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[Davio]

You're strolling around your Dominion(r)(c)(tm) when you're noticing the peasants have organized a little Tournament in one of your Provinces. And look, they've pooled their money to buy some Prizes to give to the winners: An old crooked but Trusty Steed, a shiny fake Copper Diadem, a Bag of Gold-painted coins, a working girl called Princess and a travelling band called the Followers.

Aggrevated that they're not plowing the fields or paying taxes you've decided to teach them a lesson; you're going to dress as a common man, participate in their tourney and snag all the prizes. However, you have better things to do, like counting your Gold, so you'll want to make it quick. As quick as possible.

1) Easy mode: With divine intervention (perfect shuffle luck), what's the quickest way to snag all 5 Prizes?
2) Hard mode: With rotten shuffle luck, what's the quickest way to snag all 5 Prizes?

Assume a solitaire game for simplicity's sake.

[Captain_Frisk]

Easy Mode: 6 turns

T1 - Ironworks
T2 - Chancy
T3 - IW / Chancy / 3 Copper
Play Ironworks -> Gain Tournament
Play Chancy (Reshuffle)
Buy Cache(!!!!)
T4 - IW, Tournament, Cache, Chancy, Copper | Copper on top of deck
Play IW -> Gain Tournament
Play Tournament - Draw Copper
Play Chancy
Buy Province ($1 from tournament, $2 from Chancy, $3 from Cache, $2 Copper)
T5 - Tournament x2, Province, Ironworks, Chancy
Play Tournament (Reveal Province) - Gain Trusty Steed (Prize #1)
Play Trusty Steed (+2 Actions +4 Silvers) - deck reshuffles
Play Ironworks (gain great hall) - draw province!
Play Tournament Again -> Gain Princess (Prize #2)
Play Chancy (Reshuffle)
Buy Throne Room, Tournament
T6 - Province, Trusty Steed, Chancy, Tournament, Throne Room | Tournament, Tournament, IronWorks, Great Hall
Play Tournament (Gain Prize Followers (Prize #3)
Play Throne Room (Trusty Steed)
Trusty Steed 1 (+2 cards , 2 actions) (draw tournament x2)
Trusty Steed 2 (+2 cards, +4 cards )  (draw Ironworks + Great Hall)
(2 actions)
Play Ironworks (Gain Great Hall) - Draw Province
Play Tournament (Gain Prize #4)
(Still 2 actions)
Play Chancy - reshuffle
(1 action remaining)
Play Great Hall - Draw Province
Play Tournament - gain prize #5!

Rejoice - at having driven another player from Dominion.

[Tables]

That hard one is going to be very, very hard to solve... but I'll set an upper bound at 16 turns.


T1/2: Buy Chapel, Tournament
T3/4: Buy Lighthouse, Chapel 4 coppers
-Now we have 9 cards in deck. We want to trim our deck as fast as possible, which unfortunately means foregoing a Silver here (as the worst drawing is 3E/2C, 4C/Chap, and Tournament can be in the chapel hand or miss the reshuffle, it doesn't matter).

T5: Draw Chapel, 3C/LH, play LH, trash 1 Copper, buy Silver
-Alternatively, we could draw the Chapel with some Estates. I'm reasonably confident in saying that would be faster (so it doesn't happen).
Deck: 3 Copper, 1 Silver, 1 Lighthouse (in play), 3 Estates, 1 Chapel, 1 Tournament

T6: Draw 3E/Tournament/(shuffle)Copper/(Tournament)Copper. Play Tournament, have 5, buy Mining Village
-We need extra money to hit that province, and Mining Village will be 2 moneys later. Again, we had to reach 4 here (Lighthouse, Tournament (if that was last turn we'd have trashed an extra copper plus having it this shuffle), +2 money cards or 1 and chapel (and chapel with the estates is again great)), so I'm happy this is about the worst we can do.
Deck: 3 Copper, 1 Silver, 1 Lighthouse, 3 Estates, 1 Chapel, 1 Tournament, 1 Mining Village

T7: 1 Chapel, 1 Silver, 1 Copper, (Shuffle) 1 Lighthouse, 1 Mining Village. Play MV, draw Copper. Play Lighthouse, Trash 2 copper, buy Nothing
- Clearing our deck some more.
Deck: 1 Copper, 1 Silver, 1 Lighthouse (in play), 3 Estates, 1 Chapel, 1 Tournament, 1 Mining Village

T8: 1 Copper, 3 Estates, 1 Tournament. Play tournament (shuffle), draw MV, play that, draw Silver. Buy MV.
-With Silver (2), Tournament (1), MVx2 (4) and Lighthouse (1), we have the required money. We just need to clean the rest of our deck a little more.
Deck: 1 Copper, 1 Silver, 1 Lighthouse, 3 Estates, 1 Chapel, 1 Tournament, 2 Mining Village

T9: Chapel (shuffle), Silver, Lighthouse, Copper, Estate. Trash Copper, Estate, play Lighthouse, buy nothing
-The deck can't stop us trashing Estates forever. Now it has to bite the bullet and we get them out of the way.
Deck: 1 Silver, 1 Lighthouse (in play), 2 Estates, 1 Chapel, 1 Tournament, 2 Mining Village

T10: Estate, Estate, Tournament, 2 MV. Play MV, MV, trashing both, play Tournament. Draw Chapel, Silver. trash Estates. Buy Province
-And we clean the deck up. With our deck being so small even if the MV's missed the shuffle (were drawn on turn 9) we'd still draw them again here and get our Province.
Deck: 1 Silver, 1 Lighthouse, 1 Chapel, 1 Tournament, 1 Province

T11: Draw deck. Play tournament, gain Trusty Steed. Play Lighthouse, play TS, Coin & action. Trash Silver. Buy Tournament
-Final Consolidation. We have 4 again for another tournament (and we're now going to hit twice, of course).
Deck: 1 Lighthouse (in play), 1 Chapel, 2 Tournament, 1 Province, 1 Trusty Steed

T12: Draw deck. Tournament for Followers, Trusty Steed for Action & Cards, Tournament for Bag of Gold.
-3 Prizes down
Deck: 1 Lighthouse, 1 Chapel, 2 Tournament, 1 Province, 1 Trusty Steed, 1 Followers, 1 Bag of Gold

T13: Draw Chapel, Bag of Gold, Tournament, Tournament, Followers. Do nothing.

T14: Draw Province, Trusty Steed, Lighthouse, (shuffle) Chapel, Bag of Gold. Trusty Steed for Card+Actions, draw Tournament+Tournament. Tournament for Diadem. Trash Lighthouse.
-Unfortunately, we can't guarantee we get to the province again with another Tournament to play.
Deck: 1 Chapel, 2 Tournament, 1 Province, 1 Trusty Steed, 1 Followers, 1 Bag of Gold, 1 Diadem

T15: Draw Followers, Tournament (shuffle), Tournament, Bag of Gold, Diadem. Do nothing.
-It should be noted, TS can't be in this hand, or we can draw our deck with it+Followers.

T16: Draw Trusty Steed, Province, Chapel (shuffle), Bag of Gold, Diadem. Play Trusty Steed for cards+actions, definitely draw a tournament, play it for Princess. Buy a victory copper.

If you're okay with trashing prizes, I think you can change what you do from about turn 13, and cut about 2 turns off this solution. Also, as with any 'worst luck' solution I've made a number of assumptions, many of with are hard to justify. In particular regarding chaple hands and getting certain amounts to make buys.

And there's probably a mistake somewhere anyway...

[Deadlock39]

I think your worst luck scenario has to be your Chapel ending up on Turn 5.  If you look up the Lucky Chancellor problem, there is some good discussion and strategy for quick Chapel-ing with worst case shuffle luck.

[Captain_Frisk]

I think your worst luck scenario has to be your Chapel ending up on Turn 5.  If you look up the Lucky Chancellor problem, there is some good discussion and strategy for quick Chapel-ing with worst case shuffle luck.

I also assumed that the Hard mode solution was going to share alot in common with the lucky chancellor problem.