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[Chris is me]

You can't compare combos directly in a vacuum if they can be accelerated by adding other cards, so evaluating "relative strengths" becomes difficult.

You totally CAN do this, and quite easily in fact. It's just a question of how valuable it is to do so and what the resulting information means.

There's still a lot to dispute and a lot to measure analyzing these strategies in a vacuum - but at least in theory most of this can be simulated, so getting these results is a lot easier than getting other, more actually useful results.

[tim17]

You can't compare combos directly in a vacuum if they can be accelerated by adding other cards, so evaluating "relative strengths" becomes difficult.

You totally CAN do this, and quite easily in fact. It's just a question of how valuable it is to do so and what the resulting information means.

There's still a lot to dispute and a lot to measure analyzing these strategies in a vacuum - but at least in theory most of this can be simulated, so getting these results is a lot easier than getting other, more actually useful results.

Yes, in fact the goal of this exercise is to attempt to do this.  There are obviously shortcomings to this idea.  Of course there could be other cards that could help or hinder these combos.  Of course there may be attacks or other cards present that could interrupt the combo.  There are other shortcomings as well.  My hope is that, if say one were to evaluate a board with fool's gold, wharf, and forum, one might be able to start by saying wharf fool's gold is better than forum fool's gold, and then from there figure out whether parts of the two strategies could be combined, or whether there are other cards/events/landmarks that might help or hinder one versus the other.

You may believe that the benefit of having such a "vacuum" ranking is marginal at best, and you're probably right.  I personally find the question interesting and tractable enough to explore it.  If you disagree, feel free to spend your time focusing on more useful questions or approaches.

[tim17]

I’m pretty sure very few people still have any interest in this thread, but I have for whatever reason continued to look at things, and I’ll likely stop soon, so I decided to talk about what I’ve found in case anyone else ever wants to look more at it. 

After having looked at a bunch of combos (again with no simulator data, so my results are not really substantiated), I’ve come up with the list currently in the OP.  I’ve gotten other combo suggestions, but none that seem like they would place particularly high on the list.  My rankings are based on playing combos against each other head to head IRL, attempting to get a sense of which one wins the majority of the time based more on feel than a large sample size (again, not rigorous by any means).  Since the 3-4/4-3 start happens 5/6 of the time, I didn’t look at what happens on a 5-2, so that also introduces some error (though perhaps not too much).  I wanted to do some sort of summary; initially I considered writing up something about each combo, but I don’t really like the idea of going through all of the mediocre combos that are just barely better than straight money.  Instead, I think I’ll just talk about the better combos on the list, and maybe hit a few bullet points mentioning any other surprising results.  I’ll do this the less climactic way of starting at the top and working my way down.  I’ve included some descriptions of how I was playing the combos, but I’m not sure how close to optimal my approaches were.  I’ll separate each one into a different post.

[tim17]

1. Counting House/Travelling Fair

After having seen this combo in action previously, I wasn't surprised to see it at the top of the list.  On the first shuffle, I’d buy tf topdecking as many coppers as possible each turn, hoping to hit 5 before the first reshuffle.  It turns out that this only fails if you get 4 the first 3 turns, which I believe happens with probability 1/6 here.  Additionally, you want to avoid the counting house coming up in the first hand of the second shuffle.  The probability of either of these bad events happening is still below 50% I believe, and if neither of them happen, you should be able to topdeck ch’s and coppers to avoid a second reshuffle.  If this all works out, the combo reaches 4 provinces in roughly 9 turns and 8 provinces in roughly 11 turns.  It beats the other top strategies simply because more than half the time neither of the bad events happen, and assuming they don’t, it’s just too fast for anything else to compete with.

[tim17]

2. Ferry/Rebuild

This one was suggested earlier in this thread and ended up obviously being quite strong.  There’s nothing too subtle about it; ferry rebuild on T1, buy a rebuild T2, then grab a few more rebuilds on the next few turns, eventually adding in more estates as necessary (you likely won’t ever hit 5 to buy a duchy).  It reaches 4 provinces in 9-10 turns, and then starts stalling on green a bit, taking somewhere around 17 turns to get all 8 provinces, though it can pile the provinces in probably around 12-13 turns if it tries to mill them.  While it can sometimes be about as fast as CH/TF (when neither of the bad things happen for CH/TF), it usually loses anyway because CH/TF  has somewhat better endgame control.

[tim17]

3. Royal Carriage/Bridge

No surprise to see this here; I think most of us know roughly how this works.  Open bridge/silver and try to get a bunch of RC’s as fast as possible.  I think you do want to add in a couple more silvers and maybe another bridge or two if you fail to hit 5 or have a spare buy, but you probably don’t want the deck to get too big.  Once you have at least 6 carriages on the mat and a bridge in hand, it’s all over.  With 5 carriages you can get 3-4 provinces in a turn, but usually you try to get 6 on the mat and it ends up being all or nothing.  It appears to take around 12-13 turns to hit the megaturn, at which point it’s simply a question of whether the number of provinces/duchies you can buy will give you the lead.

[tim17]

4. Villa/Jack of all Trades

Somewhat of a surprise to see this here, though maybe it shouldn’t be, since both of these are particularly strong 4s.  Open Jack/silver, then pick up more jacks when you hit 4.  On turns when you have at least 4 dollars and a jack in hand, you’ll want to play all treasures to pick up a villa, then use your jack to draw.  Once you have a couple villas in your deck, you have the +buy to pick up several jacks at once.  This builds to a bit of a megaturn where you go through your deck, buying out most of the remaining villas, and end up with enough to buy usually 3 provinces at once, at which point the provinces slow down future turns quite a bit.  Some care needs to be taken to leave enough villas in the supply so that you can get through your deck on the megaturn, and for this reason is somewhat less viable in realistic situations when your opponent is contesting villas.  Often you’ll hit the megaturn on T8 or T9, and then pick up a 4th province on the next turn.  With all the silvers, it should still only take around 5 more turns to get the last 4 provinces, so it picks up all 8 provinces in around 15 turns.

[tim17]

5. Masterpiece/Feodum

Not too much of a surprise to see this here.  It has the advantage of not competing for provinces, so any deck that struggles to get all 8 will not do well against it.  Open Silver/Silver, picking up more silvers and masterpieces whenever you hit at least 5.  Maybe pick up a feodum on a random 4 hand, but usually don’t start taking feoda until you’re around 21 silvers.  From here, the decision to buy feodum vs masterpiece can usually be made greedily.  It reaches the 27 point threshold in 11-12 turns, and the 51 point threshold in around 15 turns.

[tim17]

6. Dungeon/Tunnel

This was probably the biggest surprise of the list for me.  Of the four combinations dungeon/warehouse + tunnel/treasure map, I would have guessed that dungeon + tunnel would be the strongest, but I did not expect it to be this much stronger.  The key is that, in order to activate tunnel, you only have to play a dungeon on this turn or last turn.  If you open dungeon/tunnel and alternate between dungeons and tunnels after that, it is likely that you’ll never fail to activate a tunnel.  Once you have 3-4 of each, you’ll start hitting 8 and buying provinces.  It gets to 4 provinces in slightly more than 10 turns on average, and then struggles with the green a bit more, taking probably around 17-18 turns to get all 8.  The added points from the tunnels means that other combos often need to win the province split in order to win.

[tim17]

7. Hermit/Market Square

I think this combo has already been looked at in considerable detail previously.  Open Hermit/Hermit, then pick up some odd number of hermits and at least 4-5 market squares while turning hermits into madmen.  The number of each of these will depend on how big of a megaturn you’ll need to win.  5 Madmen, 2 Hermits, and 4 Market Squares should be enough to hit 4 provinces (though remember that you probably trashed your estates).   Usually, you’ll want to get more like 5 or 6 market squares to have enough coin and buys to win on your megaturn.  If you need all 8 provinces, probably you’ll want something like 6 madmen, 3 hermits, and 7 market squares.  For the 4 province threshold, it takes about 11-12 turns, and around 14 turns for the 8 province threshold.

[tim17]

8. Ferry/Governor

Nothing too interesting here.  Ferry governor T1 and then pick up governors with 3, using governors mostly to gain golds early on.  Unfortunately you can’t remodel anything into more governors.  Usually you’ll build until you have around 8 governors and then have a big turn where you draw a bunch and remodel a couple golds into provinces and buy another province.  It takes around 11 turns to get to 4 provinces.  You can get all 8 in around 14 turns, though you have to build a bit more if you want to do this.  It seems to come up a little short against Hermit/Market Square partially because H/MS has better pile control, and partially because the silvers and draw from the governors can be a decent help to H/MS.

[tim17]

9. Scavenger/Stash

Again, something most of us probably knew about.  Open Scavenger/Silver, then pick up a second scavenger and stashes on subsequent turns.  Once you can play a scavenger to top deck your other scavenger, you can add more stashes, hoping your scavengers don’t collide along the way.  4 stashes is enough for full reliability with no opponent interaction, but probably it’s more optimal to stop at 2 or 3 and just start picking up provinces.  It reaches 4 provinces in 10-11 turns, and 8 provinces in 14-15 turns.  It seems to lose to Ferry/Governor partially because F/G has better control, and partially because the draw from governor can be bad if it causes scavengers to collide.

[tim17]

If you’ve actually read this far, I’m really surprised.  You also might be wondering how far into the list I’m going to go.  I’ll still go a decent bit further, though maybe in a little less detail.  In particular, the next 7 combos are all boring money/attack decks, so I won’t talk about them individually.  The most noteworthy thing I found was that Courtyard/Delve appears to beat Junker/Delve.  Delve is great with courtyard, and this deck just gets provinces before the junker manages to hurt it too much.

[tim17]

17. Crossroads/Gear

This is one of my favorite combos (and perhaps it should be a little lower on this list since my “wanting it to win” may have biased my intuition).  Still, its speed is undeniable.  Open Gear/Gear and pick up a Crossroads T3.  The idea is to set aside green and possibly a crossroads with the gears.  To start your turn, play a crossroads, hopefully to draw a decent amount, then play gears to set aside the green and maybe another crossroads if you have one and can afford to set it aside.  Pick up a gold when you hit 6 (it’s not too unlikely that this happens T4), and then pick up provinces whenever you hit 8, picking up more gears and crossroads/ when you miss.  If you have 3 crossroads and 4 gears, you should be able to set aside a crossroads and 3 green cards each turn, which is often enough to draw a deck of up to 21 cards.  The nice thing about this though is that after picking up green, the crossroads just start drawing more, so the deck can often just power through and keep drawing itself.  It manages 4 provinces in 10-12 turns, and all 8 in 16-17.  It doesn’t like junking, so it loses to the junker/money strategies.

[tim17]

18. Inheritance/Ironmonger

This is kind of boring.  Pick up ironmongers and silvers until you hit 7, at which point the inheritance makes it fairly easy to repeatedly hit 8.  If you ever miss, you often want an estate, though perhaps a duchy if it’s late enough.  It reaches 4 provinces in 11-12 turns, and all 8 in around 16 turns.

[tim17]

19. Bonfire/Jack of all Trades

Open Jack/Bonfire.  Use bonfire to trash coppers and the jack to trash estates.  On turn 6 or 7, your deck will consist of a jack and 4 silvers (maybe a gold if you missed jack but not bonfire one turn).  Here, you’ll want to just start buying provinces, probably picking up treasures when you miss since this deck doesn’t like greening much.  It should hit 4 provinces in around 10-11 turns, and then takes somewhat longer to get all 8.  It seems to lose to the above combos because they stand up better to greening and keep their estates.

[tim17]

20. Hunting Party/Tournament

Open Tournament/Silver, picking up hunting party on 5+, tournament on 4, and silver on 3 over the next few turns.  Once you hit 4-5 hunting parties/tournaments, you should be able to hit 8 and get a province.  From here, hunting parties are great for activating tournaments, and you can sometimes even get 2 prizes in a turn with them.  Steed and Followers are always great, princess can also be valuable here and can sometimes be worth picking up first to get more buys for more HP’s and tournaments.  It hits 4 provinces in 11-13 turns, and all 8 in around 17 turns, though it can also pick up duchies along the way, and get a couple extra points from followers.  It gets crushed by anything that can parry a tournament before it hits 8, so it doesn’t do well against Jack/Bonfire.

[tim17]

21. Apprentice/Market Square

While it might not be too surprising that this combo works, it sure is a lot of fun to play.  Open Silver/Silver, and then pick up market squares on 3 or 4 and apprentices on 5+.  Prioritize trashing estates and silvers over coppers, and activate market square’s discard as early as possible.  Once you collide an apprentice with a gold, start trashing golds with your apprentices to draw your deck, still discarding market squares.  After you have around 6 or 7 apprentices, the first 3 or 4 will draw your deck, and the remaining ones can pick up extra golds.  To illustrate, suppose your deck and discard pile are empty.  Trash a gold with an apprentice, discarding 3 market squares, and then draw the 3 golds and 3 market squares.  Each apprentice is effectively “gain 2 golds, putting them into your hand”.  It turns out this does drain the gold pile, so don’t plan on having one huge megaturn where you buy all the provinces.  It usually takes 2 turns at the end of the game to get enough green to win.  This hits 4 provinces in 12-13 turns, and all 8 in 14-15 turns.  While it doesn’t keep its estates, it often has enough late pile control to make up for it; just make sure you have enough market squares to get to the number of buys you need.

From here, I’m just going to pick out a few of the remaining combos that I like or think are interesting.

[tim17]

26. Storeroom/Encampment

Storeroom gives encampment exactly what it needs: +buy and a guarantee of hitting 4 to double up on encampments early, and sifting to find plunders later.  Open Storeroom/Storeroom, then usually you’ll be able to pick up 5 encampments on the next 3 turns.  On T6, use an encampment and a storeroom to get a plunder.  T7/T8 is when shuffle luck makes the biggest difference; it hurts a lot if the plunder ends up on the bottom of the shuffle.  From here, pick up any remaining encampments and more plunders, using storerooms to find encampments and plunders in your deck.  Usually even if you don’t hit a plunder with your first encampment, you can play a storeroom to probably find one, meaning it’s rare that you’ll have to return multiple encampments in a turn.  Pick up a 3rd storeroom if you have a spare 3 or 4.  Ultimately, you’ll want to be playing as many plunders as possible and start to buy provinces.  Even if you lose the province split, the plunder points will often give you the edge.  This usually reaches 27 points in 12-14 turns, and 51 points in 17-19 turns, but offers decent control and stands up reasonably well to greening.

[tim17]

29. Forager/Highway

This combo is interesting in that it has a somewhat narrow path to victory.  Everything is nonterminal and there’s no sifting or draw, so it really doesn’t like green.  The goal is to get a bunch of highways in play and then play 3 foragers to pick up 4 provinces.  After that, you’ll probably have to trash foragers to foragers to avoid trashing provinces if you want more +buy.  Open Forager/Forager, then pick up another forager and a silver on T3/T4 (unless you hit 5).  Be sure to trash a copper and silver ASAP so that your foragers are worth 2.  Feel free to pick up more foragers until you hit 5.  At this point, load up on highways while trashing everything else.  Once you get at least 7 highways in play and have hopefully 3 foragers in hand, play them all to get 4 provinces.  This usually happens around T11/T12.  Since it doesn’t like green, it takes quite a bit longer to get all 8, though often you’ll be able to afford to trash a couple provinces in order to pile them more quickly.

[tim17]

34. Fishing Village/Wharf

I’m mentioning this because to me it represents a standard engine that can be built with 2 cards.  It has +Actions, +Cards and +Buy, but no trashing, not much payload besides treasure and no alt vp.  This deck usually builds up to double provinces before it starts greening.  It gets 4 provinces in 13-14 turns, and all 8 in around 16 turns.  In real games, I’d imagine that there may sometimes be a question between playing one of the combos on this list (or something similar) and playing an engine.  In theory, one could try to determine whether the engine is better or worse than FV/Wharf and use that along with this list to maybe answer such a question.

[tim17]

35/37. Beggar/Gardens, Ironworks/Gardens

I believe these are two of the fastest (2 card) gardens strategies in dominion.  I have the beggar one ahead on my list, but I’m not sure if that is in fact accurate or not.  Again, I point this out in attempt to give a sense of how gardens rushes/slogs stack up against other combos.

[tim17]

40. Forum/Fool’s Gold

For whatever reason, I like this combo.  Maybe it’s just because fool’s gold makes good use of the non-handsize-decreasing sifting as well as the +buy on gain of forum.  Open FG/FG, hope you hit 5 to pick up a forum (though if you don’t initially it’s not the end of the world), and then pick up more forums and FGs as you go.  Ideally you’d like to hit 13 to go Forum/Province when you start greening, and the additional forums will help manage the provinces well.  It takes 13-14 turns to hit 4 provinces, and 18-19 to get all 8.  It is one of a number of “1 province a turn” strategies on this list.

[tim17]

41. Counterfeit/Capital

I mention this only because I find it interesting to have a deck that merely attempts to collide 2 stop cards in a hand of 5 cards repeatedly.  The counterfeit trashing helps a little.  The thing that makes it work is that, when you do collide counterfeit and capital, you have at least 13, sometimes 16, enough to buy 2 provinces.  It’s speed has a bit higher variance than a lot of other combos, due to the necessity to get lucky with collisions.

[tim17]

49. Embassy/Tunnel

Another “benchmark” type combo.  While the tunnels do help, this isn’t too far off from embassy/bm.  The tunnels provide some extra vp so you don’t necessarily need to win the province split.  Open Silver/Silver, then buy only embassies, tunnels, and provinces for the rest of the game (except for maybe the odd duchy/estate late game).  It usually takes around 14 turns to hit 4 provinces, though it does have some variance depending on embassy collisions.  Again, the tunnels often give the vp edge when up against a more standard “4 provinces in 14 turns” deck.