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[timchen]

Suppose you have a deck consisting of 12 coppers, 12 estates, 12 islands and 12 curses. They are all in the draw pile.

You have the freedom to choose what is in your hand and you start with 1 action. No Throne Room, King's court, or Tribute. No supply constraints. (Yes, you can have 12 council rooms in hand but that only draws 4.)

Now the question is:
(1) for the best possible luck you can have, how many cards do you need to draw the entire deck? My best answer is 3
(2) for the worst possible luck, how many cards do you need to guarantee you can draw the whole deck? My best answer is 11

For example, if we have a hand with Labs then both answer will be 24.

[O]

Perfect shuffle luck solution
1) Scrying Pool- Draw 12 Islands and an Estate
2) Crossroads-Draw the remaining estates
3) Crossroads

[chester]

#2: 5 cards Apprenticex2, Colonyx2, Cellar

[timchen]

Sorry I should clarify. You have to draw them all in hand. If you discard some of them, you have to redraw them.

On the other hand I forgot about apprentice. So the worst luck number would be 10 I suppose. How about in a game without Colony?

[ftl]

Hey, I thought the Cellar was clever :-p

With Apprentice, you can get them all in hand starting from 8.


3x(Apprentice + colony) draws 33,
Of these, 9 must be VP cards, if the first 24 were coppers/curses, so play crossroads to draw 9 (which are all green cards) and then one more crossroads to draw the rest.

So a hand of 3x apprentice, 3x colony, 2x crossroads draws everything.

[Captain_Frisk]

Perfect shuffle luck solution
1) Scrying Pool- Draw 12 Islands and an Estate
2) Crossroads-Draw the remaining estates
3) Crossroads

With no supply constraints couldn't i just define my hand to be:

CrossRoads + 48 Duchies

[O]

Perfect shuffle luck solution
1) Scrying Pool- Draw 12 Islands and an Estate
2) Crossroads-Draw the remaining estates
3) Crossroads

With no supply constraints couldn't i just define my hand to be:

CrossRoads + 48 Duchies

Yes.. but that requires 49 cards. The puzzle is cards-in-hand, not cards played

[timchen]

This best-of-both-worlds trick is clever. I was wrong to say 10. Still, what if Colony/platinum is not available?

[Deadlock39]

<ninja'd>
I get worst case with Apprentice at 8.

Apprentice 3 Colonies, drawing 12 Coppers, 12 Curses, and 9 of the VP cards.
Play Crossroads twice to draw the rest.
</ninja'd>

Without Colony, you can do the same thing using 4 Apprentices and 4 Provinces for a total of 10 cards.

I can't find your solution without Apprentice.  Crossroads, Chancellor, Counting House can get you the Coppers.  We still have to draw 12 Curses before we can draw any VP cards to exploit Crossroads, and already used its extra actions, so that messes with things.   Farming Village is guaranteed to draw an Island once we have the Coppers, but I haven't found a good way to exploit that.

[Tables]

Worst case scenario with 7. I think. It was a little tough to think through .

Short version:
Apprentice two Colonies, then play a Cellar on the non-victory cards, then play two Crossroads. The deck can't stop us getting enough victory cards for the second crossroads to draw everything.

Details:
Apprentice*Colony (draw 11)
Apprentice*Colony (drawn 22)

Now it gets complicated. We're going to play Cellar and discard all of our non-victory cards. At worst, this leaves us with 10 victory cards (discard 12 Non, draw 12 Non). If it leaves us with 13, we're done (the next two actions are Crossroads, Crossroads, drawing 26 cards which is everything). It will definitely leave us with 13 if we had anywhere above or equal to 13 Victory at the start (tautologically), or 7 or less (as we will discard 15 Non, drawing 15, which must include at least 6 Victory).

So we have 5 annoying cases, where we started with 8-12 victory cards. Fortunately we can solve them all the same way. We Cellar away our 10-14 non-Victory cards, and draw 6-12 non-Victory cards (and 0-6 victory cards). More to the point, the rest of our deck is at least 10 victory cards! We Crossroads, with at least 10 Victory cards in hand, drawing those victory cards, then play the other crossroads to comfortably finish off everything.

I'm pretty sure this will be much harder to make work if Colony isn't available. The lost 6 cards from having to use Provinces make a big big difference to this strategy (Ending up with only 16 cards drawn means you can only guarantee 4 victory cards in hand... obviously not enough.

Of course, it suggests an easy solution with 9, by adding an extra Apprentice+Province at the start.

[ftl]

You can't use Farming Village for anything. The worst-case shuffle luck is that it discards nothing for you and just draws one card off the top, which is an estate or island. I don't think that's enough to be useful.



Here's an attempt without apprentice:

Crossroads, Chancellor, Counting house. Draw 12 coppers. Back to 1 action remaining.
3xcity to draw 6 cards, and trigger a shuffle. 4 actions remaining. Hand has 12 coppers and 6 either curses or VP.
1x cellar, discarding all coppers and curses (at least 12, up to 18), drawing replacements. After that, you are guaranteed to have 6  VP in hand, and at most 12 curses. The 12 copper are in the discard.
1x crossroads, draw 6. You have at least 12 VP.
1x crossroads, draw the remaining 12 vp in the deck.
1x crossroads, trigger the reshuffle and draw the remaining coppers and curses.

Total: 4x crossroads, 3x city, 1xcellar, chancellor, counting house. 10 cards.

[timchen]

It's better than my solution! I didn't include the use of crossroad to draw cards. My 11-card solution just uses Counting House and cellar multiple times to draw all the cards. 3 cellars+4 counting houses+1 chancellor=8, and 1 crossroad and 2 villages to play them.

[chester]

Of course, it suggests an easy solution with 9, by adding an extra Apprentice+Province at the start.

I think you can get no-colony down to 8 with Apprenticex2, Provincex2, Cellar, Crossroadx3

If your first 16-card hand has at least 4 victory cards, play Cross, Cellar, Cross, Cross.  With three or fewer victories, start with cellar, then play all three crosses. 


Edit: No that doesn't work on the 12/4 split; you only draw 44 cards total

[dghunter79]

6 No Colony

Crossroads, Crossroads, Golem, Scrying Pool, University, University

Play University, gain Counting House
Play Golem; reveal Counting House; play Counting House; put 12 coppers in hand. All other cards are now in discard.
Play University; gain Inn; move 12 Islands, 1 Inn from discard to draw deck.
Play Scrying Pool; draw 12 Islands, 1 Inn, 1 curse.
Play Crossroads; reveal 12 Islands; draw 11 curses, 1 estate.
Play Crossroads, reveal 12 Islands, 1 estate, gain 11 estates.

[timchen]

Interesting idea but a slight flaw there:
Island will be hit by the Golem. At least it is inconsistent to assume it won't be hit and at the same time can be brought back by inn...

[chester]

Interesting idea but a slight flaw there:
Island will be hit by the Golem. At least it is inconsistent to assume it won't be hit and at the same time can be brought back by inn...

Building on this idea:

Village, Chancellor, University (gain inn -> shuffle islands), Scrying pool, Crossroads x3 is still 7 cards.

[dghunter79]

Interesting idea but a slight flaw there:
Island will be hit by the Golem. At least it is inconsistent to assume it won't be hit and at the same time can be brought back by inn...

You're right.  Darn.

Building on this idea:

Village, Chancellor, University (gain inn -> shuffle islands), Scrying pool, Crossroads x3 is still 7 cards.

Yeah, that's what I started with.  Alternatively, use Trusty Steed in place of the Village and Chancellor, but then the 4 Silvers give you three more cards than three Crossroads can reliably grab.  Even using the Inn to trade out two Silvers leaves one pesky card.  (I guess that's why Trusty Steed gives you four Silvers.)  I needed either a fourth Crossroads or a Watchtower to close, and that puts me back up at 7.

[dghunter79]

Building on this idea:

Village, Chancellor, University (gain inn -> shuffle islands), Scrying pool, Crossroads x3 is still 7 cards.
[/quote]

Replace the first Village, to start with these 6: University, Chancellor, University, Scrying Pool, Crossroads, Crossroads.  Play the first University and gain a Crossroads.  Then Chancellor. University for the Inn, shuffle in the Islands, Inn, and Crossroads.  Scrying Pool to draw the Islands, Inn, and Crossroads.  Play three Crossroads to draw the deck.  That's not that elegant, but it's 6 cards.

[timchen]

I think it's clever.