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[Dingan]

I've never known if it's best to open Cultist/Copper or Cultist/-, and similarly for Witch.  I open Cultist/Copper on games like these:

http://gokosalvager.com/static/logprettifier.html?http://dominion-game-logs.s3.amazonaws.com/game_logs/20160225/log.0.1456375411518.txt
http://gokosalvager.com/static/logprettifier.html?http://dominion-game-logs.s3.amazonaws.com/game_logs/20160220/log.0.1455985486171.txt

because playing a Cultist on T4 causes a shuffle, and hence your next shuffle will miss your Cultist (and you most likely could not afford one on T3).  Then again, not opening with the Copper, and playing the Cultist on T3, would cause a shuffle at the start of T4, which I would think is generally a good thing.  Obviously, this latter situation would be ideal, but it cannot be guaranteed.  So what is better in these situations -- opening Cultist/-, and hoping for the best?  If you opened Cultist/-, and draw the Cultist on T4, would you just not play it that turn?

Same would go for Witch instead of Cultist, or any other $5 card that draws +2 (I can't think of any others -- are there?).

Seems like this might a good question for the simulators.

EDIT: Vault.  But maybe because it's not a powerful junker, I would never open with the Copper.

[wachsmuth]

Same would go for Witch instead of Cultist, or any other $5 card that draws +2 (I can't think of any others -- are there?).

Ghost Ship, Sir Destry, Laboratory and Lost City. Hunting Party, Tribute and Wharf could be argued to belong here, but probably don't.

[Dingan]

Same would go for Witch instead of Cultist, or any other $5 card that draws +2 (I can't think of any others -- are there?).

Ghost Ship, Sir Destry, Laboratory and Lost City. Hunting Party, Tribute and Wharf could be argued to belong here, but probably don't.

Oh man, duh.  My brain hurts this morning.  I guess the question remains for each of these: would you open with a Copper (provided there are no good $2 cards), to decrease the probability of them missing the second reshuffle?

I would definitely not open with the Copper on any of those except maybe Ghost Ship.  But even then, probably not.

[liopoil]

I think copper is rarely the right call here. The odds of it missing the reshuffle go from 6/11 to 1/6, which is nice, but you lose a 5/11 chance of a really nice second shuffle and actually increase the chance of not getting it until T5, which is even worse. Most importantly, though, you are putting another bad card in your deck! If there's a crummy 2-cost I might pick it up where I would otherwise pass, however.

[dedicateddan]

Let's look at the shuffles on turns 3-4 for Witch/- versus Witch/Copper

Witch/-
AAAAA/BBBBB/C

(5/11): Play witch on turn 3. Draw 4 cards, trigger a shuffle, draw a card (1/8 chance of drawing witch again) - Great!
(5/11): Play witch, draw a card, shuffle 6 cards into deck, draw again - Slightly below average
(1/11): Witch misses shuffle - Ouch!

Witch/Copper
AAAAA/BBBBB/CC
(5/12): Play witch - Average
(5/12): Play witch - Average
(2/12): Witch misses shuffle - Ouch!

For a Witch/- opening, (5 card hand + 5 card hand + witch = 12 cards drawn with an 11 card deck) which triggers a shuffle early. The cards drawn on turn 3 are likely to be drawn again on turn 5. This means that drawing witch in the first 5 cards is great, drawing in then second 5 is OK, and drawing the witch as the 11th card is terrible.

For Witch/Copper, there's a 10/12 chance of a full shuffle at the start of turn 5 and a 2/12 chance of the witch missing the shuffle.

In conclusion, Witch/- seems better than Witch/Copper overall, and having witch in the top 5 cards of the shuffle is a big boost.

[DG]

Simulator says for both witch and cultist it is about 54%:43% in favour of not buying copper.

Last time it was discussed, all tests and simulations suggested that almost none of the possible openings with copper were anything other than detrimental.