Opening Probabilities: Hitting 3P

Similar to the last post, here I am looking at your chances of hitting 3+P on turns 3 or 4. I am borrowing heavily from this post.

Potion/Nothing: 60.61%

Potion/Silver: 65.40%

Potion/Poor House: 65.66%

Potion/Lighthouse (or Fishing Village):  65.78%

Potion/Sage: 66.92%

Potion/Oasis (I'm only about 90% I calculated this right): 71.97%

Potion/Moat (or Shanty Town, any draw 2): 77.02%

Potion/Great Hall (Trashing Hovel): 83.33%

The key insight here is that not drawing your potion is actually MORE important than the nightmare of 2+p. So cycling goes a long ways - which is good, because that also synergizes with what you want to do with the potion-costing cards anyway, whether at 2p or 3p. This changes, of course, once you start needing 4p, though the potentially bigger issue there is that you don't really want Golem before you have actions to go with it.

Dominion Opening Theory: Money Matters

This post pulls heavily from sources here and here with some math of my own as well (but it's all the same, pretty elementary combinatorics).

Here, I am just going to look at chances of hitting 5 and 6 coins from various openings. Knowing these can really help to inform how you want to open the game quite a bit, as you plan out your turns 3 and 4. Hitting high coin amounts are definitely not the only factor you should consider - but it is an important one.

The following probabilities assume no funny business or interference from opponents.

Silver/Silver
(Silver/Terminal Silver is Equivalent)

Chance of hitting 6+: 42.4%

Chance of hitting 5+: 91.2%

Chance of hitting two 5+: 14.9%

Terminal Silver/Terminal Silver

Chance of hitting 6+: 17.7%

Chance of hitting 5+: 72.2%

Chance of hitting two 5+: 12.6%

Terminal Collision: 30.3%

Baron/Silver

Chance of hitting 6+: 67.7%

Chance of hitting two 6+:   5.1%

Chance of hitting 5+: 87.4%

Chance of hitting two 5+: 29.0%

Baron drawn and whiffs:  17.7%

Salvager/Silver

Chance of hitting 6+: 24.7%

Chance of hitting 5+: 78.3%

Chance of hitting two 5+: 13.6%

Salvager drawn and whiffs:  17.7%

Feast/Silver

Chance of hitting 6+:   8.8%

Chance of hitting 5+: 94.9%

Chance of hitting two 5+: 34.1%

Chance of 5+5+3:   6.3%

Horse Traders/Silver

Chance of hitting 6+: 38.7%

Chance of hitting 5+: 94.9%

Chance of hitting two 5+: 27.2%

Moat/Silver

(Equivalent to Shanty Town or any other draw 2)

Chance of hitting 6+: 24.6%

Chance of hitting 5+: 94.9%

Chance of hitting two 5+:   0.0%

Oasis/Silver

Chance of hitting 6+: 32.2%

Chance of hitting 5+: 91.8%

Chance of hitting two 5+:   8.2%

Tournamnet/Silver

(Or any other Peddler variant)

Chance of hitting 6+: 37.9%

Chance of hitting 5+: 91.8%

Chance of hitting two 5+:   8.2%

Curse/Silver

(Any Non-economic card)

Chance of hitting 6+:   8.8%

Chance of hitting 5+: 49.4%

Chance of hitting two 5+:   0.0%

Silver/Nothing

(Or with any cantrip that does actual nothing - Pearl Diver is better)

Chance of hitting 6+: 15.2%

Chance of hitting 5+: 60.6%

Chance of hitting two 5+:   0.0%

Tournamnet/Nothing

(Or any other Peddler variant)

Chance of hitting 6+:   7.6%

Chance of hitting 5+: 54.5%

Chance of hitting two 5+:   0.0%

Silver/Great Hall (trashing Hovel)

Chance of hitting 6+: 27.8%

Chance of hitting 5+:  100%

Chance of hitting two 5+:   0.0%

 

Instructional Game #4 Clean, Clear Subtleties

Game Log

Setup:

The first thing that jumps out at me here is Ironworks/Highway. Of course, in retrospect, there isn't that much support for it. In order for that to be a key or even significant part of your strategy, you need to be drawing good chunks of your deck pretty reliably. The only draw here is Torturer (a terminal with no village) and Vagrant (which doesn't help get the components together). The other way you can get to drawing that much is by thinning, but the only thinning is Counterfeit. It's possible to try to get Counterfeit to work, but it's pretty slow - and your opponent probably WILL be contesting you on Highways. So at best, that's a friendly interaction that can come up.

My opponent - again, a strong player - opened Ironworks/Silver. I actually think this is just a mistake here. Counterfeit/Highway probably should be a pretty central part of your plan, because Counterfeit thins and gives buys, and Highway leverages that pretty nicely. Perhaps more important, if you let one player get too many Highways, they might actually be able to do some pretty degenerate things. In any case, the important thing to note is that 5s are key. And Ironworks here, without a Highway in play, pretty much just grabs Silver. Now Silver is probably a reasonable card on this board, but here's where we look at the percentages: Silver/Silver is about 91% to hit at least one 5, including about 15% to get two. Ironworks/Silver is about 73% to get at least one 5, including about 1% to get two. Furthermore, if you use IW to grab a Silver in order to hit your $5, then you're not up anything over what Silver/Silver would have done unless you hit that 1% (in which case you've got an extra Ironworks). So where your real advantage lies, after the second shuffle, is in that, if you miss with your Ironworks hand in a way that you hit exactly $3 after gaining Silver, you end up with an extra Silver after that shuffle. (There's also some weird cases where your Ironworks misses the shuffle and then collides well, but these are really really fringe, and require getting Highway before Ironworks, and I really don't think you can bank on that). I in no way believe that that extra Silver can compensate for the lowered chance at hitting 5s. This thought process is what was going through my mind (not the exact percentages, mind, just the generalities) when I deferred my Ironworks until later - I want it to gain 5s, it can't do that soon, so I'd rather start my decks rolling.

Okay, so the game proceeds such that he does actually get that Ironworks leading him to $3, also hitting $5 on the other turn, equal spot, so that after the 4th turn, he straight up has an extra Ironworks compared to me. But the next shuffle is unkind to him (at this point, our shuffles become highly uncoupled due to the differing number of cards in our decks). By the end of turn 7, our decks look like this:

I have an extra Counterfeit. He has an extra Silver, Copper, and Ironworks. It looks at first blush that I might be a little ahead. But looks can be misleading - this advantage is already quite large, and he's going to need some good draws (more realistically, for me to have bad draws) in order to come back.

Over the next four turns, we can see how easy it is for an advantage like this to snowball: My deck is slightly trimmer, more efficient, and this compounds in on itself to get even sleeker (the extra Counterfeit is very nice for this as well), while picking up significant payload in a non-fattening way: the Card-neutral Highway. Thus, by turn 11, we are looking at:

I want to point out that my opponent has, given his situation, played very well here over the past few turns! His deck has lots of high-quality treasures and is set up like a quite decent Big Money deck ready for a healthy greening phase. Of course, the sleekness of my deck *ought* to leave me ahead here, but... over the next few turns, I play rather badly: I get a third Counterfeit (which I cannot support), and load up on Vagrants over Silvers. This is based on me still thinking of getting nice Highway chains capped off by Ironworks, but this is really an unrealistic pipe dream. My opponent keeps playing cleanly and hangs in the game the whole time. I make just one more good play, buying an Estate for effective $4 on turn 15 with 4 Provinces left - I am at the top of a shuffle and know I will never meaningfully see the next one, and given that the score is at all close, the point is absolutely worth it. Fortunately for me, my big early lead combines with a touch of first player advantage to overcome my later attempts to throw the game away, and I win on the 17th turn of the game.

Card Studies: Governor #1

One of the things I would like to do on the blog is take more in-depth looks at certain cards. This is probably based more about what I'm learning myself (and I feel like it's fairly often that I will 'level up' on a card) than on what I feel like I have some kind of mastery over. Anyway, I'd like to do this by looking at some game logs I think are instructive, one-at-a-time and then hopefully with some compilation pages for those different key cards. Over time, we can hopefully build up a pretty good repository.

Anyway, I'm going to start with Governor, which is a card I didn't feel like I had a very good feel for only a short time ago, but which I feel I've made a huge leap forward with in order to get to... mediocre with it.



Game Log

Setup:

Some notes on the opening here: Looking at it now, I kind of like double Silver. Priority number one is to get Governors ASAP. It's also somewhat important, though, to ease your burden in drawing through your deck. I actually don't think that's super important, but it's nice if you can get it done.

I actually opened Wishing Well/Silver, but I think that's not the greatest, since I want to be able to multi-Governor quickly. Buying multiple Governors in a shuffle is going to be facilitated by getting the second silver, and the Wishing well cycles you to playing those Governors faster, it's true, but not by THAT much. The other thing to note is that Governor trashing a 3 into a Governor can be a real way of upping your Governor count fast, but if that silver is such a huge part of your economic output, that becomes less of a possibility. I get a second Silver on turn 4, which I need to do at some point, but I think it's just better to do this sooner rather than later.

My opponent went for a Loan, which is the other thing to consider here, but I don't really like it. You have to get treasures at some point fairly soon, and you take a pretty significant hit to your chances to hit 5 - I don't think the bit of trashing is worth it. And specifically he pairs it with Wishing Well, which I like even less, as it will crimp is ability to Governor up reliably. Of course, in this case, it works out okay, as he gets a 3/5, which puts him 'in the game', but I don't think the reward for this justifies the 25-30% (not an exact number) of the time you are WAY behind.


As the game progresses, I get more Wishing Wells, and he gets quite a bit more in the way of actions.

He gets a huge turn 9, which lets him triple Governor and win the split 6-4. I gain a couple Golds and buy a Province (trashing Hovel) on my own 9th turn. I think the most critical turn of the game is turn 10: My opponent draws a lot of cards and then... does nothing but build a lot. He gets a Prince, two Embassies, a Storeroom, and a Throne Room. The problem with this is that it just doesn't work very well in the style of Governor. At the end of it all, he only has $8 in his deck (Storeroom notwithstanding), including just one Silver and one Gold. Of course, all this building would be great in a lot of situations, but with Governor around, he is simply not going to have the time with those cards in his deck for it to pay off.

On my turn 10, I only have to use one Governor for draw, and I'm still able to double Province and pick up an Expand (which has a little bit of extra value here by virtue of its $7 cost - can be defensively upgraded into Province).

My opponent's turn 11 he really goes off with his engine, but in the end, he picks up no points, and another Prince. And he's drawn me 4 cards in the process. This lets me choose my time and 'go for it', double Provincing while using Expand to mill another. This gets us to this point:

And while I don't technically have 50% of the VP here, it really is a hard lock - he needs the last Province and 7 Duchies, which will take him a couple turns at least - and in the meantime, I will get some more points, which means he'll need basically all the rest of the estates, which will simply take him too long.



Takeaway:
Governor games end quickly - don't spend too long building.
Winning the split is big, but having an eye on what to do afterwards is also important.
Be cognizant of when you need to start greening - it's usually pretty quickly.