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werothegreat

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Dominion 101: What is an engine?
« on: October 11, 2017, 11:54:22 pm »
+11

Dominion 101 is a series geared toward newer players.

What is an engine?

One of the most important strategic concepts in Dominion is the engine.  Most experienced Dominion players will spend their first few moments of a game looking at the Kingdom and figuring out if an engine is possible, and if so, how they can cobble one together.  Engine strategies can reliably beat most decks that just buy bigger and bigger Treasures (called Big Money decks), and getting an engine running is for many players one of the most satisfying and rewarding parts of playing the game.

So what exactly is an engine?  An engine is characterized by two main features:
  • Strong draw, typically being able to draw your entire deck in a single turn
  • Payload, powerful cards that either help your deck, hinder your opponent, or let you gain multiple Victory cards in a turn
If the strong draw and/or payload is terminal (that is, not giving any +Action when played), an engine will also require a card that gives at least +2 Actions (usually called Villages, after the simplest Kingdom card that gives this effect).

For an example of each of these, we need look no further than the recommended First Game from the Base Set: Cellar, Moat, Merchant, Village, Workshop, Militia, Remodel, Smithy, Market, Mine.  (If you don’t recognize Merchant, it was added in the Second Edition, which we’ll discuss next time, and replaces Woodcutter in this game.)  For our strong draw, we have Smithy, which gives a snazzy +3 Cards for the low, low price of .  However, it is also terminal - if you play Smithy as your first Action on a turn, you can’t play any more Actions afterwards, which undermines the whole point of making an engine in the first place.  So we’ll also rely on Village to give us the extra Actions necessary to play enough Smithies to draw our entire deck.

But we can’t stop here; one of the common pitfalls newer players experience is grabbing a bunch of Villages and Smithies, but not adding in anything else to the mix other than maybe a couple Treasures.  That kind of deck can pretty reliably draw itself, but then you’re stuck with a bunch of coins and only one Buy, and now you’re not doing any better than the Big Money deck, except you’re actually a few turns behind; while you were picking up the Villages and Smithies, the Big Money player was picking up Silvers and Golds and has already bought a Province or two, and there’s no way you’ll catch up to them at this point.  What you need is the final, and most crucial, engine ingredient: payload.

Payload is just a fancy word for “whatever makes your engine worth it”.  This can be a +Buy card like Market, or an Attack like Militia.  An engine may have several different payloads, and the engine from the First Game has room for a few.  You could pick up a Mine, which increases the overall buying power of your Treasures.  You’ll also need Markets, so that you have the extra Buys necessary to gain multiple Provinces a turn near the end of the game, and a Militia would certainly be recommended, to slow down your opponent.

Engines do take a bit of time to get going, and an opponent that’s more focused on Treasures will probably start buying Provinces while you’re still building.  This process can be helped along by “engine enablers”: essentially any card that speeds up your engine construction.  In the First Game, both Workshop and Remodel serve this role, as both can help you add more than one engine piece to your deck per turn.  Remodel is also the only way to get rid of your Estates on this board, and as we discussed last time, that’s quite important to do, particularly so for an engine, which can’t afford to hit a snag like drawing an Estate instead of a card that can actually draw.  Besides gainers and trashers, enablers can include sifters (cards that cycle through your deck) like Cellar, and +Buy cards like Market.  There is a bit of overlap with payload cards, as many payload cards, like Market, also function as enablers.

If there are enablers on the board, you’ll most likely want to open with them, to get your engine going as quickly as possible.  Look specifically for trashers (like Remodel), and gainers (like Workshop).  Notice that Mine, despite being a trasher, is not an enabler, but only payload; this is because it replaces a trashed Treasure with another Treasure, keeping the number of “stop cards” (cards that don’t draw) in your deck constant.  While an engine will usually need a couple stop cards to serve as payload, most cards in an engine should be helping you draw the rest of your deck.  Once you’ve picked up your enablers, focus on getting your engine pieces (your draw and Villages), before starting to pick up payload.  Once your engine is mostly drawing your entire deck, and has enough payload to gain more than one Province per turn, you should start grabbing some Victory cards.  Be careful, though: start buying Provinces too soon, and your engine will sputter, and you will lose.  But hold off buying Provinces too long, and your opponent will get more Victory cards than you, and you will lose.  Knowing exactly when to start doing each step is not an exact art, and will take some practice to get right. 

Specifically for the First Game, my preferred method would be to open Silver/Remodel (or Workshop/Remodel, if I’m feeling lucky), then pick up a Mine with my first , and Markets with each subsequent , getting Villages, Smithies, and a single Militia as I can along the way.  Remodel turns my starting Estates into Villages and/or Smithies, then a Silver or two into an extra Market, and later in the game can turn Golds I get from Mine into Provinces.  A typical late game turn should see me draw my entire deck, play my Militia, Mine a Silver into a Gold, then immediately Remodel that Gold into a Province, then buy 2 more Provinces and maybe one other cheap card (usually Cellar).

Remember that, unless you’re pulling off a particularly wacky strategy, you’re still going to need some coins in order to buy everything.  The First Game provides this rather naturally, sticking it onto Market and Militia in addition to their +Buy and Attack payload.  Mine also serves this purpose in slowly upgrading your Treasures.  If a Kingdom has draw, +Action, and other sources of payload, but no useful Actions that give extra coins, then it’s perfectly fine to pick up a couple Golds to help serve as a payload.  However, in general, your engine should be made up almost entirely of Action cards, if possible.

So now when you see a board with good draw, a Village, and some cool payload cards, you’ll think to yourself, “It’s engine time.”
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Re: Dominion 101: What is an engine?
« Reply #1 on: October 12, 2017, 12:52:15 am »
0

Pretty nice article. It goes over the essentials of the first game engine without being too bogged down by text. Be sure to emphasize that it would be a good idea to practice the first game engine to get a feel for how the engine is built.

I'm not sure how great this is, but you can mention how Remodel can be used to turn Silver or even Workshop into a Market while still in the building phase.

You say this line:

"However, in general, your engine should be made up almost entirely of Action cards, if possible."

I didn't feel like you made it clear why this should be the case. Maybe refer back to your article on trashing once again here.
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Re: Dominion 101: What is an engine?
« Reply #2 on: October 12, 2017, 01:48:44 am »
+1

I'm going to disagree with the idea that an engine "typically" draws your entire deck each turn.  Often, perhaps.  But I don't think it's even 50% of engines.  The engine you describe has too many coins in it to reliably draw the deck each and every turn, as it has enough treasures that it's likely to draw no Villages before drawing two terminals.
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Re: Dominion 101: What is an engine?
« Reply #3 on: October 12, 2017, 02:26:58 am »
+1

However, in general, your engine should be made up almost entirely of Action cards, if possible.
This is not good advice. I mean, it is true that most treasures that exist right now aren't good for engines, but that fact is purely coincidental. It's like saying "If possible, your engine should be made up almost entirely of cards that start contain the letter K". Maybe all cards with the letter K happen to be good engine cards, and the others are not, but that does not teach newbies anything about the game. And it might change in the future, just as the Treasure paradigm has: We now have Counterfeit, Charm, Fortune, Plunder, Coin of the Realm, all of which are best used in engines (and we even have some engine cards that want you to have basic treasures in your deck).
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Re: Dominion 101: What is an engine?
« Reply #4 on: October 12, 2017, 03:16:29 am »
+3

However, in general, your engine should be made up almost entirely of Action cards, if possible.
This is not good advice. I mean, it is true that most treasures that exist right now aren't good for engines, but that fact is purely coincidental. It's like saying "If possible, your engine should be made up almost entirely of cards that start contain the letter K". Maybe all cards with the letter K happen to be good engine cards, and the others are not, but that does not teach newbies anything about the game. And it might change in the future, just as the Treasure paradigm has: We now have Counterfeit, Charm, Fortune, Plunder, Coin of the Realm, all of which are best used in engines (and we even have some engine cards that want you to have basic treasures in your deck).

If possible your engine should consist mostly of King's Courts actually.
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Re: Dominion 101: What is an engine?
« Reply #5 on: October 12, 2017, 04:31:21 am »
0

I'm going to disagree with the idea that an engine "typically" draws your entire deck each turn.  Often, perhaps.  But I don't think it's even 50% of engines.

It's way above 80% of engines and the remaining decks all have Goons, Fortune or cost reduction in them.
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Re: Dominion 101: What is an engine?
« Reply #6 on: October 12, 2017, 05:38:09 am »
0

I'm going to disagree with the idea that an engine "typically" draws your entire deck each turn.  Often, perhaps.  But I don't think it's even 50% of engines.

It's way above 80% of engines and the remaining decks all have Goons, Fortune or cost reduction in them.

Is this differing play styles or differing definitions of engines? What percentage of total games would you guys say you end up drawing your deck each turn?
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Re: Dominion 101: What is an engine?
« Reply #7 on: October 12, 2017, 05:45:04 am »
0

I'm going to disagree with the idea that an engine "typically" draws your entire deck each turn.  Often, perhaps.  But I don't think it's even 50% of engines.

It's way above 80% of engines and the remaining decks all have Goons, Fortune or cost reduction in them.

Is this differing play styles or differing definitions of engines? What percentage of total games would you guys say you end up drawing your deck each turn?

More than 50℅ of all games.
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Re: Dominion 101: What is an engine?
« Reply #8 on: October 12, 2017, 08:10:08 am »
+1

This is pretty great for a basic article, and I think a lot of these comments could make it into a follow up article about the concepts of other kinds of engines. I think it’s important to start with this as your base so that you can branch out to sketchier low draw engines later, rather than starting at Big Money and adding Good Stuff.

But maybe change Draw to cycling, and point out that draw is far more effective cycling than not-draw? We’ve all seen magic Forum engines before, and using cycling instead of draw as a term accommodates those cantrip based engines we all love (since the payload also cycles you need less draw).
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Re: Dominion 101: What is an engine?
« Reply #9 on: October 12, 2017, 08:43:09 am »
0

An engine is a group of cards that do more together than they do individually.

Let's wait to define it further until after Nocturne is released.
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Re: Dominion 101: What is an engine?
« Reply #10 on: October 12, 2017, 08:44:25 am »
+1

Nice article.  I think this article could most be improved by linking to a video of a strong player building the engine on the First Game.  For some people, an engine isn't going to click until they see someone play it.

Once your engine is mostly drawing your entire deck, and has enough payload to gain more than one Province per turn, you should start grabbing some Victory cards.  Be careful, though: start buying Provinces too soon, and your engine will sputter, and you will lose.  But hold off buying Provinces too long, and your opponent will get more Victory cards than you, and you will lose.  Knowing exactly when to start doing each step is not an exact art, and will take some practice to get right.

There is nothing special about being able to gain 2 or more Provinces each turn.  In fact, I think it would be more helpful to suggest that players continue to add draw to supplement the stop cards they add to their deck while greening.

The usual phrase is to contrast "exact science" with "more of an art".
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Re: Dominion 101: What is an engine?
« Reply #11 on: October 12, 2017, 09:08:05 am »
0

I'm going to disagree with the idea that an engine "typically" draws your entire deck each turn.  Often, perhaps.  But I don't think it's even 50% of engines.

It's way above 80% of engines and the remaining decks all have Goons, Fortune or cost reduction in them.

Is this differing play styles or differing definitions of engines? What percentage of total games would you guys say you end up drawing your deck each turn?

More than 50℅ of all games.

I feel like I made a big skill jump once I wrapped my head around the fact that "draw your deck" means "no, like literally draw your whole deck every turn."
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Re: Dominion 101: What is an engine?
« Reply #12 on: October 12, 2017, 09:15:28 am »
0

I'm going to disagree with the idea that an engine "typically" draws your entire deck each turn.  Often, perhaps.  But I don't think it's even 50% of engines.

It's way above 80% of engines and the remaining decks all have Goons, Fortune or cost reduction in them.

Is this differing play styles or differing definitions of engines? What percentage of total games would you guys say you end up drawing your deck each turn?

More than 50℅ of all games.

I feel like I made a big skill jump once I wrapped my head around the fact that "draw your deck" means "no, like literally draw your whole deck every turn."

More like I kept losing to people who would end up drawing their deck. Learning the hard way, and that awful feeling where you see your opponent with no deck or discard pile when you can't do the same with your deck.
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Re: Dominion 101: What is an engine?
« Reply #13 on: October 12, 2017, 09:19:39 am »
+1

I don't know if this is a "common plateau" type thing or if it was just me but I distinctly remember having a mindset like "yeah yeah I get it, I wanna draw my deck. but once I can get to $8 for a couple turns in a row I'd be a greedy sucker not to just buy provinces at this point"
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Re: Dominion 101: What is an engine?
« Reply #14 on: October 12, 2017, 11:52:41 am »
0

I'm going to disagree with the idea that an engine "typically" draws your entire deck each turn.  Often, perhaps.  But I don't think it's even 50% of engines.

It's way above 80% of engines and the remaining decks all have Goons, Fortune or cost reduction in them.

Is this differing play styles or differing definitions of engines? What percentage of total games would you guys say you end up drawing your deck each turn?

Hrm... I guess I would say something closer to 30%.  Maybe it's differing play abilities.
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Re: Dominion 101: What is an engine?
« Reply #15 on: October 12, 2017, 01:02:31 pm »
+18

I'm going to disagree with the idea that an engine "typically" draws your entire deck each turn.  Often, perhaps.  But I don't think it's even 50% of engines.

It's way above 80% of engines and the remaining decks all have Goons, Fortune or cost reduction in them.

Is this differing play styles or differing definitions of engines? What percentage of total games would you guys say you end up drawing your deck each turn?

Hrm... I guess I would say something closer to 30%.  Maybe it's differing play abilities.

Draw your deck "each turn" is such a nice dream, I wish it could happen to me as much as Awaclus claims.

I'm not sure what the relevant thing to count is, should it be the % of games where you successfully draw the deck for X turns in a row (this percentage will be quite small even if X is some not huge number like 4-5), or games where you manage to draw the entire deck a few times period, or just games where you are aiming to draw your deck (often you only get to do it once or twice before the piles run out, but I'd still consider these full deck drawing engines)?

These are the last 18 decks I played in the tournament:
- Spice Merchant/Minstrel/Caravan/Replace engine (I drew my deck some turns, but not all, once the engine was going, I certainly was trying to draw my deck though)
- Donate/Duplicate not engine (Drew my deck after donating :) but did not build any engine here and just sort of muddled around getting green cards)
- Amb/Encampment/Wharf/Goons engine (eventually drawing deck each turn)
- Baker/Masq/Treasury/Legionary/HoP/Secret Passage/Mission/Legionary engine (never drew entire deck)
- Giant/Witch mess, not engine
- Overlord/Sentry/Legionary engine(or was it?) (drew my deck once I was trashed, but this stopped as soon as I was greening)
- Spice Merchant/Ironmonger/City Quarter/Hoard/Pillage engine mess (I drew my deck some turns but not consistently, I had to gain treasures to have any extra buys and it didn't work out, my opponent did not try to draw cards and won)
- Bonfire/IW/Ferry/Treasury/Peddler/Replace/Castles engine(or not?) (drew my deck after trashing, did not continue once greening started)
- Bandit/Junk Dealer/other stuff not engine
- Governor/Forager engine (Certainly possible to draw the deck consistently, not necessarily the right play every turn with your Governors)
- KC/Torturer/Pawn/Magpie/Mill/Expedition engine (Uh huh)
- Alchemist/Militia/Hireling/Minstrel/Counterfeit/Graverobber/Artisan engine (I got to a point where I was drawing the deck, my opponent did not build up that much draw and beat me)
- KC/Gear/Swamp Hag/Sea Hag/Mill/Royal Carriage/Moat/Vagrant/Graverobber engine (Think I only managed to draw the entire deck on the turn I ended it, maybe once before that. If I needed to have the game last longer I probably could have drawn the deck most turns because of Gear)
- Swindler/Alchemist/Lost City/Crossroads/Hamlet engine (It was possible, but hard to draw the entire deck here without trashing, my deck was wrecked by Swindler, my opponent drew a lot of their deck but not all of it consistently)
- Uni/WT/Ratcatcher/Advisor/Merchant/Hermit/Seaway engine (I drew my whole deck several turns)
- Urchin/Rats/Upgrade/Fishing Village/Chariot Race/Storyteller/Merchant Ship/Mountebank/Dominate engine (I drew the deck pretty consistently once cleaned up, but needed to find Storyteller to kick off so not every turn).
- IGG/Treasure Trove (I drew 0 cards and won, my opponent did Apo/Villa/Enchantress but no trashing so the deck would never get drawn consistently)
- City Quarter/Pawn/Upgrade/Chariot Race/Highway/Militia engine (I got to deck drawing fairly consistently, but dependent on having CQs in starting hand).

To me, drawing your deck is a great thing to target as a building goal, but it's not realistic to claim it always happens consistently.

Games played: 18
Engines (by my reckoning, I am counting the two questionable games as 0.5): 13
Not engines: 5
Held the entire deck in hand at least once: 13 (this includes 1 not engine and the two 0.5 engines)
Drew deck "consistently" (I am just going with my gut here): 6-8ish

Sorry this post is a mess!
« Last Edit: October 12, 2017, 03:52:57 pm by Mic Qsenoch »
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Re: Dominion 101: What is an engine?
« Reply #16 on: October 12, 2017, 04:30:51 pm »
+1

Thanks for all the feedback!  The key point of contention seems to be the deck drawing.  I would argue that being able to draw your entire deck should be seen as something you not only aspire to, but is achievable.  I've played many games with new players where they are astounded when I draw my entire deck, and wonder how I did it.  And I've drawn my entire deck in that First Game engine many times, but that might be a bias of playing with newer players - I usually get more than half of the Village pile, and enough Smithies and Markets to ensure I draw everything at least a few times.  It's probably not as viable against a competent player, but it's certainly possible.
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Re: Dominion 101: What is an engine?
« Reply #17 on: October 12, 2017, 05:32:16 pm »
+1

I really don't want this discussion to split off into a whole different thing, but
Quote
an engine will also require a card that gives at least +2 Actions
could maybe be changed to
Quote
an engine will also require a card that allows multiple terminals to be played per turn
or even just
Quote
an engine will usually also require a card that gives at least +2 Actions
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Re: Dominion 101: What is an engine?
« Reply #18 on: October 12, 2017, 05:39:21 pm »
+1

I really don't want this discussion to split off into a whole different thing, but

ftfy
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Re: Dominion 101: What is an engine?
« Reply #19 on: October 13, 2017, 07:14:45 am »
+6

I'm missing the sole cantrip engines, like the stack of Grand Markets or Higway/+Buy cantrip(Market Square, Market, ...) which can work without strong draw if there's adequate trashing.
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Re: Dominion 101: What is an engine?
« Reply #20 on: October 14, 2017, 01:37:04 am »
0

In tableau-building games you'd call an engine something that consistently (not necessarily constantly; an engine can start late in the game) provides VPs or something else that is important to win the game.
Usually that "dynamic" way of generating VPs stands in contrast to "static" VPs via something like buildings.

In deck-building games this static-dynamic trade-off is absent but I think the notion that an engine implies consistency, reliability, smoothness or however you wanna call it applies as well.
I also think that how you achieve the very repetition of a pattern is fairly irrelevant. Decks that heavily rely on Treasures usually green early and then have issues with all the junk, i.e. they behave differently in different phases of the game. But you could e.g. call a deck with lots of Silver due to Delve or Trader or Jack or whatever an engine as all the Silver smooth our your deck and you got enough to buy a Province each turn.
Now I am not arguing that one should call such decks an engine. I definitely don't. But one should keep in mind that such decks provide the same smoothness as a draw-your-entire-deck engine or the 8 Peddler cantrip decks assemble mentioned.
« Last Edit: October 14, 2017, 01:40:00 am by josh56 »
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Re: Dominion 101: What is an engine?
« Reply #21 on: October 14, 2017, 03:48:04 am »
+1

I also think that how you achieve the very repetition of a pattern is fairly irrelevant. Decks that heavily rely on Treasures usually green early and then have issues with all the junk, i.e. they behave differently in different phases of the game. But you could e.g. call a deck with lots of Silver due to Delve or Trader or Jack or whatever an engine as all the Silver smooth our your deck and you got enough to buy a Province each turn.
Now I am not arguing that one should call such decks an engine. I definitely don't. But one should keep in mind that such decks provide the same smoothness as a draw-your-entire-deck engine or the 8 Peddler cantrip decks assemble mentioned.
I think that is explicitly not how engines in Dominion work. Big Money decks green early because they can cope with green rather well. Engines green as late as possible because usually they fall apart once green cards are added. That is because in an engine, there are many tiny pieces that have to come together to make it work, and a small amount of stop cards can cause you to draw a dud.
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Re: Dominion 101: What is an engine?
« Reply #22 on: October 14, 2017, 06:21:32 am »
0

I also think that how you achieve the very repetition of a pattern is fairly irrelevant. Decks that heavily rely on Treasures usually green early and then have issues with all the junk, i.e. they behave differently in different phases of the game. But you could e.g. call a deck with lots of Silver due to Delve or Trader or Jack or whatever an engine as all the Silver smooth our your deck and you got enough to buy a Province each turn.
Now I am not arguing that one should call such decks an engine. I definitely don't. But one should keep in mind that such decks provide the same smoothness as a draw-your-entire-deck engine or the 8 Peddler cantrip decks assemble mentioned.
I think that is explicitly not how engines in Dominion work. Big Money decks green early because they can cope with green rather well. Engines green as late as possible because usually they fall apart once green cards are added. That is because in an engine, there are many tiny pieces that have to come together to make it work, and a small amount of stop cards can cause you to draw a dud.
As I tried to point out, that's a narrow Dominion-specific perspective that has little to do with the general use of the term engine in boardgame.
If I play a BM deck which adds Silvers while greening, thus compensating for the adding of green, that's a smoothly running engine. It's like playing Imperial Settlers or Race for the Galaxy and making X VPs each turn. How you achieve something is really not that important, what matters is that is reliable and works every turn.
That's more easy to achieve via Action cards that draw: if you always draw your entire deck you have as much consistency as possible. But it is also possible via having lots of Silver in your deck and buying a Province each turn (and perhaps gaining another Silver en passant).
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Re: Dominion 101: What is an engine?
« Reply #23 on: October 14, 2017, 02:37:40 pm »
0

I also think that how you achieve the very repetition of a pattern is fairly irrelevant. Decks that heavily rely on Treasures usually green early and then have issues with all the junk, i.e. they behave differently in different phases of the game. But you could e.g. call a deck with lots of Silver due to Delve or Trader or Jack or whatever an engine as all the Silver smooth our your deck and you got enough to buy a Province each turn.
Now I am not arguing that one should call such decks an engine. I definitely don't. But one should keep in mind that such decks provide the same smoothness as a draw-your-entire-deck engine or the 8 Peddler cantrip decks assemble mentioned.
I think that is explicitly not how engines in Dominion work. Big Money decks green early because they can cope with green rather well. Engines green as late as possible because usually they fall apart once green cards are added. That is because in an engine, there are many tiny pieces that have to come together to make it work, and a small amount of stop cards can cause you to draw a dud.
As I tried to point out, that's a narrow Dominion-specific perspective that has little to do with the general use of the term engine in boardgame.
If I play a BM deck which adds Silvers while greening, thus compensating for the adding of green, that's a smoothly running engine. It's like playing Imperial Settlers or Race for the Galaxy and making X VPs each turn. How you achieve something is really not that important, what matters is that is reliable and works every turn.
That's more easy to achieve via Action cards that draw: if you always draw your entire deck you have as much consistency as possible. But it is also possible via having lots of Silver in your deck and buying a Province each turn (and perhaps gaining another Silver en passant).
No; it's not possible with lots of action cards, as you need specific combinations of action cards to fire off your deck-drawing engine, and as soon as you add green that won't work anymore. The problem is that what you same is a factor for a (general) engine is more or less the opposite of what engine means in Dominion. What you're describing is either a slog or a Golden Deck.
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Re: Dominion 101: What is an engine?
« Reply #24 on: October 14, 2017, 04:48:29 pm »
+3

I also think that how you achieve the very repetition of a pattern is fairly irrelevant. Decks that heavily rely on Treasures usually green early and then have issues with all the junk, i.e. they behave differently in different phases of the game. But you could e.g. call a deck with lots of Silver due to Delve or Trader or Jack or whatever an engine as all the Silver smooth our your deck and you got enough to buy a Province each turn.
Now I am not arguing that one should call such decks an engine. I definitely don't. But one should keep in mind that such decks provide the same smoothness as a draw-your-entire-deck engine or the 8 Peddler cantrip decks assemble mentioned.
I think that is explicitly not how engines in Dominion work. Big Money decks green early because they can cope with green rather well. Engines green as late as possible because usually they fall apart once green cards are added. That is because in an engine, there are many tiny pieces that have to come together to make it work, and a small amount of stop cards can cause you to draw a dud.
As I tried to point out, that's a narrow Dominion-specific perspective that has little to do with the general use of the term engine in boardgame.

You're technically correct, but we're not talking about other board games here.  RFTG is a much, much different game.  Dominion engines don't do the same thing as many engines in other games, fine, but we're on a Dominion forum reading a Dominion article that will be put on a Dominion blog, so I don't think any reasonable reader is going to pipe up and say "But that's not what an engine looks like in RFTG."  Because the answer to that is "No shit, Sherlock."
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Re: Dominion 101: What is an engine?
« Reply #25 on: October 15, 2017, 01:14:50 am »
0

An engine is something that works reliably all the time. Be it an actual engine, a board game engine or a Dominion engine.
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Re: Dominion 101: What is an engine?
« Reply #26 on: October 15, 2017, 04:21:32 am »
+1

Regarding deck taxonomy, I think maybe a key distinction is this: if you were to replace each card in your deck with n copies of itself (for n=2 the starting deck becomes 14xCopper, 6xEstate), would you typically be drawing the same number of cards each turn, or the same proportion of your deck?

I haven't done the math, but I would assume that Smithy/BM draws the same 5-sometimes-8 cards if you double/triple/etc. the deck, and most conventional (village+smithy) engines continue drawing 100% of the deck when you double it, since drawing deck is a function of total +cards, having enough +actions to support that, and drawing those in the right order, all of which stay the same when you add more of everything while preserving proportions (I gut-sense). [hand-wavy justification-ish: sampling with and without replacement converge to the same limit when the thing sampled from grows to infinity. Variance decreases as n increases—the sum of more dice looks more bell-shaped and less flat.]

So my distinguishing criterion seems to do the right thing for typical BM and typical engine decks. Probably it also works for engines that draw 70-90% of the deck, e.g. 10xCity plus starting deck plus some Bridges—though I definitely would want to do the math here and verify that nothing weird happens when you double all the things.

The impact of drawing O(1) cards vs. Ω(n) cards is of course that your output on a typical turn is proportional to the average/total per-card output, respectively, and that changes how you build your deck. So even though I'm not running the deck-doubling thought experiment when analyzing a board, I probably am thinking through the implications of that math.

One open question: are there in-betweens? Are there decks where you draw something like Θ(sqrt n) or Θ(log n) as you double/triple/n-plicate your deck? What do they look like?

MQ raises both the trivial point that decks are not static over time (duh) and the non-trivial point that this makes "draws the deck" undefined unless we're talking about one or more points in time. For my O(1)-vs.-Ω(n)-criterion, "when you start greening" sounds like a good point in time, or else "at the maximum" (and please don't tell anyone that O(...) is a partial ordering)—these seem roughly to be what we mean when we try to distinguish between engines and non-engines. (I also read MQ's post as saying "there's quite a bit of gray area". I'm not addressing that here.)
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Re: Dominion 101: What is an engine?
« Reply #27 on: October 15, 2017, 02:11:44 pm »
+5

An engine is something that works reliably all the time. Be it an actual engine, a board game engine or a Dominion engine.
I mean that is just a random component of an engine. I have a spoon at home that works reliably all the time; that does not make it an engine.

According to wikipedia:
Quote
An engine is a device that converts energy in one form into mechanical energy.
So I guess in Dominion terms an engine is anything that makes your opponent sufficiently mad to topple over the table you are playing on.
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Re: Dominion 101: What is an engine?
« Reply #28 on: October 15, 2017, 02:21:28 pm »
0

One open question: are there in-betweens? Are there decks where you draw something like Θ(sqrt n) or Θ(log n) as you double/triple/n-plicate your deck? What do they look like?
I think draw.to-X engines with some Treasures would probably fit in here. You can draw your deck with like 4 Treasures, but with more you'll stop at some point.
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Re: Dominion 101: What is an engine?
« Reply #29 on: October 15, 2017, 09:43:43 pm »
0

An engine is...
"Engine" is a word with many meanings. But that's not important right now; in Dominion it's a term of art with a specific meaning.
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Re: Dominion 101: What is an engine?
« Reply #30 on: October 16, 2017, 01:01:20 pm »
+5

I haven't done the math, but I would assume that Smithy/BM draws the same 5-sometimes-8 cards if you double/triple/etc. the deck, and most conventional (village+smithy) engines continue drawing 100% of the deck when you double it, since drawing deck is a function of total +cards, having enough +actions to support that, and drawing those in the right order, all of which stay the same when you add more of everything while preserving proportions (I gut-sense).

Unfortunately, this doesn't work out in practice.  Here's a simple example to show it.

Suppose you have a simple draw-your-deck engine:
1x Village
1x Smithy
1x Woodcutter
3x Treasure

We'll define drawing the deck as having an empty deck and discard during your turn (which is being a little generous, since that doesn't guarantee that you get to play your woodcutter).  But with this simple deck, it's impossible not to draw it.  But now let's double it:

2x Village
2x Smithy
2x Woodcutter
6x Treasure

This deck only draws itself about 38% of the time.  If we triple it:

3x Village
3x Smithy
3x Woodcutter
9x Treasure

It's now literally impossible for this deck to draw itself.
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Re: Dominion 101: What is an engine?
« Reply #31 on: October 16, 2017, 01:18:37 pm »
+3

I haven't done the math, but I would assume that Smithy/BM draws the same 5-sometimes-8 cards if you double/triple/etc. the deck, and most conventional (village+smithy) engines continue drawing 100% of the deck when you double it, since drawing deck is a function of total +cards, having enough +actions to support that, and drawing those in the right order, all of which stay the same when you add more of everything while preserving proportions (I gut-sense).

Unfortunately, this doesn't work out in practice.  Here's a simple example to show it.

Suppose you have a simple draw-your-deck engine:
1x Village
1x Smithy
1x Woodcutter
3x Treasure

We'll define drawing the deck as having an empty deck and discard during your turn (which is being a little generous, since that doesn't guarantee that you get to play your woodcutter).  But with this simple deck, it's impossible not to draw it.  But now let's double it:

2x Village
2x Smithy
2x Woodcutter
6x Treasure

This deck only draws itself about 38% of the time.  If we triple it:

3x Village
3x Smithy
3x Woodcutter
9x Treasure

It's now literally impossible for this deck to draw itself.
This just goes to show that a deck with 50% basic treasures is probably not an engine. Your suggested deck is not an engine.
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Re: Dominion 101: What is an engine?
« Reply #32 on: October 16, 2017, 03:36:59 pm »
+1

An engine is something that works reliably all the time. Be it an actual engine, a board game engine or a Dominion engine.
I mean that is just a random component of an engine. I have a spoon at home that works reliably all the time; that does not make it an engine.

According to wikipedia:
Quote
An engine is a device that converts energy in one form into mechanical energy.
So I guess in Dominion terms an engine is anything that makes your opponent sufficiently mad to topple over the table you are playing on.

Amusingly, your definition there means that while the spoon isn't an engine, your arm is when it lifts the spoon.
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Re: Dominion 101: What is an engine?
« Reply #33 on: October 16, 2017, 04:13:03 pm »
+7

An engine is something that works reliably all the time. Be it an actual engine, a board game engine or a Dominion engine.

Clearly you’ve never worked on a car before. :)

No but seriously, your definition isn’t used by anyone else in the Dominion community. Our definition is for our game and is specifically useful for our game because of the way we use it. Let’s not make our communication shitty because you’re stubborn.
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Re: Dominion 101: What is an engine?
« Reply #34 on: October 16, 2017, 04:45:53 pm »
+1

An engine is something that works reliably all the time. Be it an actual engine, a board game engine or a Dominion engine.

Clearly you’ve never worked on a car before. :)

No but seriously, your definition isn’t used by anyone else in the Dominion community. Our definition is for our game and is specifically useful for our game because of the way we use it. Let’s not make our communication shitty because you’re stubborn.
I don't care if you are a sect member and cannot accept that the most general (easy to get lost in trivial details) attribute of an engine over all deck- and tableau-building games is reliability and consistency.
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Re: Dominion 101: What is an engine?
« Reply #35 on: October 16, 2017, 05:29:54 pm »
0

Unfortunately, this doesn't work out in practice.  Here's a simple example to show it.

Suppose you have a simple draw-your-deck engine:
1x Village
1x Smithy
1x Woodcutter
3x Treasure

We'll define drawing the deck as having an empty deck and discard during your turn (which is being a little generous, since that doesn't guarantee that you get to play your woodcutter).  But with this simple deck, it's impossible not to draw it.  ...

If we triple it:

3x Village
3x Smithy
3x Woodcutter
9x Treasure

It's now literally impossible for this deck to draw itself.
This just goes to show that a deck with 50% basic treasures is probably not an engine. Your suggested deck is not an engine.

To me, this example shows that a very thin deck is easier to draw all of than a multiplied version of that deck, because you need to draw fewer additional cards above your 5 starting cards to draw the whole deck.

The percentage of basic treasure in your deck that you can have while still having a high chance to draw your deck depends on the size of the deck and the strength of the draw available. 50% or higher basic treasure is consistent with having a high chance to draw the deck if the draw is good enough. For example, decks like 2 Margrave (with +Action token), 4 Gold, or 4 Margrave (with + Action token), 8 Gold draw themselves reliably.
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Re: Dominion 101: What is an engine?
« Reply #36 on: October 16, 2017, 05:44:12 pm »
0

An engine is something that works reliably all the time. Be it an actual engine, a board game engine or a Dominion engine.

I think people are getting hung up on this definition because you've made the requirement too strict. Very, very good Dominion engines can still fail to fire X% of the time.

If I fail to draw my entire deck with probability 0.01, does that mean I haven't built an engine?
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Re: Dominion 101: What is an engine?
« Reply #37 on: October 16, 2017, 07:02:47 pm »
+2

I don't care if you are a sect member

We don't look kindly on ad hominem attacks around these parts, mister.

Quote
(easy to get lost in trivial details)

Dude, that describes 80% of the discussion on this board and almost every relevant post in this thread.

Quote
most general... attribute of an engine over all deck- and tableau-building games is reliability and consistency.

We've already told you that you are technically correct, but that this definition doesn't apply to Dominion.

The most common attribute of worker placement games (ignoring the literal placing of workers) is that you get one action on your turn, barring rare exceptions, but oh wait! Here comes Manhattan Project, where that's totally untrue for most of the game.  Are you going to tell me it's not a worker placement game?

Dominion engines aren't necessarily reliable or consistent.  So they don't always fit the more general definition.  And that's all right!  If we all fit general definitions, life would be boring. 
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Re: Dominion 101: What is an engine?
« Reply #38 on: October 17, 2017, 10:26:36 am »
+2

To me, this example shows that a very thin deck is easier to draw all of than a multiplied version of that deck, because you need to draw fewer additional cards above your 5 starting cards to draw the whole deck.

The percentage of basic treasure in your deck that you can have while still having a high chance to draw your deck depends on the size of the deck and the strength of the draw available. 50% or higher basic treasure is consistent with having a high chance to draw the deck if the draw is good enough. For example, decks like 2 Margrave (with +Action token), 4 Gold, or 4 Margrave (with + Action token), 8 Gold draw themselves reliably.

Even this deck falls victim to the same principle.  The 2 Margrave (with +action) and 4 gold deck is 100% reliable.  Double it and it drops to 89%.  Triple it and you're at 76%.

In terms of combinatorics, as you increase the size of the deck (keeping the proportions the same), a smaller and smaller proportion of the possible starting hands has the cards that you need to kick off.  I've not yet quite wrapped my mind around why this should be the case in general.  I'm not sure if it's only due to having a fixed-size starting hand or if there are other combinatorics principles in play also.
« Last Edit: October 17, 2017, 10:28:28 am by ben_king »
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Re: Dominion 101: What is an engine?
« Reply #39 on: October 17, 2017, 10:56:20 am »
+3

Even this deck falls victim to the same principle.  The 2 Margrave (with +action) and 4 gold deck is 100% reliable.  Double it and it drops to 89%.  Triple it and you're at 76%.

In terms of combinatorics, as you increase the size of the deck (keeping the proportions the same), a smaller and smaller proportion of the possible starting hands has the cards that you need to kick off.  I've not yet quite wrapped my mind around why this should be the case in general.  I'm not sure if it's only due to having a fixed-size starting hand or if there are other combinatorics principles in play also.
The larger the deck you have, the more it becomes like a random walk.  Suppose that all the draw is from labs.  Draw a lab, that's one step forward; draw anything else, and it's one step back.  If the random walk ever reaches zero, then you dud.

So we have the question "What is the probability that a random walk will reach zero within a given number of steps?"  If your deck can exactly draw itself (not including the starting 5 cards), then the probability of dudding approaches 100%.  However, if you have a little bit of overdraw, the probability approaches something less than 100%.  (See this stack exchange question)
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Re: Dominion 101: What is an engine?
« Reply #40 on: October 17, 2017, 05:47:38 pm »
0

I don't care if you are a sect member
We don't look kindly on ad hominem attacks around these parts, mister.
And I don't look kindly upon exclusionary "we do and call things our way in our club so you either comply or STFU" games.


Quote
The most common attribute of worker placement games (ignoring the literal placing of workers) is that you get one action on your turn
That's a feature of many games which are not worker placement games and anything but a general feature of all worker placement games. For example in Caylus you first place several of your workers before you later get to execute the actions. In Tzolkin you leave the worker on the slot and execute the action in one of the following rounds.

The key feature of all worker placement games is that there is a competition for slots which are rival in their nature, i.e. me taking doing A makes it impossible for anybody else doing A this round, which makes the game more interactive than a Euro often is. Whether you take one or several actions per round, when they are executed and so on are details which differ over games.

Same in the case of engines. You can get lost in trivial details or care about the general stuff. I am definitely a fan of the latter, especially as the details folks pick out, as we just saw with your dubious worker placement definition, are often simply wrong.
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Re: Dominion 101: What is an engine?
« Reply #41 on: October 17, 2017, 07:29:30 pm »
+1

I don't care if you are a sect member
We don't look kindly on ad hominem attacks around these parts, mister.
And I don't look kindly upon exclusionary "we do and call things our way in our club so you either comply or STFU" games.

This is, quite literally, exactly what you are doing. You are saying “this is my definition I use in a completely different context and everyone else who uses any other definition is wrong”.

We’re giving you the definition *basically everyone who plays Dominion* uses. There aren’t dozens of threads by other board gaming fans here talking about your specific definition, even though we have dozens of people who play those games. I really don’t think it is nearly as common or universal across all similar games as you’re implying, honestly. But in any case, we are saying, this is what everyone means when everyone says it here, and that’s not going to change because one dude who plays a bunch of completely different games uses it completely differently.

What’s your end game here? What do you hope to get out of this?
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Re: Dominion 101: What is an engine?
« Reply #42 on: October 17, 2017, 08:05:52 pm »
0

I don't care if you are a sect member
We don't look kindly on ad hominem attacks around these parts, mister.
And I don't look kindly upon exclusionary "we do and call things our way in our club so you either comply or STFU" games.

We’re giving you the definition *basically everyone who plays Dominion* uses.

To be fair, I don't think f.ds is representative of "basically everyone who plays Dominion." I happen to think it's representative of those who like to exhaustively discuss Dominion strategy. But then again, maybe someone from another Dominion strategy sect would disagree.
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Re: Dominion 101: What is an engine?
« Reply #43 on: October 17, 2017, 08:49:07 pm »
0

I don't care if you are a sect member
We don't look kindly on ad hominem attacks around these parts, mister.
And I don't look kindly upon exclusionary "we do and call things our way in our club so you either comply or STFU" games.

This is, quite literally, exactly what you are doing. You are saying “this is my definition I use in a completely different context and everyone else who uses any other definition is wrong”.

We’re giving you the definition *basically everyone who plays Dominion* uses. There aren’t dozens of threads by other board gaming fans here talking about your specific definition, even though we have dozens of people who play those games. I really don’t think it is nearly as common or universal across all similar games as you’re implying, honestly. But in any case, we are saying, this is what everyone means when everyone says it here, and that’s not going to change because one dude who plays a bunch of completely different games uses it completely differently.

What’s your end game here? What do you hope to get out of this?
I never play exclusionary games, I never claim to be right just because I represent some group opinion and I never speak for anybody but myself.
By the way, I find it revealing that you seem to imply that playing boardgames besides Dominion is a liability.

Anyway, back to the actual topic. Of course I never use the term engine when playing Dominion for the consistent Silver-gaining decks I mentioned which are pretty smooth and reliable. But if you zoom out and think about what engines are really about, that it is not about Treasures vs. Actions (e.g. Relic can be a better engine piece than Lighthouse), then calling such smooth decks engines would make sense.
« Last Edit: October 17, 2017, 08:55:32 pm by josh56 »
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crj

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Re: Dominion 101: What is an engine?
« Reply #44 on: October 17, 2017, 09:55:52 pm »
+13

And I don't look kindly upon exclusionary "we do and call things our way in our club so you either comply or STFU" games.
It's normal for specialist domains to have specialist vocabulary. It's not exclusionary, it's just pragmatic.

Please, go and tell software engineers that a map is anything that shows you where things are rather than specifically an associative array. Tell a driver in the UK that an "indicator" is anything that indicates anything and can't be used in the specialised sense of a turn signal, or a chemist they can't use "indicator" specifically to mean something that indicates pH. Insist to a chef that "mise en place" can refer to putting anything where it ought to be. Tell an oceanographer that a gyre is anything that goes round in circles. Demand that climbers accept that many large-ish vertical things are big walls, not just climbs which will take more than one day to complete.

Indeed, go tell automotive engineers that the entire vehicle is an engine.

I'm sure they'll all be delighted to hear from you.
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Re: Dominion 101: What is an engine?
« Reply #45 on: October 17, 2017, 10:12:12 pm »
+6

Civility aside, I think these kind of unproductive discussions are mostly a natural and inevitable conclusion on deciding to try and write about terminology.

I'm also convinced that the majority of time wasted with having "less exact" terminology is wasted by those who are adamant on defining a single set of terminology -- if we could all just live with messy terms that mean different things to different people, I don't think we lose that much ability to communicate and I think we do lose a lot of heated yet inconsequential discussions.
« Last Edit: October 18, 2017, 12:41:09 am by O »
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Cave-o-sapien

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Re: Dominion 101: What is an engine?
« Reply #46 on: October 17, 2017, 11:54:55 pm »
0

Civility aside, I think these kind of unproductive discussions are mostly a natural and inevitable conclusion on deciding to try and write about terminology.

I'm also convinced that the majority of time wasted with have "less exact" terminology is wasted by those who are adamant on defining a single set of terminology -- if we could all just live with messy terms that mean different things to different people, I don't think we lose that much ability to communicate and I think we do lose a lot of heated yet inconsequential discussions.

But we would also lose this comment, which was awesome:

It's normal for specialist domains to have specialist vocabulary. It's not exclusionary, it's just pragmatic.

Please, go and tell software engineers that a map is anything that shows you where things are rather than specifically an associative array. Tell a driver in the UK that an "indicator" is anything that indicates anything and can't be used in the specialised sense of a turn signal, or a chemist they can't use "indicator" specifically to mean something that indicates pH. Insist to a chef that "mise en place" can refer to putting anything where it ought to be. Tell an oceanographer that a gyre is anything that goes round in circles. Demand that climbers accept that many large-ish vertical things are big walls, not just climbs which will take more than one day to complete.

Indeed, go tell automotive engineers that the entire vehicle is an engine.

I'm sure they'll all be delighted to hear from you.
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Re: Dominion 101: What is an engine?
« Reply #47 on: October 18, 2017, 01:19:04 am »
+2

I think we do lose a lot of heated yet inconsequential discussions.
But that's what makes f.ds fun!
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Re: Dominion 101: What is an engine?
« Reply #48 on: October 18, 2017, 01:24:47 am »
+3

I think we do lose a lot of heated yet inconsequential discussions.
But that's what makes f.ds fun!

Wait I just described FDS mafia...
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Re: Dominion 101: What is an engine?
« Reply #49 on: October 18, 2017, 08:28:04 am »
0

And I don't look kindly upon exclusionary "we do and call things our way in our club so you either comply or STFU" games.
It's normal for specialist domains to have specialist vocabulary.
I referred to the exclusionary game that poster played, not to specialist language. Not that engine is Dominion-specific language in the first place, as I pointed out it is used more generally in virtually all tableau- and deckbuilding games. Of course if you consider Dominion to be something that exists on its own plane, as something that should never be compared to other boardgames, such a perspective is not something you would appreciate. Obviously I have a different view and always, mostly involuntarily, compare boardgames with each other when I play them.
« Last Edit: October 18, 2017, 08:31:25 am by josh56 »
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crj

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Re: Dominion 101: What is an engine?
« Reply #50 on: October 18, 2017, 09:37:13 am »
+4

Not that engine is Dominion-specific language in the first place
Yes, "engine" is Dominion-specific language.
Quote
it is used more generally in virtually all tableau- and deckbuilding games
The term "engine" also has a diversity of other, less specific, meanings. But when talking about Dominion specifically, it has a Dominion-specific meaning.

Why are you finding this so hard to understand or accept? You could, if you really wanted, suggest that the Dominion-specific meaning is unhelpful or misguided in some way, but you seem to be trying to say "Engine" doesn't have a Dominion-specific meaning.

You're wrong; it does.
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Re: Dominion 101: What is an engine?
« Reply #51 on: October 18, 2017, 10:04:07 am »
+2

As far as I know, Dominion is unique among deckbuilding games in having a static tableau.  All the other deckbuilders I've seen have a "center row" of sorts where a selection of cards is presented, and once one is taken, another randomly replaces it from a shuffled deck.  It'd be like playing Dominion without a Kingdom, but everyone has a Princed Black Market.

What this means is that it's a lot easier to make a consistent engine in Dominion than, say, Ascension or Legendary.  In the former, you can plan out your strategy from the get-go, whereas in the latter, you have to scrounge from the scraps that get thrown out, hopefully before anyone else grabs them.
« Last Edit: October 18, 2017, 10:05:46 am by werothegreat »
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Re: Dominion 101: What is an engine?
« Reply #52 on: October 18, 2017, 10:45:06 am »
+1

I don't even know what it means to say a Dominion engine is "reliable" and "consistent".  Like, are reliability and consistency two different things, or are they just redundant synonyms?  And it seems to me that engines can be less consistent than a plain old Big Money deck.  Engines can dud, which produces a large variance between turns.  Big Money decks, on the other hand, are supposed to be robust to card order.
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Re: Dominion 101: What is an engine?
« Reply #53 on: October 18, 2017, 05:08:22 pm »
0

Not that engine is Dominion-specific language in the first place
Yes, "engine" is Dominion-specific language.
The term engine is used in other games.
As I already said, it is fine to have a Dominion-is-the-only-game-in-the-world perspective but I prefer a view that focuses on the commonalities among different games.


As far as I know, Dominion is unique among deckbuilding games in having a static tableau.
Nightfall also has draftable cards which are available to everybody without changing throughout the entire game. I am not a fan of the Star Realms like dynamic tableaus in deck-building; as you pointed out they usually lead to less strategic and more random play.
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Re: Dominion 101: What is an engine?
« Reply #54 on: October 18, 2017, 05:23:33 pm »
+1

The term engine is used in other games.
As I already said, it is fine to have a Dominion-is-the-only-game-in-the-world perspective but I prefer a view that focuses on the commonalities among different games.

Why do you think that it needs to mean the same thing in all games?
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Re: Dominion 101: What is an engine?
« Reply #55 on: October 19, 2017, 07:34:41 am »
+2

Unfortunately, this [definition of an engine] doesn't work out in practice.  [Counterexample: Village/Smithy/Woodcutter/3xTreasure, times 1, 2 and 3]

This just goes to show that a deck with 50% basic treasures is probably not an engine. Your suggested deck is not an engine.

To me, this example shows that a very thin deck is easier to draw all of than a multiplied version of that deck, because you need to draw fewer additional cards above your 5 starting cards to draw the whole deck.

The percentage of basic treasure in your deck that you can have while still having a high chance to draw your deck depends on the size of the deck and the strength of the draw available. 50% or higher basic treasure is consistent with having a high chance to draw the deck if the draw is good enough. For example, decks like 2 Margrave (with +Action token), 4 Gold, or 4 Margrave (with + Action token), 8 Gold draw themselves reliably.

Even this deck falls victim to the same principle.  The 2 Margrave (with +action) and 4 gold deck is 100% reliable.  Double it and it drops to 89%.  Triple it and you're at 76%.

In terms of combinatorics, as you increase the size of the deck (keeping the proportions the same), a smaller and smaller proportion of the possible starting hands has the cards that you need to kick off.  I've not yet quite wrapped my mind around why this should be the case in general.  I'm not sure if it's only due to having a fixed-size starting hand or if there are other combinatorics principles in play also.

The larger the deck you have, the more it becomes like a random walk.  Suppose that all the draw is from labs.  Draw a lab, that's one step forward; draw anything else, and it's one step back.  If the random walk ever reaches zero, then you dud.

So we have the question "What is the probability that a random walk will reach zero within a given number of steps?"  If your deck can exactly draw itself (not including the starting 5 cards), then the probability of dudding approaches 100%.  However, if you have a little bit of overdraw, the probability approaches something less than 100%.  (See this stack exchange question)

I'm happy to see that my comment inspired a bit of discussion (of the civil kind to boot, woop!). I had overlooked the effect of the starting hand. I had a gut sense that a random walk might be a useful way of modelling deck draw. I think I phrased my criterion in terms of number of cards drawn, not probability of drawing all the cards, which is different, but hey, it's still interesting that overdraw is necessary to get the dud probability below 100% in this model.
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Re: Dominion 101: What is an engine?
« Reply #56 on: October 19, 2017, 07:28:14 pm »
0

Yes, "engine" is Dominion-specific language.
The term engine is used in other games.
That's irrelevant.
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Re: Dominion 101: What is an engine?
« Reply #57 on: October 19, 2017, 07:38:54 pm »
0

The larger the deck you have, the more it becomes like a random walk.  Suppose that all the draw is from labs.  Draw a lab, that's one step forward; draw anything else, and it's one step back.  If the random walk ever reaches zero, then you dud.

So we have the question "What is the probability that a random walk will reach zero within a given number of steps?"  If your deck can exactly draw itself (not including the starting 5 cards), then the probability of dudding approaches 100%.  However, if you have a little bit of overdraw, the probability approaches something less than 100%.  (See this stack exchange question)

I'm happy to see that my comment inspired a bit of discussion (of the civil kind to boot, woop!). I had overlooked the effect of the starting hand. I had a gut sense that a random walk might be a useful way of modelling deck draw. I think I phrased my criterion in terms of number of cards drawn, not probability of drawing all the cards, which is different, but hey, it's still interesting that overdraw is necessary to get the dud probability below 100% in this model.

If you can only draw the deck exactly, as it gets bigger and bigger your chance to draw the whole deck decreases towards zero. But a "dud" usually is used to mean a bad turn. Referring to any hand that does not draw the entire deck as a "dud" implies that a turn that doesn't draw the deck is bad. If you have a large deck and you draw almost all of it, that is probably a great turn. So the average number of (non-drawing) cards in hand in line with what you had initially proposed may be a better way to conceptualize the strength of deck.
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trivialknot

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Re: Dominion 101: What is an engine?
« Reply #58 on: October 19, 2017, 09:07:22 pm »
+1

The larger the deck you have, the more it becomes like a random walk.  Suppose that all the draw is from labs.  Draw a lab, that's one step forward; draw anything else, and it's one step back.  If the random walk ever reaches zero, then you dud.

So we have the question "What is the probability that a random walk will reach zero within a given number of steps?"  If your deck can exactly draw itself (not including the starting 5 cards), then the probability of dudding approaches 100%.  However, if you have a little bit of overdraw, the probability approaches something less than 100%.  (See this stack exchange question)

I'm happy to see that my comment inspired a bit of discussion (of the civil kind to boot, woop!). I had overlooked the effect of the starting hand. I had a gut sense that a random walk might be a useful way of modelling deck draw. I think I phrased my criterion in terms of number of cards drawn, not probability of drawing all the cards, which is different, but hey, it's still interesting that overdraw is necessary to get the dud probability below 100% in this model.

If you can only draw the deck exactly, as it gets bigger and bigger your chance to draw the whole deck decreases towards zero. But a "dud" usually is used to mean a bad turn. Referring to any hand that does not draw the entire deck as a "dud" implies that a turn that doesn't draw the deck is bad. If you have a large deck and you draw almost all of it, that is probably a great turn. So the average number of (non-drawing) cards in hand in line with what you had initially proposed may be a better way to conceptualize the strength of deck.
Yeah, that's a good point.  If you draw like a hundred cards out of two hundred, it's hard to see that as a dud.  Uh let's just call it an early termination.

By my reckoning, if you're overdrawing slightly, then the average number of cards you draw increases as O(N).  This is easy to prove, because as I already argued, there's a nonzero probability p of drawing everything.  So the average number of cards you draw is at least p*N.

On the other hand, if you have no overdraw, then the math is difficult.  After playing around with it for a while, I think it's still O(N).  Even if the probability of early termination approaches 1, it approaches 1 really really slowly.
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Beyond Awesome

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Re: Dominion 101: What is an engine?
« Reply #59 on: November 06, 2017, 11:45:18 pm »
+2

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Re: Dominion 101: What is an engine?
« Reply #60 on: November 07, 2017, 12:02:20 am »
+1

It would be great if when the article says "Cellar, Moat, Merchant, Village, Workshop, Militia, Remodel, Smithy, Market, Mine", you link to the pages for these cards on the Wiki so that the reader can easily find what these cards do. 
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Re: Dominion 101: What is an engine?
« Reply #61 on: November 07, 2017, 01:52:28 pm »
+4

It would be great if when the article says "Cellar, Moat, Merchant, Village, Workshop, Militia, Remodel, Smithy, Market, Mine", you link to the pages for these cards on the Wiki so that the reader can easily find what these cards do.

I will do that. I meant to add the hyperlinks but forgot.
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jonaskoelker

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Re: Dominion 101: What is an engine?
« Reply #62 on: November 11, 2017, 05:02:33 pm »
0

If you have no overdraw, then the math is difficult.  After playing around with it for a while, I think it's still O(N).  Even if the probability of early termination approaches 1, it approaches 1 really really slowly.
Care to share the math? I would love to see it.

Related, is the following an engine board? At the end of the game, off of 5xLab, 6xWarehouse and 3xStables, Qvist can draw 37 cards (plus the starting 5) out of 49 total. This requires discarding 3xCopper and 18 cards of his choice (he has 5xColony, 3xEstate, 3xTunnel and 5 ruins, so that's 16 blanks). Adam's deck is similar. I lean towards saying yes, this is an engine, although a somewhat peculiar one.


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trivialknot

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Re: Dominion 101: What is an engine?
« Reply #63 on: November 11, 2017, 06:27:02 pm »
0

If you have no overdraw, then the math is difficult.  After playing around with it for a while, I think it's still O(N).  Even if the probability of early termination approaches 1, it approaches 1 really really slowly.
Care to share the math? I would love to see it.
Okay, here’s how I did it.  Suppose we have a balanced random walk starting from origin.  It will eventually either reach +n or -n, each with probability 1/2.  The expected number of steps required is O(n^2).

So let’s say that the random walk starts from position 5, and it terminates if it ever reaches 0.  Well there’s a 1/2 probability it will reach 10 first, and 1/2 probability it will reach 0 first, and this takes O(5^2) steps.  If it reaches 10 first, then after O(10^2) steps, it will either reach 0 or 20 first.  And if it reaches 20 first then we wait another O(20^2) steps, and so on.

So if we continue this process, the expected time before terminating is O(5^2) + O(10^2)/2 + O(20^2)/4 + ...  This series diverges..  So even though an engine without overdraw will eventually terminate in an infinite deck, the expected time to terminate is infinite.
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Re: Dominion 101: What is an engine?
« Reply #64 on: November 14, 2017, 02:49:00 pm »
0

Okay, here’s how I did [the math].
Nice, thanks :)

O(10^2) = O(1) but I know what you mean. Open questions, at least in my head: is the constant hidden by O(⋅) the same for all terms? Does it matter?
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trivialknot

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Re: Dominion 101: What is an engine?
« Reply #65 on: November 14, 2017, 03:31:52 pm »
0

O(10^2) = O(1) but I know what you mean. Open questions, at least in my head: is the constant hidden by O(⋅) the same for all terms? Does it matter?
Yeah that math notation is not really accurate.  I was on a mobile device at the time and trying to be brief.  My assertion that it takes O(n^2) implies that the constant hidden by O(⋅) converges to a constant for large n.  Although, I don't actually know how to prove the O(n^2) assertion.  I was just thinking in terms of a diffusive process, and thinking back to my statistical mechanics classes.

I think this is a fairly interesting problem that could probably be understood within the theory of phase transitions.  I just don't have the time to think it through.  Also, I'm skeptical of the relevance to Dominion anyway.  Real decks aren't infinite in size.
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Re: Dominion 101: What is an engine?
« Reply #66 on: November 14, 2017, 04:27:18 pm »
0

My assertion that it takes O(n^2) implies that the constant hidden by O(⋅) converges to a constant for large n.
I think you need Θ(⋯) for that.

Consider 1/(2^n): that's O(1), but sum(c for k ∈ ℕ) is divergent while sum(1/(2^k) for k ∈ ℕ) is not, where c is any non-zero constant.

Also, I'm skeptical of the relevance to Dominion anyway.  Real decks aren't infinite in size.
Sure. The context of this is me proposing that we use "draws O(1) cards" vs. "draws Θ(n) cards" to distinguish engines and non-engines. Just like money density math and computer simulations give very precise answers to somewhat wrong questions, my criterion would give a well-defined, rigorous and very precise criterion which would divide decks more-or-less-approximately between engines and non-engines.

The fact that the only infinite decks occur in thought experiments and the calculations in my math wouldn't make it bad at distinguishing between engines and non-engines. (Maybe something else, such as its low resolution, would.)

So, just because there are no infinite nails doesn't mean you can't hammer in the finite ones with the handle of my high-precision screwdriver ;)
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Re: Dominion 101: What is an engine?
« Reply #67 on: November 14, 2017, 08:44:49 pm »
0

I work in condensed matter physics, not math, so I'm not familiar with the distinction between O() and Θ().  :P

Incidentally, the theory of phase transitions also assumes a system of infinite size.  Well say I have a cup of water, that's about 10^23 molecules, it's practically infinite, right?  And if you had a deck of 10^23 cards I think phase transition theory would apply there too.  I'm more skeptical about applying it to a deck of 20 cards.  But hey, 20 is still >> 1, so I maybe I'm being overly cautious.  I definitely don't think it applies to the 5-card golden deck though.
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Re: Dominion 101: What is an engine?
« Reply #68 on: November 15, 2017, 12:38:44 pm »
+1

I work in condensed matter physics, not math, so I'm not familiar with the distinction between O() and Θ().  :P
I don't know that's it's taught in math curricula, but it's a staple of computer science.

O(⋅) is a set of functions (typically from ℕ to ℝ). f is in O(g) if there exists a c and an N such that for all n > N, f(n) ≤ c*g(n). Loosely speaking, g (eventually) grows faster than f.

Θ(⋅) is a set of functions. f is in Θ(g) if f is in O(g) and g is in O(f). They grow equally quickly.

Examples: n^k is O(n^(k+d)) for constant k and any d > 0. In particular, sqrt(n) is O(n) and n is O(n^2).

O(⋅) induces a weak partial ordering. Θ(⋅) is the corresponding equivalence relation ("both x ≤ y and y ≤ x").

It's useful for analyzing the time and space usage of algorithms in the abstract. If one e.g. sorting algorithm takes O(n log n) time and another takes O(n^2) time to sort n things, the latter might run faster on your computer than the former runs on mine, if your computer is a constant factor faster than mine and n is small enough, but this doesn't really show that the former isn't preferable. Ignoring that constant factor (in cases where it isn't relevant) is one motivation for using this concept.

(OTOH, constants matter. While Fibonacci heaps are useful for Dijkstra's shortest path—in theory, using O() analysis—in practice a bog standard left-packed-tree-in-an-array heap is faster, at least for data that all fits in memory simultaneously.)
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Re: Dominion 101: What is an engine?
« Reply #69 on: November 16, 2017, 06:36:51 pm »
+3

So the math about a deck of exactly $n$ labs and $n$ coppers is wrong.  After playing around with this for awhile, it is $\Theta(\sqrt{n})$. Your argument that it is infinite in an infinite deck only implies that it is greater than $O(1)$, but not that it is necessarily $\Theta(n)$.

Here's a rough proof:
We can think of the ordering of the deck as a dyck path from $(0,0)$ to $(n,n)$, where going up represents drawing a lab, and going right represents drawing a copper. Falling below the diagonal is equivalent to terminating. Since there are ${2n \choose n}$ ways to shuffle the deck, and $C_n={2n \choose n}/(n+1)$ such paths that stay above the diagonal, so the propability of drawing the whole deck is $1/(n+1)$.

Now consider the probability of drawing any particular number of cards $2k$. First, there must have been exactly $k$ labs and $k$ coppers before that point, and they must be in an order that lets you draw all of them. The probability of there being exactly $k$ of each is $\Theta(1/k)$. This is because as long as $k$ is a little less than $n$, the draws are mostly independent, and thus look like a binomial distribution, which has standard deviation $\Theta(k)$. From the argument before about the whole deck, the probability that this intital segment is in the right order to draw all of it is $\Theta(1/k)$, which means the probability of drawing exactly $2k$ cards is $\Theta(1/k^{3/2)})$.

To find the EV, we thus sum up $\Theta(k/(k^{3/2}))$ for $k$ from 1 to $n$, to get $\Theta(\sqrt(n))$

I have also found explicit values up to $n=5000$ and they are definitely growing with $\sqrt{n}$
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trivialknot

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Re: Dominion 101: What is an engine?
« Reply #70 on: November 16, 2017, 07:17:40 pm »
+1

Since there are ${2n \choose n}$ ways to shuffle the deck, and $C_n={2n \choose n}/(n+1)$ such paths that stay above the diagonal, so the propability of drawing the whole deck is $1/(n+1)$.
Oh, sweet, you found an explicit formula.  I'm not sure how you found C_n, but I guess once you have it you can just prove it by induction.

Now consider the probability of drawing any particular number of cards $2k$. First, there must have been exactly $k$ labs and $k$ coppers before that point, and they must be in an order that lets you draw all of them. The probability of there being exactly $k$ of each is $\Theta(1/k)$.
Was this a typo where you meant $\Theta(1/\sqrt{k})$?  With this correction, I follow and agree with the rest of the argument.

So it appears that I was correct to say that the number of cards you draw diverges, but I was incorrect to say it was O(n).  That's funny, because earlier in the thread, people were wondering if there exists a "hybrid" deck where the number of cards you draw is more than Θ(1) but less than Θ(n).  The hybrid deck was right in front of us all along, in the form of an engine without overdraw.
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mad4math

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Re: Dominion 101: What is an engine?
« Reply #71 on: November 21, 2017, 04:21:15 pm »
+1

Yes that was supposed to be $\Theta(1/\sqrt{k})$. C_n is just the catalan numbers.
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ThetaSigma12

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Re: Dominion 101: What is an engine?
« Reply #72 on: November 21, 2017, 05:13:05 pm »
+2

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