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[Psyduck]

Guildhall + Beggar

Even without +Buy or other help, these two together can make for a surprisingly fast Province rush.  Guildhall gives you +1 Coffers every time you gain a treasure, which means Beggar essentially reads +$6.  There's probably some optimization here that I haven't figured out yet, but the basic strategy is to open Beggar-Beggar, buy Guildhall with your first $5 (which should be very easy with a Beggar play), then buy Province every time you play Beggar, and buy extra Beggars on hands without Beggars.  I can usually get 7-8 Provinces in about 12 to 13 turns, and I've had a few games where I emptied Provinces by turn 10 or 11.

On a related note: Guildhall + Masterpiece
Buy Guildhall with your first $5, then Masterpieces, overpaying as much as possible. Uncontested, Silver runs around turn 8, afterwards you can easily buy a Province per turn. In a mirror, Silver runs around turn 6-7, and the game ends by turn 10 or 11. Obviously Gardens and Feodum love this.

[Awaclus]

Guildhall + Beggar

Even without +Buy or other help, these two together can make for a surprisingly fast Province rush.  Guildhall gives you +1 Coffers every time you gain a treasure, which means Beggar essentially reads +$6.  There's probably some optimization here that I haven't figured out yet, but the basic strategy is to open Beggar-Beggar, buy Guildhall with your first $5 (which should be very easy with a Beggar play), then buy Province every time you play Beggar, and buy extra Beggars on hands without Beggars.  I can usually get 7-8 Provinces in about 12 to 13 turns, and I've had a few games where I emptied Provinces by turn 10 or 11.

On a related note: Guildhall + Masterpiece
Buy Guildhall with your first $5, then Masterpieces, overpaying as much as possible. Uncontested, Silver runs around turn 8, afterwards you can easily buy a Province per turn. In a mirror, Silver runs around turn 6-7, and the game ends by turn 10 or 11. Obviously Gardens and Feodum love this.

Doesn't emptying the Silver pile seem a little excessive if it's just a Province game?

[Aleimon Thimble]

Guildhall + Beggar

Even without +Buy or other help, these two together can make for a surprisingly fast Province rush.  Guildhall gives you +1 Coffers every time you gain a treasure, which means Beggar essentially reads +$6.  There's probably some optimization here that I haven't figured out yet, but the basic strategy is to open Beggar-Beggar, buy Guildhall with your first $5 (which should be very easy with a Beggar play), then buy Province every time you play Beggar, and buy extra Beggars on hands without Beggars.  I can usually get 7-8 Provinces in about 12 to 13 turns, and I've had a few games where I emptied Provinces by turn 10 or 11.

On a related note: Guildhall + Masterpiece
Buy Guildhall with your first $5, then Masterpieces, overpaying as much as possible. Uncontested, Silver runs around turn 8, afterwards you can easily buy a Province per turn. In a mirror, Silver runs around turn 6-7, and the game ends by turn 10 or 11. Obviously Gardens and Feodum love this.

Doesn't emptying the Silver pile seem a little excessive if it's just a Province game?

Well, in a BM game you need a money density of $1.6/card to buy a Province every turn on average. Your deck starts out at 10 cards with $0.7/card, so if all you do is buy Silvers ($2/card), you'll need more than 20 Silvers to get your money density high enough. Considering the fact that Masterpieces themselves are just Coppers, it gets even worse. I wouldn't be surprised if getting around 30 Silvers is optimal, which is not quite an empty Silver pile but pretty close to it.

[Awaclus]

Guildhall + Beggar

Even without +Buy or other help, these two together can make for a surprisingly fast Province rush.  Guildhall gives you +1 Coffers every time you gain a treasure, which means Beggar essentially reads +$6.  There's probably some optimization here that I haven't figured out yet, but the basic strategy is to open Beggar-Beggar, buy Guildhall with your first $5 (which should be very easy with a Beggar play), then buy Province every time you play Beggar, and buy extra Beggars on hands without Beggars.  I can usually get 7-8 Provinces in about 12 to 13 turns, and I've had a few games where I emptied Provinces by turn 10 or 11.

On a related note: Guildhall + Masterpiece
Buy Guildhall with your first $5, then Masterpieces, overpaying as much as possible. Uncontested, Silver runs around turn 8, afterwards you can easily buy a Province per turn. In a mirror, Silver runs around turn 6-7, and the game ends by turn 10 or 11. Obviously Gardens and Feodum love this.

Doesn't emptying the Silver pile seem a little excessive if it's just a Province game?

Well, in a BM game you need a money density of $1.6/card to buy a Province every turn on average. Your deck starts out at 10 cards with $0.7/card, so if all you do is buy Silvers ($2/card), you'll need more than 20 Silvers to get your money density high enough. Considering the fact that Masterpieces themselves are just Coppers, it gets even worse. I wouldn't be surprised if getting around 30 Silvers is optimal, which is not quite an empty Silver pile but pretty close to it.

With all the coffers you get from that last Masterpiece?

[Aleimon Thimble]

Guildhall + Beggar

Even without +Buy or other help, these two together can make for a surprisingly fast Province rush.  Guildhall gives you +1 Coffers every time you gain a treasure, which means Beggar essentially reads +$6.  There's probably some optimization here that I haven't figured out yet, but the basic strategy is to open Beggar-Beggar, buy Guildhall with your first $5 (which should be very easy with a Beggar play), then buy Province every time you play Beggar, and buy extra Beggars on hands without Beggars.  I can usually get 7-8 Provinces in about 12 to 13 turns, and I've had a few games where I emptied Provinces by turn 10 or 11.

On a related note: Guildhall + Masterpiece
Buy Guildhall with your first $5, then Masterpieces, overpaying as much as possible. Uncontested, Silver runs around turn 8, afterwards you can easily buy a Province per turn. In a mirror, Silver runs around turn 6-7, and the game ends by turn 10 or 11. Obviously Gardens and Feodum love this.

Doesn't emptying the Silver pile seem a little excessive if it's just a Province game?

Well, in a BM game you need a money density of $1.6/card to buy a Province every turn on average. Your deck starts out at 10 cards with $0.7/card, so if all you do is buy Silvers ($2/card), you'll need more than 20 Silvers to get your money density high enough. Considering the fact that Masterpieces themselves are just Coppers, it gets even worse. I wouldn't be surprised if getting around 30 Silvers is optimal, which is not quite an empty Silver pile but pretty close to it.

With all the coffers you get from that last Masterpiece?

That's a fair point, but by the time you get enough coffers from a single Masterpiece not to need so many Silvers anymore, the Silver pile is also almost empty.

[Psyduck]

Doesn't emptying the Silver pile seem a little excessive if it's just a Province game?

That's a good point. Getting all Silvers even allows to pile Colonies. For Provinces, getting roughly half of the Silver pile is enough, which allows to get all Provinces by turn 14.

[aku_chi]

Inventor + Alms

Alms is already pretty great with Bridge, but its even better with Inventor.  You can open double Inventor.  When you play a single Inventor, you can gain a $4 (which could be another Inventor) and a $5.  If there's a village that costs $5 or less, you can easily chain Inventors for more spectacular results.  Building this way is so fast, it could be reasonable to skip or defer weak trashing.

[connorbr011]

I haven’t tested it out yet, but
Lost Arts/Inventor
Lost Arts mitigates the main drawback of Inventor: it being terminal. That way, you can get crazy turns where you can gain and play a bunch of Inventors without needing an exorbitant amount of village support.

[Dingan]

Ferry / Chariot Race
Say your opponent has a lot of Smithys and few Workers Villages, while you have a lot of Workers Villages and few Smithys -- Ferry the Smithy pile so that your Chariot Races get activated while theirs do not. Ferry'ing the Chariot Race pile itself could even be neat if, say, you have few CRs and your opponent has a lot, and you have a lot of Villages, your CRs will activate on your Village when against a CR. I haven't done the math on if this is actually beneficial, but it's certainly neat.

[Commodore Chuckles]

Seer + Scheme
Use Seer to draw the Schemes, which then draw other cards. Then use Scheme to top deck the Seers.

[aku_chi]

I decided to try my hand at optimizing some Guildhall combos.

Beggar + Guildhall
This can be insanely fast, but it's very inconsistent; if your Beggars clump together, you lose a lot of turns.  My strategy was to always get three Beggars and Guildhall in the first 4 turns.  Buy Provinces when possible.  Buy additional Beggars on turns 5-7 if you miss Province.  After that, buy Silvers instead.
   Turn 8-12: 4 Provinces, ~27 VP
   Turn 10-14: 6 Provinces, ~39 VP
   Turn 13-17: 8 Provinces, ~51 VP

Delve + Guildhall
This combo is pretty comparable with Masterpiece, but with slightly higher highs and lower lows.  My strategy is to buy Guildhall ASAP (a 2/5 or 5/2 is great).  Pre-Guildhall, just Delve as much as possible.  Post-Guildhall, use a Coffers if you have an odd amount of money, buy as many Delves as you can, plus a Copper.  Green starting on turn 6 if you have an amazing start, turn 7 usually, and turn 8 if you have a weaker start (often caused by Guildhall on turn 4+).  If you get $9 or $10 naturally, you can Delve + Province.
   Turn 9-11: 4 Provinces, ~27 VP
   Turn 12-13: 6 Provinces, ~39 VP
   Turn 15-16: 8 Provinces, ~51 VP

Masterpiece + Guildhall
This strategy is the most reliable to 8 Provinces, but the slowest to 4 Provinces.  I just buy Silvers pre-Guildhall.  Post-Guildhall, use all your Coffers and get the biggest Masterpiece overpay you can!  Green starting on turn 7 if you have ~15+ Silvers.  Green starting on turn 8 otherwise.
   Turn 10-11: 4 Provinces, ~27 VP
   Turn 12-13: 6 Provinces, ~39 VP
   Turn 14-15: 8 Provinces, ~51 VP

So, these are all really strong!  Monolithic Guildhall strategies are also worth looking out for with Banquet and Cache (and maybe other cards I'm not thinking of).

Edit: Banquet + Guildhall is also very strong.  The baseline Banquet for Silver isn't as strong as the above, but it isn't hard to find something on the board that helps.  A better treasure (or treasure gainer) helps, as does +buy.  I got 8 Provinces in 13 turns with Banquet + Spices + Guildhall.  Counterfeit and Charm were strong.  I expect Treasure Trove is also great.

[mameluke]

Poor House / Patron is kind of interesting.

[NoMoreFun]

Gear + Citadel

Citadel works well with decks that revolve around playing a key card card once per turn, and first.

Big Money + Gear, once set up, basically has you playing a Gear every turn as your only action. With Citadel you can increase the number of Gears in your deck without fear of terminal collision, and really work with +4 cards. I spiked an early $8 in a BM+Gear game, bought Citadel, and I was able to make 8 easily every subsequent turn.

[singletee]

City Gate + Guide

Put back the best card from your hand before you call Guide.

[Simon Jester]

Citygate + Lookout

No more shots in the dark, Lookout will always hit your junk (as long as you have any in hand at least)

[Kirian]

Searched the thread and didn't find it.  This one is extra-neat (though not extra-useful) because the cards are just two letter-steps apart despite having completely different etymologies!*

Patron + Patrol

Patrol can reveal Patrons, gaining you possibly multiple Coffers if you have enough Patrons.  You'll want a village or two to take full advantage, but you can stockpile Villagers on turns where this doesn't work out.

*Patron comes (eventually) from Latin pater (father) so from PIE *p[h2]ter (father), patrol is probably from pate (foot) so eventually from PIE *ped-

[Commodore Chuckles]

patrol is probably from pate (foot) so eventually from PIE *ped-

This is definitely wrong. In Latin "foot" is pes, genitive pedis. I don't know where you got "pate" from. Getting the form "pate" from *ped- is not a thing in any language as far as I know. My sources tell me patrol is actually from PIE *pent- ("path").

Regardless, cool combo.

[AJD]

So all sources I’ve checked seem like to agree “patrol” is from Old French patte ‘paw’; and then Wiktionary says it’s connected to *pent-; Etymonline says maybe *ped- via Celtic; OED just throws up its hands and says maybe it’s okay onomatopoeic—I think we may just have to accept the etymology of this word is unsettled.

[samath]

Golem + Mountain Village

One of the main problems with Golem-based engines is that Golems will skip other Golems. But if you hit a Mountain Village, fear not! You can put one of those skipped Golems straight back into your hand. Plus, you'll have the actions to play it.

[Simon Jester]

Flag Bearer + Changeling

Don't like junking your deck with terminal silvers? Well change them to something else then, and still get the Flag! 

[Chappy7]

Flag Bearer + Changeling

Don't like junking your deck with terminal silvers? Well change them to something else then, and still get the Flag!

Changeling is also nice with Silk Merchant.  It gives you the flexibility to spend $4 on a Changeling +1 Coffers and a Villager.  Not bad.

[Awaclus]

Changeling is nice with everything that has an on-gain benefit.

[markusin]

Changeling is nice with everything that has an on-gain benefit.

Changeling is less appealing with Border Village (village 4lyfe), but can still work out if you are racing to win the split of a cheaper pile and happen to reach $6.

[faust]

Changeling is nice with everything that has an on-gain benefit.

Changeling is less appealing with Border Village (village 4lyfe), but can still work out if you are racing to win the split of a cheaper pile and happen to reach $6.

It's actually quite good with Border Village since all you need is a Border Village in play to gain any card costing $5 or less.

[ipofanes]

So all sources I’ve checked seem like to agree “patrol” is from Old French patte ‘paw’; and then Wiktionary says it’s connected to *pent-; Etymonline says maybe *ped- via Celtic; OED just throws up its hands and says maybe it’s okay onomatopoeic—I think we may just have to accept the etymology of this word is unsettled.

I am a simple man; I see etymology discussions, I upvote.