession, on the Coppersmith.  Graverobber, getting the Coppersmith back.  Draw it with Village.

Then, gain the last Procession and do this 10 times:
- Play Procession on Coppersmith.  Rogue, getting the Coppersmith back.  Draw it with Walled Village.

King's Court the Coppersmith.

10 * 2 + 10 * 2 + 3 = 43


3)

Let's play Copper a ton... too bad we can't do this in the same game we play Coppersmith 98 times!

Kingdom:  Crossroads, Hermit (giving Madman), Counting House, Black Market, Ambassador (bane), Band of Misfits, Procession, Throne Room, Graverobber, King's Court, Mandarin
The Black Market deck contains Horn of Plenty, Native Village, a Haggler (to help us empty piles off of Black Market buys, mid-turn), plenty more Villages, and any other necessary helper cards. 

Play Native Village to draw your deck.  Play King's Court, King's Court, Tribute, Village, Shanty Town.  Play a bunch more random Villages from the Black Market deck.  Get to 30-ish actions (enough, because of Madman).

Do this 10 times:  Play Band of Misfits as Procession, on Black Market.  Play 60 Coppers, and a Horn of Plenty, gaining Mandarin (and something else), putting the 60 Coppers and a Horn of Plenty back on deck.  Play Madman to draw.

Play 4 King's Courts, giving us 7 King's Courts plays.  Play 4 Graverobbers, getting back 10 Black Markets, and 3 Ambassadors, returning 9 Mandarins back to supply.  Play one more Ambassador, putting the last Mandarin back in supply. 

Gain the last Procession.

Do this 10 times:  Play Procession, on Black Market.  Play 60 Coppers, and a Horn of Plenty, gaining Mandarin (and something else), putting the 60 Coppers and a Horn of Plenty back on deck.  Play Throne Room, Crossroads to draw.

Play 4 King's Courts, giving us 7 King's Courts plays.  Play 4 Graverobbers, getting back 10 Black Markets, and 3 Ambassadors, returning 9 Mandarins back to supply.  Play one more Ambassador, putting the last Mandarin back in supply. 

Do this 10 times:  Play Black Market.  Play 60 Coppers, and a Horn of Plenty, gaining Mandarin (and something else), putting the 60 Coppers and a Horn of Plenty back on deck.  Play Counting House to draw.

Play 60 Coppers.

(10 + 10 + 10 + 1) * 60 = 1860

16

Puzzles and Challenges / Re: Most VP in 3 Turns

« on: August 28, 2012, 04:12:23 am »

I also can't think of a way to beat 11. 

But this is such a natural question to ask that it'd be a shame if we didn't make a good puzzle of it.
 
How about if we allow for a single opponent?

17

Puzzles and Challenges / Re: One Card Deck

« on: August 28, 2012, 04:04:19 am »

With Dark Ages, it's now possible to get 3 turns, using the same ideas from http://forum.dominionstrategy.com/index.php?topic=3225.msg92794#msg92794. 

I realize that this idea solves a lot of puzzles, and this is mostly copy-paste, but I thought it was worth noting how well-tuned the solution was for also getting worst-case guarantees as well!


Kingdom: Watchtower, Develop (bane), Black Market, Fortress, Ironworks, Bridge, Procession, Band of Misfits, City, Council Room, Border Village

Turn 1:
Play Ironworks for Procession

Turn 2:
Play Procession on Ironworks, for Procession, Watchtower.  Trash Ironworks, gaining Band of Misfits.

Turn 3:
Play Procession on Procession
- 1st Procession plays Band of Misfits as Ironworks.  Gain Fortress in hand, Procession on top.  Trash Band of Misfits, gaining Border Village, Procession on top.
- 2nd Procession plays Fortress, drawing Procession, Border Village.  Trash Fortress, get it back in hand, gain Band of Misfits.
Play Procession on Border Village, drawing Procession and Band of Misfits.  Gain nothing.
Play Procession on Band of Misfits, playing it as Develop.  Play Develop on Fortress, trashing it and returning it to hand.  Gain Develop, Band of Misfits, Watchtower, Band of Misfits, all on deck.  Trash the Band of Misfits, gaining Border Village, Procession.
Play Watchtower, drawing Border Village, 2 Band of Misfits, Procession, Watchtower. 
Play Border Village, drawing Develop.

Now consider the following sequence, which starts and ends with a hand of Procession, Band of Misfits, Band of Misfits, Develop, Fortress, Watchtower:

Play Procession on Band of Misfits, playing as Procession
- 1st Procession plays Band of Misfits, playing as Procession
-- 1st Procession plays Develop
--- 1st Develop trashes Fortress, putting it in hand. Gain Council Room and Watchtower on deck.   
--- 2nd Develop trashes Fortress, putting it in hand. Gain City and Develop on deck.
--- Trash Develop, gain Procession on deck
-- 2nd Procession plays Fortress, drawing Procession and Develop.  Trash Fortress, putting it in hand.  Gain City on deck.
-- Trash the Band of Misfits, gain Border Village, Bridge on deck
- 2nd Procession plays Procession
-- 1st Procession plays Develop
--- 1st Develop trashes Fortress, putting it in hand. Gain Band of Misfits and Develop on deck.   
--- 2nd Develop trashes Fortress, putting it in hand. Gain Band of Misfits and Watchtower on deck.
--- Trash the Develop, gain Procession on deck
-- 2nd Procession plays Watchtower, drawing Procession, 2 Band of Misfits, Develop, Watchtower.  Trash Watchtower, gain Bridge on deck.
-- Trash Procession, gain City on deck
- Trash Band of Misfits, gain Border Village, Bridge on deck

This sequence puts [Council Room, Watchtower, City, City, Border Village, Bridge, Bridge, City, Border Village, Bridge] on the deck (last on top), and does not disturb it otherwise.  It nets 3 actions (and 0 buys).  It also removes 2 Watchtowers, 1 Council Room, 2 Develops, 2 Processions, 3 Bridges, 2 Border Villages, 3 Cities, and 2 Band of Misfits from supply.  We play this sequence three times. (We're then limited by the Procession and Band of Misfits piles, which are now empty, fully activating City.  Only one Bridge and one City remains.) 

Play Procession on Band of Misfits, as Bridge.  Play Band of Misfits as Bridge. 
Play Develop on Fortress, for City and Watchtower.  Play Fortress, drawing Watchtower.

We now have two Watchtowers in hand, and the following on deck (last on top):
[Council Room, Watchtower, City, City, Border Village, Bridge, Bridge, City, Border Village, Bridge,
 Council Room, Watchtower, City, City, Border Village, Bridge, Bridge, City, Border Village, Bridge,
 Council Room, Watchtower, City, City, Border Village, Bridge, Bridge, City, Border Village, Bridge, City]

We can clearly play everything.  This gives us 12 Bridges, and 26 buys, which is enough for 8 Colonies, 8 Provinces, 8 Duchies, 2 Estates.

18

Puzzles and Challenges / Cards with maximum buying value

« on: August 27, 2012, 06:39:53 am »

This one's just for fun.  And not so much a puzzle as a challenge/quiz of sorts.  A break from my usual style 

Challenge: 

You have some amount of $ to spend during your buy phase this turn.  You play a single card, and the amount of $ increases by X.  For a given card, define its maximum buying value to be the maximum X it can possibly achieve as the single card played.  From memory, give a list of the 10 Dominion cards with the largest maximum buying value, in order. 

Rules:

These are all very important.

• Don't look anything up!  Use your brain and scratch paper if you need it. 
• Don't count money obtained by playing a different card, or money obtained in indirect ways.  This is strictly about the amount of $ given directly by playing that card. (For example, under my definition, Haggler, Black Market, Merchant Ship, Cutpurse count for 2; Talisman, Venture, Counterfeit, Quarry, Ironworks, Bridge, Pawn count for 1; and Procession, King's Court, Golem, Horn of Plenty, Coppersmith, Counting House, Adventurer, University, Princess count for 0). 
  
• Must be a legal game.  Can be 6 player, involve any legal Kingdom.  Black Market can have all non-Kingdom cards, as the rules state (unlike Isotropic).  However, Treasure piles are the standard 60, 40, 30.
• Your list may not have ties, even though the actual answer may in fact have tied values.  This is because I couldn't think of a simple scoring system that doesn't encourage having lots of things being tied.  If you know something is a tie, you can just break it arbitrarily (it won't affect your score).

Scoring:

For each card which is indeed in the top 10, you get a number of points equal to 10 minus the minimal distance between your guessed ranking, and from the actual rank interval.  The maximum score is 100. 

E.g. Say you put card X at rank 5.  Then, for that card:

•   If its actual rank was 4, you would get 9 points.
•   If its actual rank was 8, you would get 7 points.
•   If it were actually tied for 7-10, then you would get 8 points.
•   If it were actually tied for 3-5, you would get 10 points. 
•   If its actual rank were 11, you would get 0!

Solutions:

Here is what I believe is the actual ranking, using cards up to Dark Ages: 

1-2. Pirate Ship, Band of Misfits (infinite)
3-5. Vault, Secret Chamber, Store Room (around $600)
6. Diadem (around $325)
7. Bank (around $280)
8. Philosopher's Stone (around $120)
9. Copper (around $100)
10. Forager ($23, I think)

Harsh!  You got 0 points for listing:

11. Trade Route ($14, I think)
   Black Market with Trade Route/Young Witch.  Tunnel bane, 9 other Kingdom VP cards.  Estate, Duchy, Province, Colony.
12. Salvager ($11)
13-14. Death Cart, Platinum: $5
Honorable mention: Poor House, Harvest, Tribute, Baron, Fool's Gold ($4)
Dishonorable mention: Poor House (around -$250?)

Explanations:
1-2. Pirate Ship, Band of Misfits
   Thanks to Rogue/Graverobber.  Pre-Dark Ages, could reach $263, or $234 in a 2 Player game.  See topic 2107.
3-5. Vault, Secret Chamber, Store Room (around $600)
   Size of largest possible deck is around 600.  6 player game.  Include a Black Market deck with all cards not in the Kingdom, including Young Witch and Tournament.  Let Rats, Hermit, Urchin, Marauder, a Prosperity card, and a Potion-cost card be piles, with VP Kingdom cards for the rest.  Ambassador/Masquerade shennanigans to get opponent's starting hands.  Native Village to draw, on the final turn. 
6. Diadem (around $325)
   Have a chain of Throne Rooms above a chain of Processions, and a parallel chain of King's Courts.  Tributes are played by King's Courts, Fortresses by Procession, and fill in rest of chain with arbitrary Villages.  Some Black Market trickery to get a Village bane, with Tournament (bringing Trusty Steed) and all remaining net-action cards in the Black Market deck (including Crossroads, Hermit bringing Madman, Dame Molly, etc).  Have Necropolis, of course.  Pre-Dark Ages was closer to $270, I think (narrowly beating Pirate Ship and Bank?  Not sure).  I believe including Graverobber/Rogue so that we can get back King's Courts/Tributes/Processions is not going to help, but haven't done the analysis seriously. 
7. Bank (around $280)
   Have a bunch of Kingdom Treasures including Philosopher's Stone, and a Black Market giving Spoils, Diadem, etc.  Use a Native Village from the Black Market deck to draw the hand. 
8. Philosopher's Stone (around $120)
   Again, the size of largest possible deck is around 600.
9. Copper ($99, maybe a bit more)
   Coppersmith!  Plus King's Court, Band of Misfits, Procession, Graverobber, Rogue, Throne Room... see http://forum.dominionstrategy.com/index.php?topic=4409.msg98564#msg98564.  It's possible you can do better than this, but I doubt it beats Philosopher's Stone.
10. Forager ($23, I think)
   Black Market with all the Kingdom Treasures, and something for Spoils, Potion, Platinum.

How'd you do?  Harder than you thought?  Anyone get 100?!

Edit:  Top 3 scores so far

• O (96)
• Schneau (85)
• qmech (84)

Average score so far:  67.111 (9 entries)

19

Puzzles and Challenges / Re: The Ultimate Challenge: All in, All gone

« on: August 23, 2012, 12:03:51 am »

Edit:  I realized that the Potion cost cards and, especially, the Victory Kingdom cards, make this quite a bit harder than I previously thought it was.  Changed some stuff accordingly.  No longer as convinced it's possible.   

now I'm curious how that last turn would go. let's see.

I highly suspect the last turn goes more like this... 

Turn 4:  You draw Copper, (reshuffle) Procession, Procession, Nomad Camp, Watchtower.

Look familiar?  And if that doesn't work, I bet this will:

Turn 5:  You draw Throne Room, Throne Room, Procession, Hunting Grounds, Watchtower.
On deck is Procession, Ironworks, Bridge, King's Court, Peddler...

This one requires a bit more explanation:

Turn 1 and 2: Open Ironworks/Chancellor

Turn 3: Draw Ironworks, Chancellor, 3 Coppers
Play Ironworks, for Procession.  Play Chancellor, discarding deck, and 3 Coppers.  Buy Watchtower

Turn 4: Draw Procession, Ironworks, Chancellor, Watchtower, Necropolis
Play Necropolis.  Play Procession on Ironworks, gaining Throne Room, Procession, Council Room on top.
Play Watchtower, drawing Throne Room, Procession, Council Room, and 2 Coppers.
Play Throne Room on Procession 
 -- 1st Procession plays Chancellor, gaining Bridge.
 -- 2nd Procession plays Council Room, drawing 5 coppers, Bridge, Hovel, Overgrown Estate.  Gain Hunting Grounds.
Play Bridge and 7 Coppers. 
With $12, 4 buys, and 1 cost reduction:  Buy King's Court, Throne Room, Ironworks, Peddler.

Whichever route we take, we then attempt to do the following:

Play Throne Room's on top of King's Courts, on top of Procession/Band of Misfits, in a huge chain.  King's Courts should always be played by King's Courts, except that a top-level one by a Throne Room.  Band of Misfits always plays as Procession. 

Keep a single Watchtower and Fortress in hand.  Make sure we have EXACTLY 2 cost reductions (e.g. the original Bridge) played the whole time.  Altar will get us the King's Courts (trashing Fortress). 

Processions and Develops generally work up and down the following ladder, typically listed starting with the most useful cards, though it depends on what stage of the turn we are at:

2 costs:  Squire, Hamlet, Pawn
3 costs:  Develop, Workshop, Hermit, Watchtower
4 costs:  Procession, Ironworks, Armory, Remake, Talisman, Potion
5 costs:  Band of Misfits, Catacombs, Haggler, Upgrade, Horn of Plenty
6 costs:  Border Village, Altar, Hunting Grounds, Grand Markets, 1 Hoard
7 costs:  King's Court

Initially, focus on gaining cards.  At the very beginning, use Ironworks, Upgrade, Armory, and Altar.  Eventually, when we can support it, switch to Develop (and then Remake when it runs out), which should often get played on Fortress.  When the time comes, there are lots of quick tricks we can use to draw lots of cards quickly.  Most likely one:  Procession a Squire, getting Scrying Pool on top.  The other likely possibility is Crossroads. 

All cards we gain but don't draw during the chain should be Hagglers, Talismans, Horn of Plenty, Potions, cards with buys, and the alt VP costing less than 6:  Great Hall, Island, Silk Road, Tunnel, Duke, Feodum, Gardens (most likely trash them with Watchtower). 

At some point, we want to play 18 potions total.  Most likely, we should gain 6 and use the Black Market + Mandarin trick twice, or something like that.

We need around 150 to 200 buys, by a rough estimate.  We may want to save some King's Courts plays for Squire (and Sir Martin).  If we saved 10 (of the 20), it would give us 60 buys!  Most likely, it won't go like that, as King's Courts are pretty precious. 

At the end of the day, we want to have a total cost reduction of exactly 5.  We also want 10 Hagglers, a couple Talismans, 10 Horns of Plenty, 10 Counterfeits, and 10 Contrabands.  About 10 of those cards can come from Horn of Plenty/Mandarin/Cultist shennanigans in the buy-phase, which also empties the Cultist pile.  This leaves about 8 Horns of Plenty in hand, which are trashed for Colonies.  Playing 10 Counterfeits in a chain, play 10 Contrabands.  This gives 39 buys. 

With Watchtower in hand, Hunting Grounds and Feodum essentially take care of Duchies (and Duchesses), Estates, and Silvers.  A single Hoard should take care of Golds.  A single Rats takes care of Rats (with Fortress around). 

So our buys are largely spent on Province, Nobles, Harem, Farmland, Fairgrounds, Possession, and Vineyards.  We Haggle for other cards (be sure to Haggle the Knights, and to get the Potion cost cards and Grand Markets off of Possession).  If any alt VP costing less than $6 remains, buy it.  And any remaining piles (Platinum and the 6/7 cost actions) should be bought, with a couple buys each, thanks to Talisman. 


Honestly, I'm not a huge fan of puzzles like this anymore, since it's essentially already been solved.  Plus, solutions with big chains involving only two of King's Court, Throne Room, and Procession already take a while to work out.

20

Puzzles and Challenges / Re: My first challenge: Turn 2 Double Colony

« on: August 22, 2012, 06:30:55 am »

Okay, with Dark Ages, we can actually end the game, getting 18 Colonies and 5 Provinces.  I mainly just replaced Throne Room with Procession, and did some more Jester trickery.  I suspect it's possible to do much better still.

Edit:  I had an error where I didn't gain cards that I could've, at the end, on Processions.  An error which gave me 3 more buys and thus 3 more Provinces... Fixed everything now.


Kingdom: Watchtower, Masquerade, Bridge, Procession, Noble Brigand, Tribute, Jester, Outpost, Council Room, Border Village

P1: Buys Noble Brigand. (Everyone reveals Estate/Copper.)
P2: Buys Masquerade. Drawing Masquerade, 4 Coppers
P3: Buys Masquerade. Drawing Masquerade, 4 Coppers
P4: Buys Tribute. Drawing Tribute, 2 Estates, 2 Coppers
P5: Buys Watchtower. Drawing Watchtower, 4 Coppers
P6: Buys Jester. Drawing Jester, 2 Estates, 2 Coppers

P1: Buys Watchtower. 
P2: Plays Masquerade. P1 passes Copper, P2 passes Copper, P3 passes Copper, P4 passes Tribute, P5 passes Watchtower, P6 passes Estate. Draws 2 Coppers, buying Border Village, gaining Bridge. 
P3: Plays Masquerade. P1 passes Copper, P2 passes Copper, P3 passes Copper, P4 passes Estate, P5 passes Tribute, P6 passes Estate. Draws 2 Coppers, buying Border Village, gaining Outpost.
P4: Buys Noble Brigand (To reduce P5's deck to 4 cards.  P1 and P2 reveal Estate/Estate, gaining Copper.  All other players reveal Estate/Copper). 
P5: Buys Procession. 
P6:

Plays Tribute, revealing Noble Brigand and Watchtower.
Plays Jester. Gain P2's Border Village, gaining Council Room, P3's Border Village, gaining Jester, and P5's Procession, top-decking all.  Let P1 gain a Copper.
Play Watchtower to draw Procession, Jester, Border Village, Council Room.
Play Border Village, drawing Border Village. Play Border Village, drawing Copper.
Play Jester. Gain P2's Bridge, P3's Outpost, P4's Copper, P5's Copper.  Let P1 gain a Copper.
Play Procession on Council Room, drawing 6 Coppers, Bridge, and Outpost.  Trash the Council Room, gaining Border Village, Council Room.
Play Outpost and Bridge.
Play 9 Coppers.

With 9 Coppers, 2 Jesters, and 1 Bridge, we can buy Procession, Procession, Procession, Border Village (gaining Council Room).

On the outpost turn:

Draw Estate, Border Village, Border Village.
Play the Border Villages, drawing 2 Council Rooms.
Play Council Room, drawing Tribute, Jester, Jester, Watchtower
Play Tribute, hitting Noble Brigand and Estate.  (This is possible, as we have cycled P1's deck enough with Tribute, Jester, and Council Room.)  Draw 2 Border Villages.
Play Council Room, drawing 4 Processions (P5 draws their Procession, having cycled enough).
Play Jester, gaining P1's Watchtower, P2 and P3's Border Villages, gaining Processions, top-decking both (all having cycled enough).  Gain 2 Copper without topdecking.
Play 2 Border Villages, drawing Border Village and Procession.  Play Border Village, drawing Border Village.  Play Border Village, drawing Procession.
Play Jester, gaining P2's Bridge and P3's Masquerade, top-decking both.  P1 gains a Copper.  Gain 2 Copper without topdecking.
Play Procession on Procession
- 1st Procession plays Procession
-- 1st Procession plays Procession
--- 1st Procession plays Procession
---- 1st Procession plays Procession
----- 1st Procession plays Watchtower, drawing Masquerade, 2 Bridges, Watchtower, and a Copper.  Trash the Watchtower, gain Procession on deck.
----- 2nd Procession plays Bridge.  Trash the Bridge, gain Council Room on deck.
----- Trash the Procession, gain Council Room on deck.
---- 2nd Procession plays Masquerade.
----- 1st Masquerade draws 2 Council Rooms, passes Estate and receives Procession.
----- 2nd Masquerade draws Procession and Copper, passes Copper and receives Copper.
----- Trash the Masquerade, gain a Procession on top.
---- Trash the Procession, gain a Jester on top.
--- 2nd Procession plays a Bridge.  Trash the Bridge, gain Jester on deck.
--- Trash the Procession, gain Jester on deck.
-- 2nd Procession plays a Council Room, drawing 3 Jesters, Procession, and 4 Coppers.  Trash the Council Room, gain Border Village, Procession on deck.
-- Trash the Procession, gain Council Room on deck.
- 2nd Procession plays Procession
-- 1st Procession plays a Council Room, drawing Council Room, Border Village, Procession, and 5 Coppers.  Gain Border Village, Council Room on deck.
-- 2nd Procession plays Procession
--- 1st Procession plays a Jester, gaining P2's Bridge each time (their only card in deck because of Council Rooms), top-decking both, and 8 Coppers without topdecking.  Nothing to gain. 
--- 2nd Procession plays Procession
---- 1st Procession plays a Jester, gaining P2's Bridge each time (their only card in deck because of Council Rooms), top-decking both, and 8 Coppers without topdecking.  Nothing to gain.   
---- 2nd Procession plays Procession
----- 1st Procession plays Jester, gaining P2's Bridge each time (their only card in deck because of Council Rooms), top-decking both, and 8 Coppers without topdecking.  Nothing to gain.
----- 2nd Procession plays Council Room, drawing 6 Bridges, 1 Council Room, 1 Border Village.  Nothing to gain.
----- Gain Council Room, on deck.
---- Gain Council Room, on deck.
--- Gain Council Room, on deck.
-- Gain Tribute, on deck.
- Gain Tribute, on deck.
Play 2 Border Villages, drawing 2 Tribute. 
Play Tribute, hitting Noble Brigand and Watchtower (P1's only cards in deck).
Play Tribute, hitting Noble Brigand and Watchtower (P1's only cards in deck).
Play 4 Council Rooms, drawing 16 Copper.
Play 6 Bridges.

We have played 10 Bridges, 12 Council Rooms.  We have 23 buys, and well over $18 money.  Everything is free, except that Colonies cost 1. 

Thus we buy 18 Colonies and 5 Provinces.

21

Puzzles and Challenges / Re: Asymptotic Dominion: Asking all Nth turn puzzles at once

« on: August 22, 2012, 02:03:55 am »

Forging Cultists... now that is weird. Seems like it can work? With the 3 cards drawn from the Cultist dying, one can be a Cultist, one can be something (such as Ironworks) to gain a new Cultist, and the third can be something else.

(Also, my excuse for forgetting about Madman is having not played with it yet. )

Nah, it's dumb, cause the Cultists are trashed (whereas Crossroads keeps the Victory cards in hand).  They could all just be Smithy, and it'd be basically the same.  Fundamentally, we'd need a linear number of cards.  I was just noting it since it was the play of a single card that caused unbounded hand-size increase, but it's probably a useless technique for puzzles.

Edit:  My previous post had initially said the behavior was similar to Crossroads/Madman, which probably misled you to making the same silly mistake as I had.  My bad  .  I always just edit my posts since I hate having wrong things on record.  It feels like I'm contributing to polluting the internet with false information.

22

Puzzles and Challenges / Re: Asymptotic Dominion: Asking all Nth turn puzzles at once

« on: August 22, 2012, 01:40:08 am »

Crossroads can maybe be subbed for Scrying Pool in the solution on the blog. The analysis becomes annoying though (because you need O(log x) Crossroads to draw your deck, then one Crossroads per batch of new cards, and then you need some amount of new ones). So there might be some loss in the goodness of the solution.

Crossroads doesn't make the solution any worse, but indeed the analysis is a bit annoying, which is why I don't mention it.  Let me sketch a proof (feel free to PM me about details):

Suppose with a hand of x, we can gain c*x cards, where c < 1.  We're aiming for a multiplicative factor of k=1/(1-c) each turn. 

First, we prove that instead of going from x to kx, we go to kx - O(log^3(x)).  In fact, kx - O(log^2(x)) if you're careful on the analysis. 
To do this, let S_i be the number of cards we have at iteration i.  So S_0 = x, and S_(i+1) = c S_i - log(S_i).  We want to lower bound sum_i=0...log(x) S_i.  Show by induction that S_i >= c^i x - i log(x).  The result follows from that.  You'll have to use the fact that the S_i are decreasing, so S_i <= x. 

So does x still grow as k^n?  We're now interested in the recurrence for number of cards per turn, T_i = k T_(i-1) - log^2(T_(i-1)).  Similar recurrence, but slightly harder since the terms are growing.  Prove by induction that T_i >= k^i - (i-1)^3 * (k^(i-1) + k^(i-2) ... + 1) * log^3(k).  The proof is just a bunch of algebra.  For k > 2 (actually, it's sufficient to have k-1>log^3(k)), this is dominated by the k^i term for large i, so we have that T_i = Omega(k^i), as desired.

Okay, so this basically proves it, except that there's a Crossroads specific detail we're ignoring.  In order for O(log x) Crossroads to draw the deck, a constant fraction of our deck has to be Victory cards!  Luckily, this analysis doesn't care what the base of the log is.  This means it doesn't matter what the density of the Victory cards are: as long as it's any constant fraction, Crossroads is good enough to get the exact same result.  So we've in fact proven that Crossroads can get (k - epsilon)^i, for any epsilon. 

But truly getting k^i is not any harder.  Just have O(sqrt(n)) Victory cards and O(sqrt(n)) Crossroads, or something like that.  The analysis is no harder than what I just did.

Similar analysis, by the way, shows that when you have Seaside, you can use Caravans/Wharves to smooth out variance and get probability 1.  But it's easier and nicer to describe using Haven, put-back cards (e.g. Courtyard, Mandarin), or discard-and-draw-tricks. 

Crossroads and Scrying Pool are AFAIK the only way to draw a non-constant amount of cards.

I realize Jomini has noted some of these things, but, just to be exhaustive:  Scrying Pool, Crossroads, and Madman all draw unboundedly many cards.  Technically, Cellar, Storeroom, and Library can also draw arbitrarily many cards, although they don't increase your hand size arbitrarily.  I suspect arbitrary hand-size increase is closer to what we care about, in which case Native Village and Counting House work.  Lastly, Apprentice deserves honorable mention because its text doesn't preclude it from drawing arbitrarily many cards, and it's possible for this to happen with introduction of new cards. 

*Technically, a single play of Forge or Count could cause an unbounded hand-size increase, with Cultists in hand, but this is less interesting since it ultimately requires a linear number of cards to draw.  With infinite players, a Jester+Watchtower can also gain us infinitely many Fortresses in hand...

23

Puzzles and Challenges / Re: Asymptotic Dominion: Asking all Nth turn puzzles at once

« on: August 21, 2012, 02:24:21 pm »

Ok, but with a hand of TR+TR+TR+TR+WS+WS+WS+CR you get 4 cards per turn: 1+3/4+(3/4)^2 ... = 4
So, this is 16^n points, isn't it?

(It gets you 6, of 8, yes.)  The problem is you can't Workshop for Council Room, so you'd need to fit in Remodel or something like that.  So then we need Bridge... but Intrigue can do better anyways, with a 6/7 ratio!

24

Puzzles and Challenges / Re: Asymptotic Dominion: Asking all Nth turn puzzles at once

« on: August 21, 2012, 05:26:33 am »

Unless of course you just need it for the play-treasures-before-your-buy-phase function. Hm.

Yup, that's why I worded it that way.

Hm, am I missing something, but he assumes 6 card hands (with Base) and 7 card hands (with Base+Intrigue)? So I'm not sure how this is possible.

You're not sure how it's possible to get 6 and 7 card hands?   Laboratory 

Nobody said you had to start the turn with those hands.

25

Puzzles and Challenges / Re: Most VPs in 4 turns (again)

« on: August 21, 2012, 02:29:20 am »

Improved to over 300 points.  The basic idea is to replace Squire with Band of Misfits, and Remake with Develop.  Crucial is the fact that playing Procession on Band of Misfits gets you a 6 cost (checked the rules). 

The solution explodes, to the point where optimizing becomes more or less impossible.  Here's my solution which obtains 308, which is optimized for being easy to understand and verify, rather than being good.  I'm sure there are many avenues for further improvement (playing Procession on Watchtower is probably dumb, for example), but it probably stops being interesting at some point to do so...  the point is that 4th turn goes off!


Kingdom: Hamlet, Watchtower, Develop, Fortress, Nomad Camp, Procession, Catacombs, Band of Misfits, Goons, Peddler

Turn 1: Draw 4 Coppers and Hovel
Play 4 Coppers, buy Nomad Camp.

Turn 2: Draw Nomad Camp, 3 Coppers and Overgrown Estate
Play Nomad Camp and 3 Coppers, buy Watchtower and Hamlet.

Turn 3: Draw Necropolis, (reshuffle), Nomad Camp, Hamlet, Watchtower and Hovel
Play Necropolis and Nomad Camp
Play Hamlet, draw Overgrown Estate, discard Hovel and Overgrown Estate
Play Watchtower, draw 6 Coppers
Buy 2 Processions and Peddler

Turn 4: Draw Copper, (reshuffle), Procession, Procession, Nomad Camp and Watchtower
Play Procession on Procession:
- Play Nomad Camp twice.  Trash Nomad Camp, gain Catacombs, trashing to gain Fortress, trashing and putting it in hand.
- Play Fortress twice, drawing Peddler and Hamlet. Trash Fortress, put Fortress in hand, gain Catacombs, trashing to gain Procession on deck.
- Trash Procession, gain Catacombs, trashing to gain Develop on deck.
Play Hamlet, draw Procession, discard Copper for +1 Buy
Play Peddler, draw Develop
Play Procession on Develop:
- 1st Develop trashes Fortress, putting it in hand. Gain Band of Misfits and Develop on deck
- 2nd Develop trashes Fortress, putting it in hand. Gain Band of Misfits and Watchtower on deck
- Trash Develop, gain Procession on deck
Play Watchtower, drawing Procession, 2 Band of Misfits, Develop, Watchtower

Now consider the following sequence, which starts and ends with a hand of Procession, Band of Misfits, Band of Misfits, Develop, Fortress, Watchtower:

Play Procession on Band of Misfits, playing as Procession
- 1st Procession plays Band of Misfits, playing as Procession
-- 1st Procession plays Develop
--- 1st Develop trashes Fortress, putting it in hand. Gain Watchtower and Duchy on deck.   
--- 2nd Develop trashes Fortress, putting it in hand. Gain Duchy and Develop on deck.
--- Trash Develop, gain Procession on deck
-- 2nd Procession plays Fortress, drawing Procession and Develop.  Trash Fortress, putting it in hand.  Gain Catacombs, trashing to gain Hamlet on deck.
-- Trash the Band of Misfits, gain Goons on deck
- 2nd Procession plays Procession
-- 1st Procession plays Develop
--- 1st Develop trashes Fortress, putting it in hand. Gain Band of Misfits and Develop on deck.   
--- 2nd Develop trashes Fortress, putting it in hand. Gain Band of Misfits and Watchtower on deck.
--- Trash the Develop, gain Procession on deck
-- 2nd Procession plays Watchtower, drawing Procession, 2 Band of Misfits, Develop, Watchtower.  Trash Watchtower, gain Nomad Camp on deck.
-- Trash Procession, gain Catacombs, trashing to gain Nomad Camp on deck
- Trash Band of Misfits, gain Goons on deck

This sequence puts Watchtower, Duchy, Duchy, Hamlet, Goons, Nomad Camp, Nomad Camp, Goons on the deck (last on top), and does not disturb it otherwise.  It nets 3 actions (and 0 buys).  It also removes 2 Watchtowers, 2 Duchies, 2 Develops, 2 Processions, 2 Catacombs, 2 Nomad Camps, 2 Goons, 2 Band of Misfits, and 1 Hamlet from supply.

We play this sequence three times, except that on the third time, we replace the drawn Develop with a Watchtower.  Then:

Play Procession on Band of Misfits, playing as Procession
- 1st Procession plays Band of Misfits, playing as Procession
-- 1st Procession plays Fortress, drawing Goons and Nomad Camp.  Trash it, putting it in hand.  Gain Band of Misfits on top.
-- 2nd Procession plays Fortress, drawing Band of Misfits and Nomad Camp.  Trash it, putting it in hand.  Gain Band of Misfits on top.
-- Trash Band of Misfits, gain Goons on top.
- 2nd Procession plays Band of Misfits, playing as Procession
-- 1st Procession plays Fortress, drawing Band of Misfits and Goons.  Trash it, putting it in hand.  Gain a Catacombs, trashing and gaining Nomad Camp on top.
-- 2nd Procession plays Band of Misfits, playing as Procession
--- 1st Procession plays Fortress, drawing Nomad Camp and Goons.  Trash it, putting it in hand.  Gain a Catacombs, trashing and gaining Nomad Camp on top.
--- 2nd Procession plays Fortress, drawing Nomad Camp and Hamlet.  Trash it, putting it in hand.  There is nothing to gain.
--- Trash the Band of Misfits, gaining Goons on top.
-- Trash the Band of Misfits, gaining Goons on top.
- Trash the Band of Misfits, gaining Goons on top.

At this point we have 30 actions, more then enough to:

Play Fortress, drawing Goons.
Play 4 Goons and 3 Nomad Camps.
Play Watchtower, drawing 2 Goons, Nomad Camp, Hamlet, Duchy.
Play Hamlet, drawing Duchy, discarding 2 Duchies for +1 action, +1 buy.
Play 2 Goons, and Nomad Camp.
Play Watchtower, drawing Watchtower, 2 Goons, 2 Nomad Camps, and Hamlet.
Play Hamlet, drawing Duchy, discarding it for +1 buy.
Play 2 Goons, 2 Nomad Camps. 
Play Watchtower, drawing Duchy, Watchtower, 2 Goons, 2 Nomad Camps.
Play 2 Goons, 2 Nomad Camps. 
Play Watchtower, drawing 2 Duchies, Hamlet, Watchtower, and a Copper.
Play Hamlet, drawing Copper, discarding 2 Duchies for +1 action, +1 buy.
Play Watchtower, drawing 3 Copper.
Play 5 Coppers.

We have 10 Goons out, 25 buys, and $45. 
Thus we can buy 4 Colonies and 21 Copper, gaining 250 VP from Goons.  With 6 Duchies, this gives us 308 Victory points.  And the game ends on piles, with Goons, Catacombs, Band of Misfits, and Procession out.


Edit:  There are some minor issues.  Pointed out and fixed by CC in a later post.