Thursday, February 1, 2018

A Data-Driven Strategy Guide for Through the Ages, Part 5

Index:

1. Introduction (Link to Part 1)
2. Data Analysis
    2.1 Classification: Infrastructure Development (Link to Part 2)
    2.2 Classification: Cards Played (Link to Part 3)
    2.3 Separating players with TrueSkill (Link to Part 6)
3. Analysis for Boardgamers
    3.1 Infrastructure Development (Link to Part 4)
    3.2 Cards Played (Current Article)
    3.3 Mistakes made by Good Players (Link to Part 7)

3. Analysis for Boardgamers

Disclaimers: 
(1) We can only learn correlations from data.  Whether these correlations actually imply causation is up to our interpretation.
(2) The data comes from 10k+ recent games at boardgaming-online . I did not separate the "level" of the games.  Thus, it represents the behavior of all players, not just good players.

3.2 Cards Played

Again, the actual data analysis procedure is described in Section 2.2. Here is the summary for boardgamers.

The most important information I will use here, is whether a card is played or not. That includes elected Leaders, discovered Technologies, FINISHED Wonders, and new governments. The data did not include when was such card played, taken, or how was it played (revolution or peaceful). It also does not include yellow cards either.

Just like in the previous section, you will see a number (weight) associated with each card in several charts. Comparing those weights within the same chart tells us how important those cards are, relative to each other.  In addition, the title of a chart will be a number, a larger number there implies how much impact it will have if we follow what the chart teaches us. This title number will not be higher than 0.7. If it is smaller than 0.54, the chart probably has no impact.

Lesson One: Leaders, Leaders, Leaders!

This chart includes all Stage A and Stage I cards. We can see that all leaders have relatively higher weights than other cards available at the same time. Also, Age I leaders are significantly better than Age A ones. So, it is ok to miss out on a Wonder, or a Technology, but we should always plan to have a leader and maximize its benefit.

This should not be too surprising. The (opportunity) costs for these cards are not identical. Leaders have (strictly) the least costs. You only spend CA to take them, and you often don't even spend CA to play them. Everything else requires you to spend CA plus science/resource/population.

Lesson Two: Early CA is key.
Among the Age A leaders, Hammurabi clearly stands out. This echoes our observation in the previous section that early extra CA is important.  In fact, the only other two technology cards which are almost as good as an early leader are Code of Laws (CoL) and Monarchy. They both give you extra CA. In fact, Warfare costs 1 less Science than CoL, but has an obviously less weight (consistent with 0). This does not mean that 1 MA is not important, but it certainly is not as good as 1 CA with a similar cost. Pyramids being lower than Library is a bit surprising. I initially suspect the reason is that even average players tend to overspend their CAs for Pyramids, but that does not seem to be the case.
Here is a chart for all Age A, I and II Wonders, regarding how often they are taken, and on average how many CA a player spends to get them. We can see that Pyramids is taken 20% more often than Library, but people only spend slightly more CA for it on average. Thus, maybe Library is really better.

Lesson Three: St. Peter's Basilica is the best happiness solution.
By the end of Age I, almost everyone will need at least 2 happy faces or some extra yellow tokens. While the 1st happy face can come from the free temple, we need to work on the 2nd one. The possible solutions are Theology, Theocracy, Bread & Circuses, Hanging Gardens, Great Wall, St. Peter's Basilica, Homer, and (Columbus + Vast Territory).  Only the last 3 options have significantly positive weights in the above chart. The opportunity cost for Columbus or Homer is another leader of the same age, which has a comparable weight. Thus, the only solution that stands out is Basilica.

In fact, we can compare across all sources of Happy Face here.
We can see that this chart has a low impact (title number close to 54%). However, the two Stage I Urban solutions for happiness are just terrible. Basilica not only stands out among contemporary cards, it even looks better than later game stuffs which produces more cultures.  If we cross-reference to the previous chart, we can see that Basilica is taken with 2 CA, which is the minimum for your 2nd Wonder. Maybe it deserves to be taken with more CA.

Lesson Four: Be opportunistic.
This chart is for all Age I and II techs for farms, mines, urban buildings and military units. First we note that the impact is quite low (55%).  We should probably avoid Theology and Bread & Circuses, but almost everything else is fine. Let us again cross reference this to how often they are taken, and how many CA spend on them.

Iron is taken twice more often than Coal, but it does have 1 more card. So that difference is not huge. The same story goes for Alchemy v.s. Scientific Method, and Cannon v.s. others.  People get more CA to spend later, thus it is nor surprising that Age II techs costs more CA on average. Among Age I techs, people do take Iron, Knights and Alchemy with more CA.

I guess the conclusion here is that almost anything here will work. Nothing is a must have, but most of them are bad either. You just get what you can, and adjust with yellow cards accordingly. The military situation is similar.  Any units can shine with the right tactics, and the chance to match with the right tactics does not seem to vary significantly.

Lesson Five: Leaders again, but Strategy catches up.
This chart shows all cards in Age II. Leaders are still good, with Napoleon on top as expected. Strategy stands out among other cards and is almost as good as Bach. The 2 CA plus military power might decide whether you are the predator or the prey. The special technologies kind of have the 2nd lowest cost on average. You only spend science, and usually an affordable amount. In fact, let us look at all those things that requires science only.
Lesson Six: "Pure" techs are good.
The above chart compares all Governments and Special Techs. They all cost you only science.  First we note that they almost all have positive weights. That is because if you spend the science on Urban Building or Military Units instead, you also need to spend population and resources to get the actual benefit. You don't always break even after those extra costs. For these things, right after spending your science, you start to get benefits.

Lesson Seven: Constitutional Monarchy sucks!!??
This incorrect impression was due to a bug in the code that confuses Monarchy with Constitutional Monarchy. After fixing that bug, CM performs slightly better than Republic.

Lesson Eight: Many ways to seal your victory, but too late for your misery.
Finally, Age III is no longer dominated by leaders. With sufficient CA and resources, Wonders seem to be the most certain way to seal your victory. But you can also leverage your science or population advantage into Democracy or Air Force. It is also not too late to boost your CA with Civil Services. Note that everything here has a positive weight. This is the post selection effect that "if you can afford these, you are probably winning anyway". Thus, it is probably only worth looking at weights significantly different from average here. 

In particular, we see that Gandhi is terrible compared to other leaders. We probably only take him as the last and usually futile defence against strong aggressors. Professional Sports also appears to be terrible, which suggests that we should have solved potential happiness problem earlier.

No comments:

Post a Comment