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1

Puzzles and Challenges / The Dominion Number

« on: September 16, 2012, 10:28:53 am »

We often ask challenges like this: Maximize/minimize n such that there is a kingdom k such that P(k,n).

This is a question of the form: Maximize/minimize n such that for all kingdoms k we have P(k,n).

As remarked by Donald, one of the most obvious choice for P is "A solo player in kingdom k can gain all Provinces in n turns."

Therefore, I ask: What is the minimal n such that a solo player can guarantee gaining all Provinces in n turns no matter what the kingdom?

This minimal n could be called "The Dominion Number" akin to God's Number for Rubik's Cube.

Clarifications:

• The shuffling is random.
• Extra turns like Outpost and Possession turns do not count (but I doubt it matters for the solution).
• Any Black Market deck is allowed (but I also doubt it matters).

2

Dominion General Discussion / Re: Greatest Isotropic Moments of 2011

« on: September 05, 2012, 05:02:39 pm »

@theory: Maybe the community can help you with finalizing the post? I'd love to see it.

3

Puzzles and Challenges / How often can you play the same card (physically the same) in one turn?

« on: September 05, 2012, 04:26:07 pm »

The goal of this challenge is to play the same card multiple times in the same turn.
Here "the same card" means physically the same card, not multiple cards with the same name.

Possession and Outpost turns count as separate turns.

For example, in Base Dominion, every card can be played at most 2 times (by TR'ing it).
But in general it's possible that played cards are moved from the play area to other locations and then be played again later.

1) Which cards can be played more than 3 times? (3 is trivial due to KC.)

2) Give a turn in which one card is played as often as possible.

4

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

« on: September 05, 2012, 04:04:52 pm »

I think jomini's answer summarizes all the available strategy kernels.

Regarding super-linear strategies, I think we can show that they do not exist.
The basic idea is to show that there is an upper bound on the number of cards that can be played during a turn (*) and thus an upper bound on the number of VP tokens that can be gained in a single turn. That yields a linear bound.

(*) This assumes that possessed turns count as separate turns. Otherwise, it's easy to have infinite turns.
Even so, it's not easy to prove. For example, there are a few ways to play the same card multiple times (e.g., Feast with Graverobber), but I assume no way to go on indefinitely.

5

Rules Questions / Why does the text on Madman say "If you do"?

« on: September 02, 2012, 01:08:57 pm »

Is there any situation, where one plays Madman and does not return the card to the Madman pile?

6

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

« on: September 02, 2012, 12:33:05 pm »

I'm interested in strategies that amass VPs indefinitely without ending the game.

To be precise, the challenge is to give a game state and, starting from that state, an infinite sequence of turns that increase the player's VP count indefinitely.

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?

Example: empty deck, empty discard, 2 KC and 3 Monument in hand; play KC, KC, Mon, Mon, Mon, do not buy anything. This collects 9n VP in n turns.

Counter-example: the Golden Deck (Bishop, Province, 3 Gold) does not work. It involves trashing and will eventually empty piles and end the game.