A Quantified Guide to Caylus

Prologue:

Caylus is an epic “worker placement” game, http://boardgamegeek.com/boardgame/18602/caylus. It is currently available on both BSW and BGA for free online play. Thanks to that, a large number of games have been played and recorded. Inevitably, most of the online games are between 2 players, which gamers call “2er”s. Due to the lack of intrinsic luck factors, 2er Caylus can be rigorously calculated, and there exists a framework of dominant strategy focused on using the 4^th track (building) favors.

This post will not be about such dominant strategy, since you can find a good description elsewhere. Actually, I will barely talk about 2er. I will instead focus on multiplayer games, 3er, 4er or 5er, where there is no dominant strategy. Don't get me wrong. The building favor is still useful, and a related strategy can still be efficient. However, that should not be the only strategy you know. If that is the case, such lack of flexibility not only decreases your own chance to win but also makes the game boring.

Disclaimer: This is NOT a strategy guide. I will not tell you exactly what to do. Instead, the main point is to demonstrate a framework of calculation and quantification. This is because multiplayer Caylus is too deep for any linearized strategy. I am simply providing the tools that everyone can use to find his/her own favorite strategy.

Chapter One:  Basic evaluation

Chapter Two:  Productive actions

Chapter three: The value of buildings

Chapter four:  Efficiency and quota

Chapter five:  Favours

Chapter six:   Risks and wars

Chapter One:  Basic evaluation

Victory is determined by victory points (VP), but during the game you will often directly acquire money (coins) and resources (cubes). We need to establish a baseline conversion rate in order to perform any calculation. Here is what I will use:

1 coin = 1 cube = 1VP

In addition, 1 gold = 3VP.

Please note that this equation is not for you to directly evaluate your immediate next move. They form the baseline of our calculation because they come from the most frequent, and usually guaranteed actions (that if one player choose to do so, others cannot or will not stop him)  throughout the game: (1) neutral buildings turn one coin into one cube and are continuously used through out the game, (2) multiple castles in the last stage turns 1 cube to 1 VP and it is common to have a lot of castle building, (3) Bank and Church turn coins into VP or equivalent golds in exactly this rate. Even you are not a very good player, you can expect this basic conversion from coins to cubes to VP to happen naturally for you, in at least this rate.

As you get better, you will manage to get yourself better conversion rates. The purpose of this guide is to provide a framework to quantify how much "better" you can get, which is convenient determined by comparing to this baseline rate.

The true value of coins and cubes are of course highly situation-dependent. By the very end of the game, you certainly prefer 1 more VP than anything else. Earlier in the game, 1 more cube can usually give you an advantage much larger than 1VP. The value of having more coins depends sensitively on how much your opponents have. Early in the game, when you have 7 coins while your opponents have 2, that is a solid 5VP lead (or maybe much more). However later in the game, when you have 20 coins while your opponents have 15, it is obviously not as good.  A smart arrangement to induce a ``bribing war’’ on Provost can efficiently reduce everyone’s money, therefore maintaining the value of your extra coins.

In addition to the actions that established this baseline value, which by definition only ``transforms’’ one form or resources into another form without increasing value, there are other actions which are “productive”: they allow higher conversion rates than the baseline. Being able to perform more and better productive actions wins the game. 

However, this does not mean transforming actions are weaker than productive actions. That is because productive actions often require you to have certain set of resources, which you can only get from doing a few transforming actions as preparation. If you are the only one who is ``prepared’’ for these productive actions, you almost guarantee that they are yours to take. For example, the Jousting Field (1 Favour) requires a cloth (purple cube), and there is absolutely no way to get a cloth before the Jousting Field activates in the same round. Therefore, if you are the only player who has a cloth left from the previous round, you pretty much guarantee the usage of Jousting Field. Likewise, being the only player to have stone somewhat guarantees your usage to the Mason. 

So getting the right transforming action is a integrated part to help you get more productive actions. Exactly how to do that, is tactic/strategy, which is not my focus. Since you eventually have to do some productive actions to win the game, my goal is to help you understand their values. Otherwise, you might have beautiful planning, getting all the productive actions you want, and still lose the game, simply because you ``wanted’’ the weaker productive actions. That would be a shame, right?

Chapter Two: Productive actions:

(1) Get coins:

(1a) Take 3 coins = -1+3 = +2 (pay 1 coin to send a worker then gain 3 coins)

(1b) Red market = -2+4 = +2 (pay 1 coin to send a worker and 1 cube then gain 4 coins)

(1c) Wood market = -2+6 = +4

(2) Take cubes:

(2a) Wood production buildings: -1+2 = +1

(2b) Stone production buildings: -1+3 = +2

(2c) Gold mine:                           -1+3 = +2

In terms of pure value, sell a resource in the wood market is the best. Although you have to be careful that spending a cube might set you back on the preparation to use other productive actions. You should also keep in mind that with a money lead, you want to reduce everyone else’s money to ensure the value of every extra coin you have.

Another thing to note is that selling in the red market and taking the stone resource building seems to have the same value. That is very rarely true considering more productive actions they can prepare you for. Usually, everyone has sufficient money but insufficient resources. So having more resources can setup for a lot of more powerful productive actions. However, when everyone has enough resource, then indeed the 3 extra cubes are only more or less equivalent to 3 extra coins. Think about the last round: the 3 extra cubes is three points for another castle building, and the three 3 extra coins is also three extra points in either Church or Bank.

(3) Build 1 Castle and get a favour that round:

Assuming the value of the favour is “x”, which will be discussed later. You may set it to 3VP for convenience.

(3a) Your first castle in every stage:  -4 + 7 + x = +3+x (pay 1 coin to send a worker, pay 3 resources, get 5/4/3 points to avoid -2/-3/-4 penalty, and get a favor)

(3b) Your second castle in every stage: -4 + (5/4/3) + 2x = +2x (I take the mean value of the castle, two favour includes the end of stage bonus for having 2 castles)

(3c) Every castle after that: -4+(5/4/3) + x = + x

Note that during the end of stage bonus, multiple favours cannot be on the same row. So the value of “x” needs to be lowered if you build a lot of castle.

(4) Build multiple Castles together and get favour that round:

(4a) Build 2 castles together in stage 1:  -7 + 10 + 2 + 2x = 5+2x

(4b) Build 2 castles together in stage 2:  -7 + 8 + 3 + 2x = 4+2x

(4c) Build 2 castles together in stage 3:  -7 + 6 + 4 + 2x = 3+2x

For the cases for building more, you can calculate it yourselves. If we compare this to the previous case of building 1 castle, one single action here gains more VP. However, if we compare with your gain per cube you need to prepare, then building 1 at a time is much better. We will come back and talk about the topic of VP per action or VP per resource later.

(5) Jousting Field: -3+x

You get exactly nothing if x=3. However, the main usage of Jousting Field is to help you climb the favour track faster and get the top reward multiple times. So in many cases it is still very useful. Also, since it spends only 1 cloth, it has the highest VP per resource efficiency. 

(6) Buildings:

The value of buildings requires a more detailed calculation that we will present in the next section. Here is a quick summary: Constructing the right buildings in the right time is the most productive action in this game.

(5a) The first few wood buildings: -3 + 4/2 + 10 = +10

(5b) Stone resource building before gold mine: -3+3+12 = +12

(5c) Regular stone building after gold mine: -3 +6 + 2 = +5

(5d) Prestige building, the weakest two are:

Statue: -6 + 7 + x = +1+x

Granary:  -7 + 10 = +3

Every other prestige buildings are quite lucrative, but their VP per resource may be low.

Chapter three: The value of buildings

(1) The long-term gain of early wood buildings:

Someone people might estimate that with 12 more rounds to go,  you will use it 4 times, your enemies use it 8 times, so you gain 8 points. That is a serious underetimation. Imagine a situation that all your opponents pass before using your wood building, should you mourn for your point loss, or should you happily take those actions yourself?

All wood buildings are productive actions except for the Peddler which buys resources. However Peddler is the most flexible source of cubes which easily prepare you for other productive actions. So being able to use these actions without competition is definitely an advantage larger than the 1VP gain. You actually gain more if your opponents do not use your wood buildings. This has not even considered the fact that going to your own place always costs 1 coin, which increases your chance to pass last and have the final say about Provost’s position.

Therefore, we should really count wood houses to produce an effective 1VP every round.

(1a) The first few wood house can produce more than 10VP.

(1b) The resource producing one are slightly weaker, since they are 2VP short to begin with, and your opponents will use them more often!

(2) Stone buildings:

(2a) Resource production buildings: Your opponents will never pass before taking these. When they use it, you gain 1VP and 1 cube, which is 2VP in the baseline rate. So it is fair to count a gain of 2VP per round. Those build before the gold mine can likely be used 6 times, so building them can give you a net gain of +12VP.

(2b) Other buildings: -3+6 for all of them, and -3+3+x for the Church. Then we need to count how often are they used. Usually, an early Bank will be used many times if many players have money to spare. Note that the VP per action here is at least comparable to the Jousting Field. The VP per resource efficiency is also very good. So consistently building these 6VP stone buildings in the mid game is the crucial source of points for everyone. 

(3) Residence: -3+2+?

The money you get from residence are mostly in the later half of the game. Also you lose the income after it becomes the Prestige building. Although you might directly gain 2 or 3VP according to the baseline rate, it is better to consider this as a transforming action which allows you to build Prestige buildings. 

(4) Prestige Buildings:

We first calculate their net gain in terms of the baseline rate.

Granary: -7+10 = +3

Weaver: -7 + 12 = +5

Theatre: -10+14+x = +4+x

Statue:  -6+7-1 = +1+x

University: -10+14+x = +4+x

Monument: -11+14+2x = +3+2x (although the two favour cannot be the same, so might be less than 2x)

Cathedral: -15+25 = +10

If we just look at the net gain in this action, some of them are also very good. However, note that they all have low VP per resource efficiency. That means you need to perform more transforming actions to prepare. That is why they are a good addition if you can conveniently build them, but you should not focus on setting up for them. Honestly, I played 200+ games and watched 1000+ games, and have not witness a victory that is due to the Cathedral.

Chapter four:  Efficiency and quota

According to the baseline rate, a wood house in the first stage has net gain of +10, while building a castle only has +3+x. The actual difference is even larger. You need three resources to build the castle, but only two for the wood house. Assuming everyone getting the same number of resources, you can build 3 wood houses instead of 2 castles.

In stage 2, you should switch into building stone houses (by either favour or Mason). Again, building them is usually more efficient VP source than castles. So in the first 2 stages, don’t be afraid of the negative points. In fact, in a 3er, if you build no castle in the first stage but own the first three wood buildings, your chance to win is significantly better than your opponents.

Note that I am counting efficiency as VP per resource, which is equivalent to VP per preparing actions, without counting the actual building action you need to perform the last step. That is because other than the last few rounds, your worker rarely runs out. So you can go to build as soon as you have prepared your resources. The only limiting effect is competing the resource spots with your opponents.

Now that we understand that the best way to get VP are through houses, another important issue emerges. The number of houses are limited! There are only 3 4-point wood buildings and 3 stone resource buildings; the early enough spaces for them to profit are also limited. After they are gone, building castles is the next best VP source. There are 7 other stone buildings. When they are gone, build favour cannot provide 5VP easily, and the VP track becomes more efficient. So when you have resources, spend them early, otherwise your options are getting worse.

Chapter five:  Favors

(1) VP:

First five steps worth 3VP on average: x=3

If you manage to repeat later: x=5

(2) Coins:

In the baseline rate this is strictly better than the VP track. However, if the total money in the game increases, the relative value of a coin decreases. So you will get this when you are short in coins, or when you are confident to reduce your opponents money, making your extra coins really powerful. x=3 is still a reasonable estimation here.

(3) Resources:

In pure value, x=1 for the first 4 steps, and x=3 for the last. It is indeed relatively week. It can shine in a game that Lawyer appeals early. You can use it to dominate the castle while other players are cube-deprived.

(4) Building:

This is indeed the best track in the hand of good players. However, it is not dominant in multi-player games. For example, in my experience, in a 3er, if 2 players uses this and the 3rd one knows how to response, the 3rd player actually has slightly better chance to win.

The point here is trying to understand how and why this track is good. That is already somewhat obvious based on our previous analysis. Building wood and stone buildings can be the most lucrative actions in this game. This track simply helps you do that. 

(4a) First stage: x=3

The favour-built house will appear later than the Carpenter-built ones. So yours will be in a later position, and the 4VP ones will be gone. Still, a single wood resource production building in the 5th or 6th spot still worths 6+VP. Since you need 2 favours to build that, x=3 is a fair estimation.

(4b) Second stage: x=14 (the first stone resource production building. note that you save 1 resource and 1 coin for the worker compare to regular building, that’s why its 14 instead of 12) 

x=5 (regular stone buildings)

The major advantage here is to build the first stone resource building very early. There are only 3 of those, so capable opponents should let you get that +14 more than once. But the +5 per favour later is still very good. You should only build Residence with Favour after the stone houses run out, or simply use the Laywer.

(4c) Stage 3: x<3

After stone houses run out, you have three options:

(4c1) Upgrade your own stone house to residence and immediately build it afterward. This is hard to execute, and the next benefit is about 6VP. 3VP is attribute to this favour while the other 3 should be attribute to the required combo action.

(4c2) Residences: Late residences worth less than 3VP, but they are require for Prestige buildings.

(4c3) Build Prestige buildings: dependes.

Unless gold is abundant or the Architects are late/absent, Prestige building basically “belongs” to whoever is prepared. Using Favour to build them has the advantage of 1 coin and less risk to be cancelled by Provost, which is not a lot. Or course, if your non-building-track opponents are foolish enough to make gold abundant and Architects late, this is a huge advantage.

In conclusion, x=3 is a fair estimation, just like what was suggested in the simplified game. It is entirely possible to win without maximizing any favour.

Chapter six:   Risks and wars

The most amazing mechanism is its risk system. Actions before the bridge and one after it will always be executed. Everything else depends on the position of Provost. Provost can move up to 12/15/18 steps in 3/4/5er games. Always every single round, there is a risk of nothing happening.

Under the appearance of an economy game, pulling Provost is very close to a concept of “war”. Players simply annihilate each others’ resources. I will analysis this “war” from the 4-level view pioneered by Sun-Tze.

(1) The war starts in planning—it is all about money.

The war of Provost directly concerns the money. The basic inflow of coins to the game is 2 per player, plus 3 from the trading post and 1 from passing. This on average allows a player to send about 3 workers. Sending more than that, or spending moneys to pull Provost, the total money decreases, somebody is definitely getting poor and has to pass early. 

Thus, how much money you have is the most direct way to measure your threat in a war. The important consequence of a war, in addition to actions being executed or not this round, is also about they leftover money situation next round. Remember that the three coins you get from the Trading Post, and money from Jousting Field favour, are both before the Bridge. So you can spend those on pulling Provost. Having more money allows you to keep sending workers to be the last one to pass, who will have the final call on Provost’s position. All these are about money. So thinking and planning about money is the first thing to do, before you enter a war.

Now, assuming you have sufficient money for a potential war, here is the next step.

(2) The next is diplomacy—find you allies.

One player, even with the Guild, can only pull 6 steps, no matter how rich that player is. Two other players can exactly pull back against that. So don’t be greedy to plan a war to benefit yourself only. You will be fighting against everyone and you will lose. After you are prepared in money, the next step is to find allies.

Note that finding allies here is not about “talking and making deals” with other players. In Caylus, allies are obviously and directly defined by your positions on the board. When someone goes to take a lucrative yet risky building that is close to Provost, go ahead and use another one next to it. You have nothing to lose if the 3rd player goes to Provost now. The three of you have sent 1 worker each. If you win the war, you get to use that action. If you lose the war, the 3rd player gains nothing.

This also teaches us to avoid taking Guild. It is a very passive and weak action compare to its alternatives. You can take 3 coins from the Trading post, which can also pull Provost 3 steps. You even get to pull it later, and you get to keep extra money if only pulling 1 or 2 steps! 

If you really really do not want someone to use some place, there are two things you can do which are both better than Guild.

(2a) Go to that space yourself. Even if you cannot perform its action, you are just spending 1 coin, the same if you went to the Guild. This way, your opponent absolutely cannot use that space.

(2b) If that space is already taken, go to a nearby space. If your opponent gets to use his space, at least you get to use yours. Actually, if you keep populating those risky spaces, your opponent might decide that his gain is not more than yours. Or a 3rd player might be jealous and go to the Guild, and your opponent might mistake you as his ally, but you will actually join and 3rd player and pull back to cancel his original action.

(2c) How about the case that all of your opponents went to the risky spaces and you are left-out. This is still NOT the chance to go to the guild. None of your opponents is spending 1 worker on the Guild to ensure the benefit of other players, so you are in no hurry. Just keep playing, make sure you have enough money and watch your opponents slowly spend theirs. You might find that in your last move, going to Guild can still manage to cancel some of those risky actions.

(2d) How about the case that all of your opponents went to the risky spaces and one of them indeed went to Guild to ensure those? Well, do you think Gold Mine is very far away? Maybe it is not! Go to that space which originally seems to be impossibly risky! Will your opponent will be willing to pull forward 3 steps? It protects their actions, but gives you the chance to spend a few coin to reach the Gold Mine! If he is not willing to pull forward anymore, he just wasted 1 coin on the Guild, and who knows what will happen to their risky spaces.

(3) Then we fight in fields—control the passing sequence.

The later you pass, the more control you have over the final position of Provost. Before we start wasting money on Provost, we sometimes have to first waste money on sending workers to simply avoid passing. 2 things can help here.

(3a) The Inn:

Always spending 1 to place, even after opponents passed, is a very efficient way to make sure that you pass last. Also, after the war, players might be poor the next round, and being in the Inn also helps you to maximize your profit. Although be careful that the Inn takes one of your workers. So later in the game it might actually force you to pass first.

(3b) Own houses that enemy does not use.

This also allows you to send a worker with 1 coin only. So it provides similar benefit as the Inn. You should counter this advantage of your opponents by going to their houses first.

(3c) Turn order.

When everyone is prepared to fight to the end, then the passing order can only agree with the turn order. You should be able to see that and plan accordingly.

(3d) Passing!

Sometimes, it is not important to be the last one to pass, but it is important that someone else is the last one to pass. In this case, when do you pass might affect that outcome. Also, if you want anyone to pass first in a war, it is the player after you. So when you try to deplete another player’s money, aim for the player after you.

(4) Finally it is the siege—finally we pull the Provost.

If you calculated the first 3 steps, this becomes very simple. Just remember that you always have two directions to pull. When your worker is furthest but your are not the last to pull, unless you can pull the Provost very far away to a safe distance, pulling forward almost never benefits you. Consider pulling backward! Strange things can happen!