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[jomini]

Nice work on the table! I think an additional column might be interesting:

Card	First play	Additional plays
Embassy	9	0
Warehouse	7	6, 5, 4, ...
Young Witch	6	0
Inn	6	5, 4, 3, ...
Vault	6	0
Hamlet	5	5
Oasis	5	4, 3, 2, ...
Horse Traders (attacked)	5	0
Navigator	5	0
Cartographer	4	4
Minion	4	3
Cellar	4	3, 2, ...
Harvest	4	0
Tactician	4	0
Secret Chamber	4	0
Horse Traders (unattacked)	4	0
Lookout	3	3
Oracle	2	0
Spy	1	1
Scrying Pool	1	1
Duchess	1	0

Obviously this is not the final word in how good each enabler is, since the cards actually, you know, DO something besides enable Tunnel, but it may be helpful in thinking about, for instance, why Cartographer/Tunnel is better than Vault/Tunnel, even though Vault has a bigger pool size AND is generally a better card.

I think your second column is off. Yes you need +actions for some of these, but they aren't that hard to setup.

For instance, the second play of vault searches through 2 new cards (the +2 you've drawn) to find the the tunnel. Also, warehouse looks at 7 the first time because you have 4 cards in hand and 3 on top deck; from thence onwards warehouse searches 3 cards at a time (barring corner cases where you have so many tunnels that you can't discard them all on the first pass). Young witch, like vault, searches two new cards on each subsequent play. Oasis looks at at only 1 new card for each subsequent play. Inn, like oasis only searches 2 new cards on sequent plays. Lastly, Secret Chamber (attacked) allows you to search through 6 cards as you can pull off the top two cards of the deck and swap them out so your search space is larger (e.g. tunnel/secret chamber can be awesome if there as discard attack going around as you can get sequences like milita - reveal SC - search 6 cards & find a tunnel, put the tunnel into hand and the SC back onto deck - discard tunnel & something and have SC ready for the next hand).

I'd also argue that second play of tactician should have something like 9 as you can go double tactician and have monster gold gaining turns.

Jack should be included with a search space of 1.


Overall, I'd think you'd have two lists: cards that enable tunnel with a +action and cards that don't. They play very differently.

[mischiefmaker]

You're correct; the additional play column should only be the number of new cards in the search space. I modified the table to reflect this. The new table looks pretty good on a pure "how good is this combo at gaining Gold" level if you order it by the sum of the two columns -- it doesn't, of course, address how good the deck will be overall, but it seems useful as a tool to understand how good the enablers are relative to each other.

[jomini]

I still think you should have separate entry of 6 for secret chamber attacked (0 on the second play). Let's say the attack is a discard attack, then you get to look at 6 other cards and put any tunnels into hand to discard the tunnels. Clearly, in this case secret chamber can look at 6 cards to discard tunnels. Suppose though you just have a cursing attacking like witch. Still, you can reveal your secret chamber, and look at the six cards. You then have the choice of putting a tunnel & secret chamber (if found) into your hand or on deck. This then allows you to discard the tunnel with the secret chamber giving an attacked secret chamber, regardless of the nature of the attack a search space of six.

I still say that for a number of these cards you can easily go engine building. Embassy, for instance allows for insanely reliable engines to be built and throw in tunnels to get some massive payouts. Two plays of embassy looks at 14 cards ... i.e. the entire deck. With hamlet or worker's village I can see pretty good incentive to set that engine up.

[mischiefmaker]

I left Secret Chamber (attacked) off the list for simplicity's sake, because it's complicated. You are correct that an attacked hand has a search space of 6, but if you don't find a Tunnel, you have the option of putting the Secret Chamber and a non-Tunnel card back on the deck for the next hand, reaching another 3 cards (unattacked) or 5 cards (attacked) but at the cost of delaying the search a turn. I couldn't figure out a way to represent that in the table that I was happy with so I just left it off.

I agree that Embassy can build reliable engines, but I don't agree that an Embassy/WV/Tunnel deck is worth building. When are you going to buy those Worker's Villages? Are you intending to build up to double-Province buys? I have a hard time believing you're going to get there fast enough to beat straight Embassy/Tunnel, and that's not even considering that it's tactically much harder to build that engine than it is to play the simple combo.

Hamlet...maybe, since Hamlet also activates Tunnel, and is much cheaper to acquire. But I'm skeptical.

[jomini]

Well in that case you could just say a range of 6-11* or 6 ... 9* ... 11 for secret chamber(attacked). With a little note next to the star saying that for these entries we are noting the effect on a subsequent hand?

As far as engines go, well opening hamlet/embassy on a 5/2 is insanely effective for setting up tunnels. If I get another 5 or 6 coin hand, what else exactly is going to be better to spend it on than more embassies? If I get a 7 coin hand with a +buy shot from a hamlet, of course I'm going to go hamlet/embassy. Likewise 10s and 13's (quite possible with gold rolling in) are going to help engine build.

As far as worker's village goes, well for a start there are colony boards which gives you a lot more time to accumulate gold & the possibilities of double colony are out there (double embassy/WV can search the entire deck and has a decent shot of double tapping tunnels; getting to 22 coin takes a good bit of gold/plat, but you can gain the gold quick enough & mix in some plats for something  like a 9 card hand - sifted out of 12 - with a 2 plats, 3 golds, and 3 coppers works). Another shot would, be a silver/remodel opening where you buy an embassy, remodel an estate to a tunnel, buy a tunnel, and buy either a WV or a second embassy (and then remodel to a WV). This can then allow you to do something like WV -> embassy -> embassy -> buy a province & WV. In turn that can set up double province hands (via remodel) or even double province & duchy. Of course now that you have a +buy you can afford to end the game with an even split of the provinces & nab a tie breaker estate or remodel an engine card into a duchy to break a tie.

And another time engine building comes out is when you have a slow attacking game that doesn't flip tunnels. Prime candidate being cut purse, though things like ghost ship also can slow the game down without enabling tunnels too much),  where you can linger forever without hitting 5 (particularly in 3 or 4 player games where it is just brutal to build up to good hands). So I have my two tunnels, my cut purse, some silver and I come across yet another 4 coin hand, why exactly wouldn't I go for WV?

Really, it is not that hard to chain two copies of these together. All you need is throne room and a reason to make it useful. For instance embassy/TR gives you a huge search space, and is much better for your deck that most 4s once you have enough tunnels. Again, I just sort the list into two where ones that give +action are grouped and ones that don't are grouped in their own spot. On a board with no source of +action, I'm quite likely to embassy/warehouse over a third embassy. On a board with with some good +action like TR or hamlet, I'm almost always going to go for a light embassy engine and never buy down to the warehouse.

[dondon151]

I don't personally think that a draw engine using only Embassy as the terminal drawer is a good idea. Note that Embassy only increases your net handsize by 1, and that each purchase of Embassy generally helps your opponent's deck as well.

[O]

I don't personally think that a draw engine using only Embassy as the terminal drawer is a good idea. Note that Embassy only increases your net handsize by 1, and that each purchase of Embassy generally helps your opponent's deck as well.

But 1) silver's usefulness is highly game dependent, and if he's mirroring you (or doing nearly any engine) its not that good at all.
and 2) Engines are often, though not always, more concerned with what cards get into your hand, not how many. In this respects embassy can be a very elite drawer. Village-embassy-bridge combos are probably more viable than village-smithy-bridge.

[dondon151]

But 1) silver's usefulness is highly game dependent, and if he's mirroring you (or doing nearly any engine) its not that good at all.

In a game with Embassy, straight BM is a very strong option, and it likes Embassy's Silvers.

and 2) Engines are often, though not always, more concerned with what cards get into your hand, not how many. In this respects embassy can be a very elite drawer. Village-embassy-bridge combos are probably more viable than village-smithy-bridge.

Perhaps - but that combo uses Bridge, which is very good at picking up many engine components. But consider if you had a +buy without the cost reduction of Bridge - you'll end up not being able to generate enough coin per hand to buy more than 2 engine components at once.

[Asklepios]

Obviously this is not the final word in how good each enabler is, since the cards actually, you know, DO something besides enable Tunnel, but it may be helpful in thinking about, for instance, why Cartographer/Tunnel is better than Vault/Tunnel, even though Vault has a bigger pool size AND is generally a better card.

Thats an interesting assertion. Has anyone successfully simulated this?

I see that Cartographer has its advantages (thins out the copper and the VP cards from the gold) but also its worth bearing in mind that Vault only needs to get one gold drawn or in hand to get a Province.

I wonder if a province game simulated properly will favour Vault/Tunnel, Vault/money or Cartographer/Tunnel.

Just running solitaire games, I seem to be having a lot more speed and success from Vault than from Cartographer, even with Tunnel on the board. To me, Cartographer has always worked best in the presence of linear solid cantrip actions (Conspirator, Grand Market, even Worker's Villages and Oases) and suffered when there is stuff getting in the way of its action chain (excessive money, or green cards, even if the point of Cartographer is to clear that stuff). Vault, otoh, synergises well with an excess of high value money and early greening... which is what Tunnel does. I think Cartographer/Tunnel can empty the gold pile a lot quicker than Vault/Tunnel, but Vault/Tunnel gets the Provinces faster.

[mischiefmaker]

I spent some time playing around with the simulator before making that claim, because it certainly doesn't seem intuitive, for the reasons that you state. Best I've been able to do so far is a 49-47 split in favor of Cartographer/Tunnel, which I suppose makes it a bit hyperbolic to say that Cartographer/Tunnel is "better", but my intuitive sense from tweaking the bots is that it's also easier to play Cartographer/Tunnel well (a naive bot that just opens Silver/Silver, buys Cartographer, then buys Tunnel, then buys Province/Cartographer/Tunnel + some endgame VP, does almost as well as the tweaked bot).

I suspect what you are seeing is that in solitaire, you have no competition for the Provinces, so you can get them more quickly with Vault/Tunnel. But in real games, you'll find that Vault/Tunnel stalls more quickly, especially once you start getting some Duchies. Cartographer/Tunnel has less of a problem with this, because you can't really overstuff your deck with Cartographers, whereas you can have too many Vaults.

* my usual disclaimer applies: I'm not that great at optimizing the bots, so folks are welcome to try and do better.

[Robz888]

I would expect Vault/Tunnel to beat Cartographer/Tunnel and Vault/Money.

For Vault, Tunnel is no worse for your deck than any other card, because you can discard it for money. Cartographer is just discarding it. And you only have to draw a single Gold with your Vault to buy a Province, so you can probably overbuy Tunnels. Those points do matter.

One thing to watch out for, though, is that your Vault can help your opponent's Tunnels, since he gets a chance to discard off your play.

Cartographer continues to fall in my estimations. Maybe that's because people tend to over buy it--unless you're doing Tunnel, it probably shouldn't be your first $5 card, and you probably don't need 6 of them!

[Robz888]

I spent some time playing around with the simulator before making that claim, because it certainly doesn't seem intuitive, for the reasons that you state. Best I've been able to do so far is a 49-47 split in favor of Cartographer/Tunnel, which I suppose makes it a bit hyperbolic to say that Cartographer/Tunnel is "better", but my intuitive sense from tweaking the bots is that it's also easier to play Cartographer/Tunnel well (a naive bot that just opens Silver/Silver, buys Cartographer, then buys Tunnel, then buys Province/Cartographer/Tunnel + some endgame VP, does almost as well as the tweaked bot).

I suspect what you are seeing is that in solitaire, you have no competition for the Provinces, so you can get them more quickly with Vault/Tunnel. But in real games, you'll find that Vault/Tunnel stalls more quickly, especially once you start getting some Duchies. Cartographer/Tunnel has less of a problem with this, because you can't really overstuff your deck with Cartographers, whereas you can have too many Vaults.

* my usual disclaimer applies: I'm not that great at optimizing the bots, so folks are welcome to try and do better.

That result surprises me. I feel like Vault handles itself pretty well in the end game slump. How many Vaults does your simulator buy?

[gorgonstar]

I think the way to analyze vault/tunnel, is that you get to reveal a tunnel from 6 cards not including the vault.  You opponent gets to reveal a tunnel from his hand of 5 cards.  So that's only a net difference of 1 card.  So gaining gold is great using the vault when playing solitaire, but not so great if you opponent is also buying tunnels.
 
The cartographer/tunnel deck should have a higher density of gold.  However the vault/tunnel deck has an easier time buying provinces.  This might be what we are seeing in the sims.  Or the sims might have a bug in them.

[Asklepios]

Too many Vaults is a rare problem, I think, as you can always discard vaults to vaults, and the vault deck doesn't hit $5 that often anyway (and $6-$7= gold, naturally, even with Tunnel around)

As for play rules for Vault-Tunnel, I'd suggest:

Silver till Vault acquired.

Then:

First $3-4, buy one tunnel, if not on $3-4 follow rules as below:

Then:

$8 = province, unless PPR applies or lose game on buy.
$5 = Vault, unless behind on VP or <5 provinces remaining, in which case duchy, or if have at least two vaults and four golds in deck, in which case duchy.
$6 = Gold, unless four or more golds in deck, in which case duchy
$3/4 = Silver, until silver > tunnel +4, then alternate tunnel/silver
$2 = estate if estimate less than two shuffles before end of game, otherwise, pass.
$1 = scream and rant a little, and end turn.


For Cartographer/Tunnel I'd suggest silver till Cartographer, then:
spend $3-4 on Tunnels until TWO tunnels, after that by silvers unless the VP from the Tunnels will affect victory outcome
$8 = province, unless PPR applies or lose game on buy.
$6 = Gold, unless four or more golds in deck, in which case duchy
$5 = cartographer, unless time for duchies
$3/4 = Silver, until silver > tunnel +4, then alternate tunnel/silver
$2 = estate if estimate less than two shuffles before end of game, otherwise, pass.
$1 = scream and rant a little, and end turn.

My instincts suggest those would be the optimal approaches, but I could be wrong. Tunnel is complicated, of course, because of its VP value, and there'll be turn by turn assessments as to whether it helps or not.

As a rule of thumb, I'd say that only buy more than one or two Tunnels when the VP is worth something to you. I think people often get too interested in the gold generation effect and over-commit to Tunnels. Unless there's Silk Roads or I'm nudging along a favourable three pile ending, I rarely want more than two tunnels. In particular, I think Vault/Tunnel loses tempo if you see the tunnel as anything more than a route to setting up the Vault/Gold engine, and indeed too many golds will stop you drawing Vaults, and might leave you on annoying 6 or 7 dollar hands, rather than the optimal Vault + Gold + three cards. I reckon that if the simulator generates more than $8 on a province buy hand on more than half the buys its buying provinces, its probably being inefficient.

[NinjaBus]

I think the way to analyze vault/tunnel, is that you get to reveal a tunnel from 6 cards not including the vault.  You opponent gets to reveal a tunnel from his hand of 5 cards.  So that's only a net difference of 1 card.  So gaining gold is great using the vault when playing solitaire, but not so great if you opponent is also buying tunnels.
 
The cartographer/tunnel deck should have a higher density of gold.  However the vault/tunnel deck has an easier time buying provinces.  This might be what we are seeing in the sims.  Or the sims might have a bug in them.

Yes, this is the issue. Be careful of the discard cards which also work for your opponent when playing tunnels. Vault, Minion, and Duchess (not really a tunnel enabler, eh) can all potentially activate opposing tunnels.

If we're just talking single player sims, I guess cartographer could win simply because you can play more than 1 per turn? Each is 4 cards searched, but you can easily get to 8 or 12, while vault is stuck at 6 every time.

[Asklepios]

I guess you're right! I don't often think hard enough about Vault's drawbacks.

[Quadell]

My instincts suggest those would be the optimal approaches, but I could be wrong. Tunnel is complicated, of course, because of its VP value, and there'll be turn by turn assessments as to whether it helps or not.

Just for fun, I simulated both those strategies on Dominiate, and both did quite well. Vault-Tunnel beat Cartographer-Tunnel 58% of the time, even with the latter taking full advantage of Vault's side effect of allowing one's opponent to discard.

[Asklepios]

My instincts suggest those would be the optimal approaches, but I could be wrong. Tunnel is complicated, of course, because of its VP value, and there'll be turn by turn assessments as to whether it helps or not.

Just for fun, I simulated both those strategies on Dominiate, and both did quite well. Vault-Tunnel beat Cartographer-Tunnel 58% of the time, even with the latter taking full advantage of Vault's side effect of allowing one's opponent to discard.

Oh! Does that mean Vault-Tunnel is actually better then?

[Quadell]

Oh! Does that mean Vault-Tunnel is actually better then?

Well, no. Strictly speaking, it just means that the Vault/Tunnel strategy you described beats the Cartographer/Tunnel strategy you described slightly more often in a head-to-head matchup, when neither strategy buys any other cards or reacts intelligently to the opponent's play. It was "just for fun", as I said. Still, it might indicate that Vault/Tunnel works better in general... I'd have to play a few dozen games to see how well it works in real games, and see if I'm missing any added flexibility or good counters to either strategy.