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[Kirian]

You are participating in a modified Swiss-style Dominion tournament.  It sounded really great until you realized that the organizers aren't particularly good.  They're using 4-player tables instead of 2-player tables, and so the Swiss system breaks down near the end of the tournament, allowing players who have previously played against one another to play again against each other; seating is random within the seeded tables, rather than being determined by prior number of losses; and, worst of all, seeding and winning is being partially determined by placement order rather than simple win-loss, such that a win is counted as 4 points, second place as 3, etc..

In the final round, the current tournament score has the top four players at your table; the top three players are tied with 23 tournament points, while you have 22.  But you've been seated at the fourth position at the table, not an enviable seat given the board for this round, and you are losing miserably, with a deck clogged with Curses, thanks in part to shuffle luck.  Nonetheless, you're giving things the old college try and counting cards and scores as you usually would.  Near the end of the game--with Curses and another pile empty, and several thin piles--on your turn, the first player sits at 37 points, the second player at 33, the third at 28, and you have a total of 12 points.  In other words, you're not going to win this game, much less the tournament.

You begin your turn holding two Curses and three different actions.  By the time you play your third action, you have drawn a fourth action, but no other actions or money.  While in the midst of playing this third action, you find yourself in a unique position.  You realize that, while you can't place in the tournament, you can, by playing the last useful card in hand, determine the order in which the other players will finish and end the game.  Before finishing this third action, you realize you have, in fact three choices:  (1) not play the last card and end your turn, gaining nothing, and let the other players fight things out; (2) play the card, gain 2 points for yourself, and let the other players fight things out; or (3) play Kingmaker, getting 4 points for your effort, determining how the others place.  Your ability to do these is certain knowledge, not just a possibility (you happen to be very fast with math to do this, though).

If the other players have been paying attention at all, they will realize you've played Kingmaker, and will have no clue that you could if you decide not to.  There is a small amount of cash on the line: $50 to 1st place, $25 to second, and your opponents are acquaintances but not really friends.  Your task is to answer the following:

(1) What actions you did play this turn?
(2) What cards must be available?  ("Any other $5 card" is an acceptable answer)
(3) What other cards are in your deck?
(4) If you decide to be Kingmaker, how can you do it?

(5) Bonus ethics question:  Are you willing to be a bit dirty?  Why or why not?  And at a meta-ethical game theory level, is your choice "proper" gameplay?  And is *any* choice proper gameplay?

There are likely several solutions.  Good luck!

[timchen]

Some points need clarification:

(1) so before I play the third action, I already draw the fourth? in the choices you mention "the card" and "Kingmaker", is "the card" the third action, and "Kingmaker" the fourth action?

(2) Is getting 4 points a necessary consequence of playing the Kingmaker, and independent of the order you decide, or is it such that you can choose not to get the points and still decide who wins?

(3) Does your ability to decide the order depend on other players' reasonable choice? Say you play a masquerade

With these questions aside, the only plausible answer I can think of right now is
You drew a Colony, a Province, and a Duchy in hand. You may have used a Hamlet to discard a curse, menagerie to draw three. The last action is Expand and you draw Golem. The only 2 other actions in your deck is Bishop and Ambassador. If you play Expand you can trash a curse and gain an estate. There is only one Colony left in supply, 2 Provinces, and 3 Duchies. If you play Golem, you can choose to reveal any victory card in hand and not returning it; each will end the game and have different player on top since the 28 player sits next to you and the 33 player sits facing you. You can trash the Expand under Bishop for 4 points.
 

[Davio]

I was thinking something along the lines of:

Kingmaking (captures most answers in one block):

Positions: You (12) - South, (28) - West, (33) - North, (37) - East

In your hand: Drawing Village (Normal, Walled, Bazaar, etc), Lab, Ambassador

Top 3 cards on deck: Colony, Province, Baron

For east to win:
Play Village, Lab.
Gain last Estate with Baron.

For west to win:
Play Village, Lab
You play Ambassador, reveal Colony, but do not return it to the supply.
There is only 1 Colony left and west gets it.

For north to win:
Do the same
You play Ambassador, reveal your Colony and return it to the supply.
Both east and north gain a Colony (pile is empty now), north has more points (43) and wins.

A lot of cards can be swapped for others, like Lab for Smithy, Alchemist, Ghost Ship, Torturer, etc..
The village could just as well be a Hamlet for instance.
Baron could be any +2$ action card.

The key card is Ambassador and the key action is you deciding whether to return a Colony to the supply.


Would I do it? No, I'd just try to achieve the best possible result for myself.

[Kirian]

(1) so before I play the third action, I already draw the fourth? in the choices you mention "the card" and "Kingmaker", is "the card" the third action, and "Kingmaker" the fourth action?

At the time you play action 3, action 4 is in hand.  The Kingmaker card is action 4, but you know before you finish playing action 3 that you can use the fourth action for the Kingmaker.

(2) Is getting 4 points a necessary consequence of playing the Kingmaker, and independent of the order you decide, or is it such that you can choose not to get the points and still decide who wins?

Neither point gain is absolutely necessary, just the best you can do for your own score.

(3) Does your ability to decide the order depend on other players' reasonable choice? Say you play a masquerade

Not in my personal solution, but I can at least imagine solutions where it might happen.  However, remember that you have certain knowledge that you can force any place order; if the other players have too many choices, you might not be able to force the order.

----

Note:  I thought I'd written in here that this is a non-Colony game, but it appears I didn't.  There may be further answers in Colony games, but I see no reason to actually restrict it.

For both answers given so far, and I'll leave my response un-spoilered to clarify:  both your answers allow you to determine the winner but not the order of placement.  In other words, you can place the other players in any order you want, 1st, 2nd, 3rd, not just determine the winner.

Davio:  Your players are in the wrong order.  With you as South, West has 37, North has 33, and East has 28.

[Davio]

Oh, I thought picking the spots was part of the puzzle and we could decide for ourselves.

"The first player sits with 37 points."

I thought "first" referred to the fact that he is in the lead, not his position at the table. 

[WanderingWinder]

I don't really have the time to solve this all the way, but...
Something where you cutpurse to see opponents' hands, then use possession and/or masq would be pretty neat

[timchen]

At the time you play action 3, action 4 is in hand.  The Kingmaker card is action 4, but you know before you finish playing action 3 that you can use the fourth action for the Kingmaker.

Sorry I am confused. So you mean you have played action 3 in all the cases you mentioned? Then in your choices, how is "the card" differ from "Kingmaker"? (Since you can choose not to play "the card", it is not action 3. Are you implying you can also play the "Kingmaker" but choose not to end the game?)

[Kirian]

At the time you play action 3, action 4 is in hand.  The Kingmaker card is action 4, but you know before you finish playing action 3 that you can use the fourth action for the Kingmaker.

Sorry I am confused. So you mean you have played action 3 in all the cases you mentioned? Then in your choices, how is "the card" differ from "Kingmaker"? (Since you can choose not to play "the card", it is not action 3. Are you implying you can also play the "Kingmaker" but choose not to end the game?)

Yes, in all cases you definitely play three actions:

Play Actions 1 and 2.  You draw Action 4 with one of these actions.
Play Action 3.  While resolving Action 3, you come to the realization that you can:

A.  Ignore Action 4, in which case your resolution of Action 3 doesn't matter;
B.  Resolve Action 3 such that using Action 4 doesn't make you Kingmaker, you gain 2 points if you wish, and the game continues, or;
C.  Resolve Action 3 such that using Action 4 makes you Kingmaker, and you gain, I now realize, 6 points if you wish.  This choice ends the game.

You then resolve Action 3, and play Action 4 or not, depending on your choice.

----

Some of the correct cards have come up so far but, interestingly, not the key card.

[Razzishi]

I'm pretty sure the key card is Swindler but I really need to go to bed and can't work out the details.

[eggnoir]

This will allow you to play kingmaker and gain 6 points, or ignore action 4 and do nothing, but not stay neutral and gain 2:

Some assumptions: Each opponent has 2 Provinces. Opponent 1 has one Duchy, Opponent 2 has five Duchies, and Opponent 3 has six Duchies (and two curses). All other VP's have come from VP tokens. There are 3 Provinces left, and the Duchy pile is the other empty pile. The kingdom cards are Peddler, Fairgrounds, Duke, Rabble, King's Court, Throne Room, Swindler, Bishop, Witch and Village.
1. Play Throne Room.
2. Use it to play King's Court.
3. Use it to play Rabble. After drawing a lot of nothing and a Swindler, each opponent ends up with a Duchy and 2 Provinces on top of their deck, in any order.
I have no actions left. However, I can now either opt to not play the Swindler using King's Court, and do nothing, or:
4. Use King's Court to play Swindler. Then, I turn all Duchies into Rabbles/Witches, and all Provinces into Peddlers, except where otherwise stated. The final scores are shown in player order (not including myself) after each combination:

1,2,3 - Each player gets 1 province (28, 24, 19)
1,3,2 - P1 gets 2 provinces, P3 gets 1 province and a duke (34, 18, 24)
2,1,3 - P2 gets 2 provinces and a duke, P1 gets 1 province (28, 34, 13)
2,3,1 - P2 gets 2 provinces and a duke, P3 gets 1 province and a duke (22, 34, 24)
3,1,2 - P3 gets 2 provinces and a duke, P1 gets 1 province (28, 18, 29)
3,2,1 - P3 gets 2 provinces and a duke, P2 gets 1 province and a duke (22, 28, 29)

Finally, buy a fairgrounds for 6 coin, and it's worth 6 VP because I cleverly bought 1 of every kingdom card and treasure during the game (no wonder I am in last place). Note that in 1 of these outcomes, this will place you higher than opponent 3, and in another 2 outcomes, you will be tied for 3rd place with player 2.

Yes, it's not perfect but it is satisfying enough for me. Very interesting puzzle!

[Razzishi]

Your initial Hand is Curse, Curse, Village, Spy, Swindler.  You play Village, Spy, drawing Remodel and Gold.  If you Remodel the Gold into a Province, you gain 6 points and end the game because there are no Provinces left.  If you Remodel a Curse into an Estate, you gain 2 points net, but this does not end the game.  The players have the following victory cards:

West: 1 Fairgrounds, 4 Province, 1 Harem, 1 Duchy - He has 24 different cards in his deck that includes a Gold, and Fairgrounds is on top.
North: 1 Fairgrounds, 3 Province, 4 Harem, 1 Estate - 19 different cards including a Gold, and Harem is on top.
East: 1 Fairgrounds, 3 Province, 2 Harem - 19 different cards and a Gold is on top.
You: 1 Province, 2 Duchy, 2 Estate, 2 Curse.

By choosing to Swindle the opponent's cards into one of Fairgrounds, Nobles, Harem, or Gold, you can make each different combination of placement possible.  There are enough of each VP card to go around still, and they can finish with the following number of points, depending on whether they you give them a Fairgrounds, Nobles, Harem, or Gold:

West: 37, 33, 31, 29
North: 37, 35, 33, 31
East: 34, 32, 30, 28

The needed cards in supply are Harem, Nobles, Black Market, Village, Spy, Swindler, and Remodel.  The rest of the curses were trashed, and the empty pile is irrelevant. 

Edit: You gained the curses because your copper got Swindled. Every else either didn't get Curses because they were nice and gave each other back Copper.

Edit 2: There might be a way to get it to work that doesn't require Black Market, as I fear that it wouldn't actually be played in a tournament setting.  I feel as though the Swindling into a Fairgrounds, Nobles, Harem, or Gold is good enough, but didn't want to work out if I can do it with Fairgrounds not being worth as much.  I'll see what I can do with multiple Fairgrounds per deck; I just wanted to get the general idea posted before seeing if I could do it without Black Market.

[Razzishi]

This will allow you to play kingmaker and gain 6 points, or ignore action 4 and do nothing, but not stay neutral and gain 2:

Buying a Harem or Nobles with your 6 could do that, but I suppose it's still not an action as specified.

[Razzishi]

Revised solution that doesn't need Black Market to pump up Fairgrounds:

Same starting hand and actions as previous solution.

All players have at least 1 Gold, 1 Copper, 1 Silver, and 1 each of the 7 non-VP Kingdom cards, and East has at least 2 Gold.

West: 3 Fairgrounds, 3 Province, 1 Harem, 1 Nobles, 3 Curse - 15 unique cards - Harem on top.
North: 2 Fairgrounds, 3 Province, 3 Harem, 1 Estate - 14 unique cards - Harem on top.
East: 3 Fairgrounds, 3 Province, 1 Harem, 4 Curse - 14 unique cards - Gold on top.
You: 2 Province, 2 Estate, 2 Curse

There are enough Fairgrounds, Nobles and Harems left to go around without emptying them, and there's 1 Province left.  Possible finishes, when given Nobles, Fairgrounds, Harem, or Gold off Swindler:

West: 31, 33, 37, 29
North: 37, 35, 33, 31
East: 36, 32, 30, 28

Verifying that all orders are possible: WNE: 37, 33, 28; WEN: 37, 36, 35; ENW: 36, 35, 31; EWN: 36, 33, 31; NEW: 37, 36, 33; NWE: 37, 33, 28



edit: Numbers updated

edit: If I need to justify the whole "my deck is clogged with Curses", add some Duchies and Curses to my player's deck.  The Curses could have all come from buying Copper and getting it Swindled, and if you had most of your starting Copper Swindled early on preventing you from getting many Silvers, buying Copper is not totally unreasonable.

edit: cards needed:Swindler, Harem, Nobles, Fairgrounds; cards that are interchangable: An Expand, Forge or Remodel; a Spy or Scrying Pool; a +2 action card; Among the last two sets, you need a way of putting into your hand one of the first set and the necessary cards to either gain 2 points or 6 - there are many possibilities.