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Subject: My First Article: Basic Dominion Decks rss

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Matt Sargent
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INTRODUCTION

I wanted to heed cosine's request for more strategy articles on BGG, so here is my contribution. Dominion is one of my favorite games of all time, and I have logged some serious time playing it, so it was the logical choice of game to write about.

What should a Dominion strategy guide be about? If a player wants to increase their skill at a game, they need to pratice the part of the game that most commonly determines if they win or lose. From what I have seen, players (including me) lose at Dominion for two reasons:

--They don't have a plan from the start of the game, or have one so bad it would fail to beat Big Money
--They don't transition to buying Victory Points at the right time.

Tactical decisions in the middle of the game tend to be straightforward in Dominion, and the choice of what to buy is determined by what you have bought already, and what your plan is, so this article will focus on making proper plans at the start of the game. We will figure out what the basic plans are, and how well they do compared to each other.

LESSON ONE: BIG MONEY

"Big Money" has established itself in the BGG Dominion lexicon as referring to a strategy that buys no kingdom cards, instead filling up on treasure until it can buy Provinces. The main feature of the Big Money strategy is that you can employ it in ANY game of Dominion. It is not such a useful strategy to play, but it is good to think about because it teaches us some important things about the game. It also serves as a convenient cutoff point: if your strategy cannot beat Big Money, it will not be able to beat anything.

So how good is Big Money? On average, it will have bought four provinces after seventeen turns. This is an important piece of information because it tells us how long we might expect a game of Dominion to last. After nineteen turns, it is very likely that both players will have bought four provinces, ending the game.

How do we play Big Money properly? You get one buy every turn, for around twenty turns. Because we are predictably drawing five cards a turn, we know how many times we will shuffle our deck.

# of turns w/o # of cards in
shuffles shuffling deck afterwards
- - 10
0 2 12
1 2 14
2 2 16
3 3 19
4 3 22
5 4 26
6 5 31


At the end of 16 turns, we have 26 cards in our deck, and shuffle for what will be the last time. During this last run through our deck, we will buy only victory points. Other cards will do us no good if the game ends before the next shuffle. On turns thirteen through sixteen, any card we buy will only come into our hand once at most. If you buy a gold on these turns, it may allow you to buy a Province instead of a Duchy, a benefit of three points. Or, we could spend our six coins on a Duchy now, for a benefit of three points. Points now are better than possible points later, so I would buy the Duchy.

A note before we continue: above I referred to two players and eight Provinces. This article deals only with two-player games, for a couple reasons. First, I enjoy two-player games the most. Secondly, two-player games are much easier to deal with, both conceptually and in simulation. I hope to be able to establish some basic information about Dominion. By restricting my study to two-player, I can eliminate a lot of complexity and establish simple facts that we know to a large degree of confidence. The lessons learned from this should carry over well to the multiplayer game.

LESSON TWO: SINGLE ACTION DECKS

The astute observer will quickly see that it is easy to improve upon Big Money. As long as there is only one action card in your deck, you will be able to play that action every time it comes up. As long as the benefit of that card is greater than the treasure Big Money otherwise would have purchased, you have the advantage.

What about purchasing a second action card? If we draw them both at the same time the second action will be completely wasted. Without cards that increase your draw, you only get four or five chances to play an action card. Losing one of those is a big deal.

Let's verify this through simulation. I have chosen some non-attack cards that require little decisionmaking. These are the easiest to program. We can play solitaire, and try buying different numbers of them. Success will be measured by how fast the deck can buy four provinces. It is not an ideal measure for fitness in actual play, but it gives us a means of comparing cards to each other.

Qty Card Avg turns
4 Wharf 14.34
1 Envoy 14.58
2 Smithy 14.89
3 Merchant Ship 15.08
4 Laboratory 15.71
2 Upgrade* 15.82
1 Chancellor 15.86
2 Explorer 15.87
1 Moat 16.04
7 Market 16.15
1 Baron** 16.16
1 Moneylender 16.20
1 Mine 16.38
1 Adventurer 16.54
1 Ironworks*** 16.69
1 Coppersmith 16.88
1 Workshop 17.89

*Upgrading Estates into Silver and trashing Copper. Not as good in an actual game because you're giving up points
**Using the Baron for +4 whenever we draw it with an Estate. This is faster than using it to gain Estates but gets fewer VP
***Using Ironworks only to gain Silver

We can see our intuition was correct. For cards with no draw, and no actions, buying one is almost always best. Lab and Market take a larger number, because their +1 action means it will never be wasted when drawn. Wharf and Merchant Ship have higher quantities because they are duration cards; they stay out of your deck for a turn after being played, so the odds of them colliding with each other are reduced.

Also, we see which action cards are the most powerful. Cards with draw are the best when combined with lots of treasure. Wharf and Envoy top the list, because they allow you to draw four cards in total, each with a slight disadvatage. Smithy with its three cards is next, and then Merchant Ship rounds out the top tier, . Should those cards be unavailable, Lab, Upgrade, Chancellor, and Explorer are all not bad. So that's a good starting table. But we left out an important class of card: attack cards. Let's rank some attack cards by how well they beat Big Money.

Qty Card Wins Ties Losses
2 Sea Hag 95.1 0.0 4.9
3 Witch 91.9 2.5 5.6
2 Swindler* 81.7 1.4 16.9
3 Militia 69.2 19.5 11.3
1 Bureaucrat 40.7 32.0 27.3
2 Saboteur 35.9 19.7 44.4
2 Cutpurse 29.6 20.0 50.7

*Swindler turned Coppers into Curses and Silvers into Workshops. Opponent used Workshops to gain Silver.

The cards that give out curses are the strongest. Now we know how good the attacks are compared to each other ... let's see how these attack cards fare vs. other decks.

Deck v.Wharf v.Smithy v.Moat v.M'lender v.Witch
Sea Hag 68.5 82.1 81.1 94.9 54.1
Witch 71.3 78.8 84.2 88.7 47.7
Swindler 52.5 59.8 69.5 74.3 25.0
Militia 36.1 36.9 48.5 74.7 21.2


My conclusion from this data is that Witch, Sea Hag, and Swindler are the top tier attacks, and that they rank above Wharf in the power ranking. Militia is quite good, losing to Wharf, Smithy and Moat, but beating all the other action cards (I ran it against Lab, Explorer, and Chancellor: all wins).

LESSON THREE: VILLAGE/SMITHY/REMODEL

I have some good news and some bad news. The good news is, the simple, single-card decks described above are not the most powerful decks in the game. The bad news is, it's much more difficult to improvise a complex deck and play it. So let's start by learning a very simple action-based deck. Then, we'll see if that tells us anything about action-based decks in general.

Suppose the kingdom contains Village, Smithy, and Remodel. Open with Village/Remodel. Remodel Estates and purchase cards until you have the following:

1x[Remodel] 1x[Gold] 4x[Village], 4x[Smithy], 7x[Copper]

Now you have a X% chance of drawing 8 coin. If you're reading this sentence, I never wrote a simulation to determine what X is, but trust me, it's high. Buy provinces with 8, or with less, buy a Smithy or Gold which you will then remodel into a Gold or Province.

I have not tested this deck via simulation, however I have yet to lose a game with it against my double Smithy robot after many attempts, so I am confident it reaches four Provinces in under 14 turns.

Ok, but so what? How many times are you going to run into three particular cards? Well, hopefully we don't need those three precise cards. Let's consider what each one adds to the process.

Village: +2 actions, +1 card. The actions are the crucial piece of the puzzle, but the single card draw helps too. For example, Festival/Smithy/Remodel would not work (or at least not in the same fashion), because without a +1 card from Festival, you are not able to cycle through your deck as well. Shanty Town seems like it should be an acceptable substitute, and it works, but after a few games trying it, it feels like it needs more gold in the deck than with Village. Native Village should work, especially because you can remodel coppers into them. Fishing Village could work; maybe you could forgo the Gold in favor of more Smithy/Fishing Villages. Oh, and Mining Village. There are a lot of villages, so it's reasonably common to have one to work with.

Smithy: An essential piece of the puzzle. Envoy is probably just as good. Nobles and Torturer can fill this slot too. The deck will be quite a bit different though, as the presence of 5+ cost cards necessitates silver. Thankfully, without Smithy, your low-action competitor isn't running double Smithy, so you may have an extra turn or two to work with.

Remodel: Gets you cards you need while replacing ones you don't. The vital role that Remodel plays is keeping your deck size down, so that your Village/Smithy combo has a good chance of drawing everything in your deck. Remodel is also great at the finish for turning Golds into Provinces. Salvager is the obvious choice to replace Remodel with. Upgrade could do well, although it can't make Provinces. Moneylender is not as good as Remodel, since you are getting rid of treasure instead of Provinces, but since it makes your deck smaller, it does work, although I'd want to add an attack card or something into the mix before I'd be confident it could destroy double Smithy. Mine is a interesting choice for this slot, although it fails because without an extra buy you increase your deck's total coin to 11, 12, or 13 but gain no benefit from it. With an extra buy though...

So that's my blueprint for a "draw everything" deck. The essential features are that it keeps the deck size small by not buying money, and is able to quickly get to the point where it draws the entire deck. It also has the key bonus of being able to remodel up for Provinces, which gets you big points without interfering much with the normal buying method.

CONCLUSION

So far I have just scratched the surface of what your starting goals may be in Dominion. I hope to write more of these articles, describing the various decks of Dominion, although I'm not great at finishing what I start, so don't hold your breath. Thank you for reading, and special thanks to

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for spreading the gospel of Playing to Win, both with and without all due tactfulness :), and

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for writing the simulation framework I have used extensively for gathering data for this article.

EDIT 1: Heavily revised the article. Made the introduction more focused and removed references to chess. Added the shuffle analysis to the big money section. Fixed thinking Fishing Village had a cost of 2. Capitalized stray uncapitalized card names. Reworded many other paragraphs.

EDIT 2: Fixed the numbers on Wharf and Merchant Ship.
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David desJardins
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Re: Dominion Strategy: My First Article
noon wrote:
My primary interest is in 2-player games, so I consider 3+ players outside the scope of this article.


Yeah. For those of us who are only interested in 3+ player games, it almost seems like we need two different Strategy forums.
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Matt Sargent
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Re: Dominion Strategy: My First Article
DaviddesJ wrote:
noon wrote:
My primary interest is in 2-player games, so I consider 3+ players outside the scope of this article.


Yeah. For those of us who are only interested in 3+ player games, it almost seems like we need two different Strategy forums.


I didn't mean that game with more players are less interesting, or that the information given would be useless. I expect that starting strategies that are good in 2p are also good in 3-6p. The bigger change with more players is anticipating the end of the game.

My statement that I would be only looking at 2p games was self serving. It's far easier to answer a question like "How many Sea Hags is optimal against Big Money? than "Suppose you have one Sea Hag, players two and three have one Witch, player four has a Witch, and player five has neither. Should you buy another Sea Hag?"

By sticking with questions that I would be able to answer with certainty, I hope to provide a foundation of knowledge that will be useful with any number of opponents.
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David desJardins
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Re: Dominion Strategy: My First Article
noon wrote:
By sticking with questions that I would be able to answer with certainty, I hope to provide a foundation of knowledge that will be useful with any number of opponents.


I think that is right, one can learn things about the 3+ player game by studying only the 2-player game. Or even by studying the "1-player game", which you can define as minimizing the time to 4 provinces, or maximizing expected score on turn 15, etc. Nevertheless, what happens pretty often in these forums (not your fault) is that generalizations about 2-player Dominion (or 1-player Dominion) get translated as "correct strategy" rather than "strategy for one narrow form of the game".
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Re: Dominion Strategy: My First Article
noon wrote:
I didn't mean that game with more players are less interesting, or that the information given would be useless. I expect that starting strategies that are good in 2p are also good in 3-6p. The bigger change with more players is anticipating the end of the game.


I disagree. Thief/Gardens immediately springs to mind as a strategy that I wouldn't try with fewer than 4 players. Many Attacks are different depending on how many players are in the game, to the point where some of them are almost broken with 6.

But also, the fewer players in a game, the more of a particular Kingdom card you can count on getting, which can affect the strategy you pursue.
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Re: Dominion Strategy: My First Article
jeffwolfe wrote:
But also, the fewer players in a game, the more of a particular Kingdom card you can count on getting, which can affect the strategy you pursue.


And the less likely that the game will end before the Provinces run out, which makes an equally big difference.
 
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R. H.
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Re: Dominion Strategy: My First Article
OMG Matt!!! I think we need to stop playing for a quarter a point and move it down to a nickel... you know too much now!!!
 
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Re: Dominion Strategy: My First Article
UlyZed wrote:
DaviddesJ wrote:

And the less likely that the game will end before the Provinces run out, which makes an equally big difference.


Agreed.

I feel as if the 2er and 3+er games are almost apples and oranges. I prefer 2er as an intellectual exercise, but enjoy 3er much more as a game.

Of course each has their merits, but I support a split in the strategy thread, or at least addendum to a title.


Regardless of whether he is talking about a 2-player game predominantly or not, I still found the article extremely interesting and very valuable.

I have seen a lot of mentions in session reports, strategy articles, and general comments on Dominion about building a deck. Up till now (and apologies to anyone who has made such a post, which I may have missed) I have not seen the construction of a specific deck (apart from a Chapel deck) described as clearly as the Village-Smithy-Remodel one above.

I am a casual Dominion player (but have played quite a lot of games), but still really struggle to know how to "build a deck" - in fact I would describe my play more as purchasing cards I think we work well toegther - sometimes it comes off and sometimes it doesn't - more often it doesn't and I generally tend to lose to my wife who plays a money heavy strategy (in general).

This may appear really dim, but the Estate to Smithy remodel idea early in the game had just not occurred to me. I knew that remodel was useful late in the game (gold to provinces, 3 costs to duchies etc) but early use to more quickly set up a deck such as you described (and to thin out the estates) might well revolutionise the game for me.

Just one point re your article - you said something about remodelling Coppers into Fishing Villages - Fishing Villages cost 3 so this wouldn't work - it would however work with Native Villages.
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Re: Dominion Strategy: My First Article
I agree with David - it'd be nice to see the number of players for whom a strategy discussion is intended noted clearly in the thread title.
 
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Re: Dominion Strategy: My First Article
chrisjwmartin wrote:
I agree with David - it'd be nice to see the number of players for whom a strategy discussion is intended noted clearly in the thread title.


I'm not really saying that. Actually, I think what he's written here is about equally applicable to any number of players. There wouldn't be much point in writing the same thing twice under two different headings.
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Yaron Racah
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Re: Dominion Strategy: My First Article
Excellent post - both the strategy primer and the data.

Some time ago, I ran my own set of simulations. Most of my results match yours, except for the duration cards, for which I got significantly better numbers:

3 Merchant Ships: 15.1 turns.
4 Wharves: 14.3 turns.

These results are in line with my intuition about the power level of the cards: +4 coins / +4 cards seem good, even if the card sometimes sits out a deck cycle.
Both my intuitions and my simulation code have been known to be wrong, though.

Can anyone else confirm/deny our results?


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Re: Dominion Strategy: My First Article
tweetlebeetle wrote:
OMG Matt!!! I think we need to stop playing for a quarter a point and move it down to a nickel... you know too much now!!!


Bah, i knew all this before, I just hadn't written it down, and see how it helped me.

My worry is that I'll teach you how to use Villages properly, and then you'll be unstoppable!
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Re: Dominion Strategy: My First Article
UlyZed wrote:
Matt, I think this shows you can offer insight to a lot of players of Dominion. The importance of Big Money, and as an extension Smithy or Double-Smithy Big Money is an astute starting point.

However, I found the format of the article difficult. I think you are trying too hard to use a style of writing that sounds important but detracts from your insights with unnecessary adjectives and cumbersome sentences. Using words like 'therefore' and 'very' repeatedly detract from otherwise good information by muddling up the message.

Also, I think your point about tactical puzzles in Chess is right (and orthodox) but for those who don't play Chess might not have been clear. The decision-making in Dominion is nearly always strategic, and tactical opportunities are not common. I'm sure you were saying this but I felt like it could have been clearer because it's and important point.

Regardless, I hope I am not coming across as harsh. You have a lot of good things to say


Thank you for the reply and the helpful insight Alex. You're quite right, my writing can get a bit formal and unnecessarily ornate in the first draft. I'm giving the article a pretty thorough revision, and I like the results so far.
 
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Re: Dominion Strategy: My First Article
For what it's worth, I appreciate your writing style. I want to read an article. Figures and tables certainly help illustrate the point, but I definitely need something to read!
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Re: Dominion Strategy: My First Article
yaron wrote:
Excellent post - both the strategy primer and the data.

Some time ago, I ran my own set of simulations. Most of my results match yours, except for the duration cards, for which I got significantly better numbers:

3 Merchant Ships: 15.1 turns.
4 Wharves: 14.3 turns.

These results are in line with my intuition about the power level of the cards: +4 coins / +4 cards seem good, even if the card sometimes sits out a deck cycle.
Both my intuitions and my simulation code have been known to be wrong, though.

Can anyone else confirm/deny our results?


I used Ian's code without revision for the Wharf, so you can take a look at it. 14.3 sounds crazy fast, but drawing six and seven cards makes it easy to buy a Province, so who knows.
 
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Re: Dominion Strategy: My First Article
Wonderful article Matt. I am going to try to reproduce some of your results with my own simulations.

Cheers,
Hans
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Matt Sargent
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I've revised this article, maybe making it easier to read, and adding to the "Big Money" section. Next up, "Lesson Four: Chapel."
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noon wrote:
I used Ian's code without revision for the Wharf, so you can take a look at it. 14.3 sounds crazy fast, but drawing six and seven cards makes it easy to buy a Province, so who knows.


If you're talking about

Dominion simulation Python framework

then it looks like there are two mistakes in wharf().

1. Each Wharf only gets played once and then never returned to the discards. You need to add

discard.extend(durations)

somewhere toward the end of the function, to put the Duration cards back in the discard pile at the end of the turn.

2. When deciding whether to buy a new Wharf, the count of how many Wharfs already bought doesn't include Wharfs on the table as Duration cards. You need to insert

wharves = all_cards.count(WHARF) + all_cards.count("Wharf 1")

With these two changes, and n=4, I get something around 14.38.
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Has anyone tried to simulate the LESSON THREE: VILLAGE/SMITHY/REMODEL against 1 smithy + BigMoney?

In my perhaps crude simulations, Village/Smithy/Remodel loses badly.

Cheers,
Hans

 
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irchans wrote:
Has anyone tried to simulate the LESSON THREE: VILLAGE/SMITHY/REMODEL against 1 smithy + BigMoney?


In part, it is not easy to simulate because there are a bunch of decisions to make. But I can try a version of it and let you know how I do. Just tuning this strategy (using rules, not judgment) is an interesting problem.
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DaviddesJ wrote:

If you're talking about
Dominion simulation Python framework
then it looks like there are two mistakes in wharf()...


Yup, that was the problem. I fixed both it and Merchant Ship. Thanks David!
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Here is an implementation of Matt's village/smithy/remodel strategy that averages 13.28 turns for 4 provinces. It could definitely be tuned a little bit more, and I haven't optimized it for anything else except "turns to 4 provinces". But it illustrates the idea.


def vsr(deck, discard, hand, turn, supply):
played = []
actions = 1
all_cards = deck + discard + hand
estates = all_cards.count(ESTATE)
villages = all_cards.count(VILLAGE)
smithies = all_cards.count(SMITHY)
remodels = all_cards.count(REMODEL)
golds = all_cards.count(GOLD)
provinces = all_cards.count(PROVINCE)
while actions > 0:
if VILLAGE in hand:
hand.remove(VILLAGE)
played.append(VILLAGE)
hand += draw(deck, discard, 1)
actions += 1
elif REMODEL in hand and (ESTATE in hand or SMITHY not in hand or
actions == 1 or len(deck)+len(discard) < 2):
hand.remove(REMODEL)
played.append(REMODEL)
actions -= 1
if ESTATE in hand:
hand.remove(ESTATE)
estates -= 1
if villages > smithies and gain(SMITHY, supply, discard):
smithies += 1
elif gain(VILLAGE, supply, discard):
villages += 1
elif (GOLD in hand and (count_coins(hand) >= 11 or provinces == 3 or
(golds > 1 and count_coins(hand) < 8)) and
gain(PROVINCE, supply, discard)):
hand.remove(GOLD)
provinces += 1
golds -= 1
elif SMITHY in hand and gain(GOLD, supply, discard):
hand.remove(SMITHY)
golds += 1
smithies -= 1
elif SMITHY in hand:
hand.remove(SMITHY)
played.append(SMITHY)
actions -= 1
hand += draw(deck, discard, 3)
else:
break
discard.extend(played)
coins = count_coins(hand)
if coins >= 4 and remodels == 0 and gain(REMODEL, supply, discard): pass
elif coins >= 8 and gain(PROVINCE, supply, discard): pass
elif coins >= 6 and gain(GOLD, supply, discard): pass
elif coins >= 4 and villages > smithies and gain(SMITHY, supply, discard): pass
elif coins >= 3 and gain(VILLAGE, supply, discard): pass
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Guy Srinivasan
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UlyZed wrote:
However, I found the format of the article difficult. I think you are trying too hard to use a style of writing that sounds important but detracts from your insights with unnecessary adjectives and cumbersome sentences. Using words like 'therefore' and 'very' repeatedly detract from otherwise good information by muddling up the message.

Whereas I found the format very friendly. I think it might depend a lot on how many math texts you've read...
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noon wrote:
DaviddesJ wrote:

If you're talking about
Dominion simulation Python framework
then it looks like there are two mistakes in wharf()...


Yup, that was the problem. I fixed both it and Merchant Ship. Thanks David!


Is 4 still the best number after the fix?
 
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SevenSpirits wrote:
noon wrote:

Yup, that was the problem. I fixed both it and Merchant Ship. Thanks David!

Is 4 still the best number after the fix?


Wharf
# turns
1 14.93
2 14.37
3 14.36
4 14.40
5 14.40
6 14.41


Whoops, it's not. I thought it was when I ran it with 10k iterations last time, but after double-checking with 100k iterations I got the above results. I think the reason why 4-6 are so similar is that it considers buying Gold first. It only buys Wharves if it has exactly five coin, so I suspect it rarely buys more than two or three no matter how high you set n.
 
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