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#### tim17

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##### Relative strengths of 2 card combos
« on: October 26, 2016, 12:45:37 pm »
+7

So the Neat and potentially useful card interactions thread is great, but one thing I often find myself asking is how good various combos are relative to each other.  For instance, we know that warehouse/treasure map and hermit/market square are both “potentially useful” combos, but is one of them significantly better than the other?  A lot of times, the answer to such a question is “depends on the board”, but I’m interested in what happens when it doesn’t.  I’d like to ask the question “If you have two combos (A and B) and neither has any board support, which wins the majority of the time when pitted against each other?”

I’m not sure if something like this has been done before.  If it has, I’d be interested to see the results.  If not, here is my attempt to do so.  Feel free to skip to the bottom where I actually start listing combos.

To formalize the game I want to play, I’m going to start with a list of 2 card (or possibly “uh, card-shaped thing”) combos and attempt to rank them.  Here are my rules:

Say we want to compare combo A and combo B.  Construct a board with only the base cards (no colonies/shelters or anything) and the components of these two combos.
-   Play a 2 player game where one player plays combo A and the other player plays combo B.
-   The combo A player can only buy base cards or components from combo A.
-   The combo B player can only buy base cards or components from combo B.
-   Both players are attempting to play optimally subject to these constraints (i.e. maximizing their probability of winning).
-   Randomize starting player.
Combo A beats combo B iff combo A wins the majority of the time.

Some qualifiers to note:
1.   Determining the winner of a matchup seems like it could be pretty difficult to do.  “Playing optimally” might be hard for more difficult combos (e.g. upgrade/rats), and determining who wins the majority of the time with confidence might also be hard for two closely matched combos.
2.   There is no guarantee that the results are transitive.  It would be nice to still have a ranking that at least closely conforms to the results, maybe with notes as to which relations are violated.
3.   Due to the constraints of the game, some notoriously good combos will not do well.  For example, king’s court/bridge is great, but it would do terribly in this game, since it has no trashing.
4.   More generally, the constraint of only getting two kingdom cards seems to be fairly restrictive.  I can think of a lot of strong deck paradigms (goons engine, horn megaturn) that wouldn’t work here.  I guess that means that dominion is actually a pretty interesting game.
5.   Along the same vein, this idea feels somewhat like a generalization of the question “What’s the best big money strategy?” since that question is more or less the one card version of my question.
6.   I’m not sure if there are things like Donate that ruin this game.  It would be less fun if the top 13 combos were Donate/X or something.  If that ends up being the case, I want to veto Donate (or whatever the offending “uh, card-shaped thing” is) for this game.  This is obviously subjective.

--------------------------------------------------------------------------------------------------------------------------------------------------------

With all this setup, I’m going to provide a starting point to build off.  I’ll list a bunch of combos and provide a preliminary guess as to how they rank.  I make no claims as to the completeness of my list (There are obviously a lot of good combos that I’ve missed/not bothered to include), or the correctness of my ranks (I’m sure a lot of my ranks are off, some are probably way off).

1. Counting House/Travelling Fair
2. Ferry/Rebuild
3. Royal Carriage/Bridge
4. Villa/Jack of all Trades
5. Masterpiece/Feodum
6. Dungeon/Tunnel
7. Ferry/Governor
8. Hermit/Market Square
9. Scavenger/Stash
10. Ferry/Cultist
11. Lurker/Cultist
12. Courtyard/Delve
13. Witch/Delve
14. Mountebank/Delve
15. Cultist/Delve
16. Cultist/Dominate
18. Inheritance/Ironmonger
19. Bonfire/Jack of all Trades
20. Hunting Party/Tournament
21. Apprentice/Market Square
22. Dungeon/Treasure Map
23. Ferry/Mountebank
24. Wharf/Fool's Gold
25. Magpie/Pathfinding
26. Storeroom/Encampment
27. Jack of all Trades/Counterfeit
28. Gear/Treasure Trove
29. Forager/Highway
30. Ranger/Lost Arts
31. Native Village/Bridge
32. Wharf/Coin of the Realm
33. Forager/Minion
34. Fishing Village/Wharf
35. Beggar/Gardens
36. Courtyard/Quest
37. Ironworks/Gardens
38. Gear/Counterfeit
39. Inheritance/Magpie
40. Forum/Fool's Gold
41. Counterfeit/Capital
42. Beggar/Triumph
43. Urchin/Save
45. Artificer/Storyteller
46. Duplicate/Duke
47. Forum/Duke
48. Hermit/Artificer
49. Embassy/Tunnel
51. Gear/Lost Arts
52. Alchemist/Dominate
53. Native Village/Apothecary
54. Treasure Trove/Gardens
56. Forager/Peddler
57. Loan/Minion
58. Junk Dealer/Graverobber

Please comment if you want to include any combos, or if you find one of the current rankings to be off (or if you have any other questions or comments).  If you want to include a combo, it would be helpful to also figure out where it ranks.  I can keep this list updated if anyone else besides me actually cares about this at all.  Also, I'm not going to include any combo that loses to straight money, even if it is good with other support (e.g. kc/bridge).
« Last Edit: December 01, 2016, 01:24:34 pm by tim17 »
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#### gloures

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##### Re: Relative strengths of 2 card combos
« Reply #1 on: October 26, 2016, 01:14:45 pm »
+2

When looking at 2 card combos, there´s a need to differentiate between combos that are strategys just by themselves (like Counting House/Travelling Fair, Hermit/Market Square, etc) and combos that just provide very good support for the cards around them, or that can at least be made a lot better by the cards surrounding it. For example, Upgrade/Rats, is a wonderful combo if there are other good 5´s around, but quite weak otherwise (do keep in mind though, that strong 5´s is actually quite common), Fishing village/Wharf is quite good by itself, but will only be amazing if there are other strong cards you can also play with all the extra actions you should have.

Sure, there are also cards that make those combos I called "strategys just by themselves" even stronger (Bank comes to mind in the Counting House/Travelling Fair one http://forum.dominionstrategy.com/index.php?topic=15459.0 ), but the diference is that those things are quite rare, most of the times you´ll be playing them with no support whatsoever.
« Last Edit: October 26, 2016, 01:16:22 pm by gloures »
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#### tim17

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##### Re: Relative strengths of 2 card combos
« Reply #2 on: October 27, 2016, 12:03:53 pm »
0

When looking at 2 card combos, there´s a need to differentiate between combos that are strategys just by themselves (like Counting House/Travelling Fair, Hermit/Market Square, etc) and combos that just provide very good support for the cards around them, or that can at least be made a lot better by the cards surrounding it. For example, Upgrade/Rats, is a wonderful combo if there are other good 5´s around, but quite weak otherwise (do keep in mind though, that strong 5´s is actually quite common), Fishing village/Wharf is quite good by itself, but will only be amazing if there are other strong cards you can also play with all the extra actions you should have.

Sure, there are also cards that make those combos I called "strategys just by themselves" even stronger (Bank comes to mind in the Counting House/Travelling Fair one http://forum.dominionstrategy.com/index.php?topic=15459.0 ), but the diference is that those things are quite rare, most of the times you´ll be playing them with no support whatsoever.

Yes, I agree.  The game I've described focuses on the former.  I'm not trying to rank combos based on how good they are with surrounding cards; I just want to rank them based on how good they are by themselves.  For instance, Upgrade/Rats can be great with other good 5s, but this game ranks it based on how well it can 3 pile rats/upgrades/duchies.  It's not that I'm not interested in how good combos are with other support; it's just that it seemed difficult to construct an exercise like this using that metric.
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#### Chris is me

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##### Re: Relative strengths of 2 card combos
« Reply #3 on: October 27, 2016, 04:06:16 pm »
0

RC / Bridge is faster than Masterpiece / Feodum. I really don't understand how it could not be.

Is Villa / Jack really all that as well?
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#### mail-mi

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##### Re: Relative strengths of 2 card combos
« Reply #4 on: October 27, 2016, 04:15:43 pm »
+1

Is Villa / Jack really all that as well?

It makes sense. You use Jack to get rid of estates, so that at the start of your turns you can play all your treasure, buy Villa, and play jack to draw 5 cards.
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#### Beyond Awesome

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##### Re: Relative strengths of 2 card combos
« Reply #5 on: October 27, 2016, 04:58:01 pm »
0

I've played both Villa/Jack and Villa/Watchtower before. Both are good if there are other engine pieces in the deck. If not, they're just okay.
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#### aku_chi

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##### Re: Relative strengths of 2 card combos
« Reply #6 on: October 27, 2016, 08:13:57 pm »
+1

Rebuild + Ferry is very fast.  Possibly the fastest 2-card "combo".

Some boring fast money strategies that use only two card-shaped-things:
Courtyard + Delve
Courtyard + Quest
Jack of all Trades + Bonfire
Jack of all Trades + Counterfeit
Gear + Treasure Trove
Gear + Counterfeit
Gear + Lost Arts
Masquerade + Lost Arts
Urchin + Save
Cultist + Ferry
Cultist + Delve
Mountebank + Ferry
Mountebank + Delve
Witch + Delve
Governor + Ferry
Governor + Mission
Wharf + Coin of the Realm
Wharf + Fool's Gold

Some great openers that might be good in isolation:
Tournament + Gear
If you get 5/2, sadness...

And then there's Donate.  What is the best single card to pair with Donate?  I'm going to guess Governor.
Turn 1: Buy Silver
Turn 2: Buy Silver
Turn 3: Buy Governor
Turn 4: Donate down to Governor + 2 Silver, pay off 4+ debt (if you can only pay off 2-3 debt, keep an extra Copper)
Turn 5: Gain Gold, pay off debt
Turn 6: Remodel Silver to Governor, buy Governor
Turn 7: Gain Gold, Remodel Silver to Governor, draw three, Gain Gold, Buy Governor
Turn 8: Do amazing things with your 5 Governors and 3 Gold (3 Provinces and net 0 Gold is a low bar)
Turn 9: Pile out the Provinces, or close to it

Sometimes you get slowed down by a turn, and you do help your opponent a little (especially if they like Silver), but this seems very fast.

Donate + Page would also be good, I expect.  Champion + mass Warrior is an option, and will wreck some decks, but a Hero + Treasure Hunter also seems really fast and solid.

Donate + Fool's Gold seems reliable.  Donate on turn 4 and keep 3 Fool's Golds.  You can pay off all debt and buy another Fool's Gold on turn 5.  Then, you can start Provincing beginning turn 6.  Guaranteed 3 Provinces before you can have a dud turn (where you can buy another Fool's Gold or a Duchy).
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#### JThorne

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##### Re: Relative strengths of 2 card combos
« Reply #7 on: October 27, 2016, 08:49:26 pm »
0

Listing Donate combos starts to get silly, almost like listing King's Court combos. I recently opened Treasure Map/Cellar/Treasure Map/Donate. Silly!

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#### Limetime

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##### Re: Relative strengths of 2 card combos
« Reply #8 on: October 27, 2016, 11:48:10 pm »
0

Quote
Rebuild + Ferry is very fast.  Possibly the fastest 2-card "combo"
This is False.
This "combo" takes at least 13 turns while counting house traveling fair takes 12 or so.
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#### LaLight

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##### Re: Relative strengths of 2 card combos
« Reply #9 on: October 28, 2016, 03:28:29 am »
+1

Donate + Page would also be good, I expect.  Champion + mass Warrior is an option, and will wreck some decks, but a Hero + Treasure Hunter also seems really fast and solid.

I once opened Peasant/page and bought Donate T3. Quite good! Disciple on Hero and you have all you need
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#### drsteelhammer

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##### Re: Relative strengths of 2 card combos
« Reply #10 on: October 28, 2016, 03:32:52 am »
0

Donate + Page would also be good, I expect.  Champion + mass Warrior is an option, and will wreck some decks, but a Hero + Treasure Hunter also seems really fast and solid.

I once opened Peasant/page and bought Donate T3. Quite good! Disciple on Hero and you have all you need

That's pretty awesome actually, they alternate being non-terminal and your fugitive can discard the silver from treasure hunter!
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#### aku_chi

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##### Re: Relative strengths of 2 card combos
« Reply #11 on: October 28, 2016, 09:07:06 am »
0

Quote
Rebuild + Ferry is very fast.  Possibly the fastest 2-card "combo"
This is False.
This "combo" takes at least 13 turns while counting house traveling fair takes 12 or so.

Not so.  It takes, at a minimum, 7 turns.  See here.  Of course, a 7-turn Province pile-out require remarkable luck, but I played some solitaire games and piled the Provinces on turn 9-10 on average.  Also, Rebuild performs very well against megaturn style decks, because it can remove a bunch of VP before the opponent's megaturn kicks off.  So, I'm confident that Ferry + Rebuild is favored against Royal Carriage + Bridge and Hermit + Market Square, and I suspect that it is favored against Travelling Fair + Counting House.  Against a money strategy, you play it a little slower, grabbing Estates on a missed 3 to grab more points.  It should be possible to get 5 Provinces by turn 11-12.
« Last Edit: October 28, 2016, 11:28:53 am by aku_chi »
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#### McGarnacle

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##### Re: Relative strengths of 2 card combos
« Reply #12 on: October 28, 2016, 09:58:23 am »
0

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#### faust

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##### Re: Relative strengths of 2 card combos
« Reply #13 on: October 28, 2016, 12:07:14 pm »
+2

So combos. I don't want to start another lengthy debate about that word, but there's a difference between "two cards that are good" and a combo. I mean there has to be some synergy beyond what the individual cards do.

Rebuild + Ferry is very fast.
Not a combo; Ferry does what it always does - make key pieces of your deck more easily attainable. Rebuild doesn't interact with Ferry in a significant way.

Courtyard + Delve
This is just Big money with 2 Big Money enablers that don't have any special synergy.

Courtyard + Quest
Here we have synergy since Courtyard brings you to 6 cards and stores away the good ones.

Jack of all Trades + Bonfire
Not even sure this beats plain DoubleJack.

Jack of all Trades + Counterfeit
Small synergy as JoaT gains Treasures and Counterfeit trashes them for benefit.

Gear + Treasure Trove
Gear + Counterfeit
Just good cards without any synergy.

Gear + Lost Arts
Masquerade + Lost Arts
This is only a combo in the sense that Lost Arts-any terminal draw is a combo.

Urchin + Save
I guess there's always synergy between Save and cards that want to be lined up with other cards.

Cultist + Ferry
Cultist + Delve
Mountebank + Ferry
Mountebank + Delve
Witch + Delve
Governor + Ferry
All non-combos due to lack of synergy. Ferry/Governor might even be bad because it lets your opponent remodel Estates into Governors during your turn.

Governor + Mission
This qualifies as a combo I think.

Wharf + Coin of the Realm
Wharf + Fool's Gold
I don't think there's any special snergy here.
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#### Chris is me

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##### Re: Relative strengths of 2 card combos
« Reply #14 on: October 28, 2016, 12:21:53 pm »
0

So I agree with most of your post so sorry for singling out a few things.

Jack of all Trades + Bonfire
Not even sure this beats plain DoubleJack.

I'm not sure you realize  how good this is if you feel DoubleJack is better. Jack / Bonfire gets you to a small deck with ~4 Silvers and a Jack extremely fast. This is one of the most potent ways to lead into many engines and it is even a passable money variant. You have to try this, it is extremely good like you wouldn't believe.

Quote
Jack of all Trades + Counterfeit
Small synergy as JoaT gains Treasures and Counterfeit trashes them for benefit.

While I wouldn't say this is a combo like Jack / Bonfire, calling this a small synergy is a big understatement. Jack thins your Estates, multiple Counterfeits thin your Copper, seems kind of obvious how this works. Similar to Jack Bonfire you can either lead into an engine or play a money variant out of this, with the benefit for the engine of dealing with the Silver load.

Quote
Gear + Lost Arts
Masquerade + Lost Arts
This is only a combo in the sense that Lost Arts-any terminal draw is a combo.

Agreed on Masq but not Gear. With Gear you basically can set aside any number of cards. It greatly magnifies the benefit of Gear's setting aside to give you gigantic hands, make all of your bad cards miss the shuffle, smooth out Provinces, etc. It kind of lubricates your Gears basically - the whole is better than the sum of the parts. Maybe not a combo if only because Gear is already pretty good terminally.
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#### Mic Qsenoch

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##### Re: Relative strengths of 2 card combos
« Reply #15 on: October 28, 2016, 12:54:15 pm »
+6

It's really not Ferry's fault that it is synergistic with a crap ton of cards, in these examples faust seems to be ignoring two general synergies involving Ferry:

- Moving the price of a card you specifically want a bunch of copies into a range where you can buy it almost every turn.
* Bonus points if the card is "monolithic" in whatever sense you please (i.e. Rebuild, Cultist, other stuff).
- Getting a card which is more powerful the sooner you get it, sooner.

These are more specific than just "a card costs \$2 less". They also happen to apply to a bunch of Dominion cards, but they are still clearly "synergistic", oh hey Ferry is really good.

The faust comment about Wharf/FG not having synergy is insane to me. Wharf gives +buy which lets you buy a bunch of FG (a card which is better when you have several copies of it), which are easier to pair up because you can draw them with Wharves, which produces big \$\$\$ which you can use effectively because Wharf gives +buy.
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#### aku_chi

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##### Re: Relative strengths of 2 card combos
« Reply #16 on: October 28, 2016, 01:53:21 pm »
+1

So combos. I don't want to start another lengthy debate about that word, but there's a difference between "two cards that are good" and a combo. I mean there has to be some synergy beyond what the individual cards do.

If you reread my post, you will notice that the only time I used the word "combo", I put it in scare quotes.  Indeed, I went out of my way to describe the two-card money strategies as "boring fast money strategies that use only two card-shaped-things".  As you and other posters have noted, some of the strategies have more synergy than others.  I believe my post followed the spirit of the OP: "this idea feels somewhat like a generalization of the question “What’s the best big money strategy?” since that question is more or less the one card version of my question."  Like the OP, I agree that this exercise demonstrates that the best strategy in a given kingdom rarely involves only two card-shaped things - and Dominion is more interesting as a result.  The very strongest two-card strategies are exceptions that prove the rule.
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#### tim17

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##### Re: Relative strengths of 2 card combos
« Reply #17 on: October 28, 2016, 01:58:22 pm »
0

So combos. I don't want to start another lengthy debate about that word, but there's a difference between "two cards that are good" and a combo. I mean there has to be some synergy beyond what the individual cards do.

Maybe I shouldn't have used the word "combos" in the title of this thread.  Oh well.

In terms of my initial list, I basically just played a bunch of them and went by feel.  For example, I'd play Travelling Fair/CH against RC/Bridge, and it felt like TF/CH would win the majority of the time.  In none of my matchups did I really get enough of a sample size to say anything conclusive.  There have been a few comments stating beliefs about strengths of some of the "combos" (quotes here because of the above quote).  If there appears to be evidence for any of these statements, I'll update the above list (I'm not questioning them, it's just not clear to me whether they're just hunches or verified facts).  I don't know much about the sims, but if they can be useful at all here, that seems like it would be valuable evidence.

I'd also like to check out ferry rebuild and see where I think it might fit in (as well as a few of the others listed if/when I get the chance).
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#### Geronimoo

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##### Re: Relative strengths of 2 card combos
« Reply #18 on: October 28, 2016, 02:45:03 pm »
+1

Sim result:

Jack+Bonfire 79% - DoubleJack 16%

This should be evidence that there's plenty of synergy to call it a combo.
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#### Geronimoo

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##### Re: Relative strengths of 2 card combos
« Reply #19 on: October 28, 2016, 02:58:44 pm »
0

Is Travelling Fair/Counting House that strong?

I only get it to 46% win rate vs DoubleJack.

Code: [Select]
<player name="Counting House/Traveling Fair"
author="Geronimoo"
description="">
<type name="Province"/>
<type name="TwoPlayer"/>
<type name="Bot"/>
<type name="UserCreated"/>
<type name="SingleCard"/>
<type name="BigMoney"/>
<type name="Optimized"/>
<condition>
<left type="countAvailableMoney"/>
<operator type="greaterOrEqualThan" />
<right type="constant" attribute="10.0"/>
</condition>
<condition>
<operator type="equalTo" />
<right type="constant" attribute="1.0"/>
</condition>
<condition>
<left type="countCardsInDeck" attribute="Counting_House"/>
<operator type="greaterThan" />
<right type="constant" attribute="2.0"/>
</condition>
<condition>
<left type="countCardsInSupply" attribute="Province"/>
<operator type="smallerOrEqualThan" />
<right type="constant" attribute="5.0"/>
</condition>
<condition>
<left type="countCardsInSupply" attribute="Province"/>
<operator type="smallerOrEqualThan" />
<right type="constant" attribute="2.0"/>
</condition>
<condition>
<left type="countAvailableMoney"/>
<operator type="greaterOrEqualThan" />
<right type="constant" attribute="7.0"/>
</condition>
</player>
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#### Rabid

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##### Re: Relative strengths of 2 card combos
« Reply #20 on: October 28, 2016, 03:03:18 pm »
0

« Last Edit: October 28, 2016, 03:05:23 pm by Rabid »
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#### Geronimoo

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##### Re: Relative strengths of 2 card combos
« Reply #21 on: October 28, 2016, 03:08:51 pm »
+1

http://wiki.dominionstrategy.com/index.php/Combo:_Counting_House_and_Travelling_Fair

I guess bot is greening to early.
Oh, I now see it. It's playing it all wrong. It's not topdecking the Coppers. Sim needs refactoring to make that combo work.
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#### aku_chi

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##### Re: Relative strengths of 2 card combos
« Reply #22 on: October 28, 2016, 03:52:32 pm »
0

There is some nuance to the Counting House + Travelling Fair combo that the wiki doesn't cover.  One common mistake is to green too late.  The cards in your deck are a resource in this strategy.  You only need to top-deck five cards if you have an empty draw pile.  For instance, with 15 coins and 3+ cards in your deck, it is usually correct to buy Travelling Fair and topdeck a Counting House and a Province.  There are some other micro-optimizations regarding when to topdeck that I mention in this topic.
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#### tim17

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##### Re: Relative strengths of 2 card combos
« Reply #23 on: October 29, 2016, 08:45:34 pm »
+1

Okay, ferry rebuild seems really good to me, courtyard delve and wharf fools gold are also strong. I'm adding them to the list and moving a couple others around after looking at them a little more, though I still don't have anything that I would call "sufficient evidence" for any of my ranks. I'll take a look at jack bonfire to try to see where it might fit in, as well as a couple others at some point.
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#### JThorne

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##### Re: Relative strengths of 2 card combos
« Reply #24 on: October 31, 2016, 11:06:14 am »
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I think some clarification is in order.

It seems to me that what you're looking for are indications of which monolithic strategies are fastest when those strategies involve a specific combination of (usually 2) cards.

The question is this: Which combos are truly monolithic? When playing Scavenger/Stash, Hermit/Market Square or Counting House/Traveling Fair, is it ever possible to add any other cards to make the deck perform faster? My guess would be no, because the interaction between those combinations of cards is extremely specific. On the other hand, Stash and Counting House cost \$5...do you open Silver/Something on a 3/4 when playing those decks?

Many of the "combos" listed cannot be said to be monolithic, because many of them are just exceptionally fast BM strategies, or quick Duchy gainers like Upgrade/Rats, or Rebuild, which can be helped by sifting and gainers, or any number of other strategies that would benefit from playing additional cards.

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

That said, an interesting starting point would be to post sim results for these combos, including the non-monolithic ones, just to see the average turns to 5 or 8 provinces.

Of course, as interesting and potentially useful as this information might be, attacks really throw a wrench in the gears of some of these, not to mention that Empires also blows up everything by adding huge number of Alt+VP in the form of token generators and Landmarks, meaning that even when you recognize a kingdom with a great combo in it, the sim results are thrown out the window.
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