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 (Link to Part 5)
3.3 Mistakes made by Good Players (Current Article)
3. Analysis for Boardgamers
Disclaimers:
(1) We can only learn correlations from data. Whether these correlations actually imply causation is up to our interpretation.
3.3 Mistakes made by Good Players
As explained in Section 2.3, we calculated the TrueSkill of each player. This allows us to use joint-statistics to answer quite a few questions which were unclear if looking at the game result along. We have also gotten enough data that we can afford to separate 2er games from 3, 4 ers. The zero-sum nature and the relative quantity of hidden information might make 2er games quite different.
We will be showing similar charts as Section 3.2, with a few improvements. First of all, the title of the chart will tell you whether this is for predicting the result of the game, or predicting the player's skill. The single number (less than 1) in the title is replaced by a percentage. It still tells you how good the prediction is. I also subtracted the performance of trivial guess already, so it is easier to see how good such a prediction really is.
Let us first look at all the cards during Age A and Age I for 2ers.
We should first note that the first chart here has a bad performance, consistent with 0% (trivial guess). That means the usage of Age A and Age I cards fails to predicting the final outcome of the game. That is not very surprising. 2ers are probably decided by big military and/or culture swings which comes much later in the game. However, we can still predict players' skill quite well. We know which cards tend to be played by stronger players (blue bars), and which tend to be played by weaker players (red bars). We cannot directly know whether these choices help you win. All we know is that those choices appear to be related to player skill.
Next we do the same thing for 3ers and 4ers.
Now this is interesting. The prediction for the game outcome is no longer consistent with the trivial guess. It becomes very informative to compare these 2 charts. The prediction for player skill is better. This is somewhat expected. Since it is quite early in the game, it will be difficult to predict the final outcome. However, good players tend to follow certain strategy, which might already be distinguishable in their early choices.
I can see 4 most striking differences here.
Pyramids vs Library of Alexandria.
Stronger players slightly prefer Pyramids over Library, more than weaker players do. However, Library performs significantly better for winning the game. I cannot see any alternative interpretation here and must conclude that this is a mistake made by strong players. Note that strong players must have performed better in many other places to make up the difference. However, there is very little doubt that at a 1-to-1 comparison, Library is better. Start to use it more!
I don't think that in the long run, Pyramids' ability is weaker. I looked at the statistics of how early do people build Age A Wonders. Pyramids and Library tend to be built as early as possible, which means delaying the 2nd Philosophy. 1 CA is better than 1 Science later in the game. However, this early in the game, Science might be slightly better, or at least equal. 1 turn earlier into any Age I technology can have a compounding effect that snowballs your economy. Combining with other benefits from Library makes it somewhat more powerful than Pyramids built at the same time.
Thus, maybe we should stop rushing to complete Pyramids. I know, it is a tempting package deal to get that CA early, delay population growth and get 1 extra food. But maybe it's not worth delaying the extra Science production.
Age I Wonders.
Stronger players do not build Age I Wonders more often than weaker players. However, except for the Great Wall, all other Age I Wonders seem to win a lot. The interpretation here requires a bit more steps. Recall that if we use Age III cards to predict the game result, Wonders performs exceptionally well. That does not mean those cards win the game. They simply "indicate" that the player has enough CA, science and resources to complete a big Wonder. Leveraging those into other developments probably wins the game, too.
We did not have to consider this "post selection" effect for Age A Wonders, because everybody starts at roughly the same condition. For Age I, we should ask whether there could be significant differences in infrastructure, which determines a player's ability to build a Wonder.
That does not seem to be the case to me. Even if someone upgrades Iron early, it will take 3 rounds before an upgraded mine to generate a net resource gain. During the prime time to build Age I Wonders, a few timely Yellow Cards probably give you more resource advantage, and that is not much. Thus, it seems like these Wonders are really contributing to victory, instead of just "indicating" someone's exiting advantage. Furthermore, if that were the case, Great Wall should have been an equally good "indicator", but it is not.
Thus, I again conclude that Taj Mahal, University, and Basilica, are under-valued by good players. Investing your early resources and CA in them seems to be a good deal, compare to other things you might have done. This is probably because all other ways to use resources require population and science. You are likely in shortage of either or both during Age I-II transition.
Code of Law vs Warfare.
Good players value them almost equally. However, CoL appears to perform significantly better. I again do not see an alternative explanation here. They have the same number of cards, and the science costs differ by only 1. Thus again, good players seem to over-value Warfare. Probably a bit paranoid and trying too hard to prevent early aggression. I won't say that's wrong. If you are indeed the better player in a game, then the most likely way for you to lose is probably a devastating early aggression. It is a good circumstantial strategy to be slightly paranoid about that and go with the mediocre Warfare. As long as a stronger player do not suffer from an early aggression, she can count on later moves to cover the lost ground.
Knights vs Swordsmen.
Good players value them almost equally, but Swordsmen performs better than Knights. This, even to me, is a surprise. Knights open up more Age I tactics, but Swordsmen are easier to discover and build. At Age II, such difference is almost gone. I would have expected them to perform equally well. My only explanation is that on average, people do spend 15% more CA to take Knights from the card row, and that is bad enough to undermine Knights' record.
3. Analysis for Boardgamers
3.1 Infrastructure Development (Link to Part 4)
3.2 Cards Played (Link to Part 5)
3.3 Mistakes made by Good Players (Current Article)
3. Analysis for Boardgamers
Disclaimers:
(1) We can only learn correlations from data. Whether these correlations actually imply causation is up to our interpretation.
3.3 Mistakes made by Good Players
As explained in Section 2.3, we calculated the TrueSkill of each player. This allows us to use joint-statistics to answer quite a few questions which were unclear if looking at the game result along. We have also gotten enough data that we can afford to separate 2er games from 3, 4 ers. The zero-sum nature and the relative quantity of hidden information might make 2er games quite different.
We will be showing similar charts as Section 3.2, with a few improvements. First of all, the title of the chart will tell you whether this is for predicting the result of the game, or predicting the player's skill. The single number (less than 1) in the title is replaced by a percentage. It still tells you how good the prediction is. I also subtracted the performance of trivial guess already, so it is easier to see how good such a prediction really is.
Let us first look at all the cards during Age A and Age I for 2ers.
We should first note that the first chart here has a bad performance, consistent with 0% (trivial guess). That means the usage of Age A and Age I cards fails to predicting the final outcome of the game. That is not very surprising. 2ers are probably decided by big military and/or culture swings which comes much later in the game. However, we can still predict players' skill quite well. We know which cards tend to be played by stronger players (blue bars), and which tend to be played by weaker players (red bars). We cannot directly know whether these choices help you win. All we know is that those choices appear to be related to player skill.
Next we do the same thing for 3ers and 4ers.
Now this is interesting. The prediction for the game outcome is no longer consistent with the trivial guess. It becomes very informative to compare these 2 charts. The prediction for player skill is better. This is somewhat expected. Since it is quite early in the game, it will be difficult to predict the final outcome. However, good players tend to follow certain strategy, which might already be distinguishable in their early choices.
I can see 4 most striking differences here.
Pyramids vs Library of Alexandria.
Stronger players slightly prefer Pyramids over Library, more than weaker players do. However, Library performs significantly better for winning the game. I cannot see any alternative interpretation here and must conclude that this is a mistake made by strong players. Note that strong players must have performed better in many other places to make up the difference. However, there is very little doubt that at a 1-to-1 comparison, Library is better. Start to use it more!
I don't think that in the long run, Pyramids' ability is weaker. I looked at the statistics of how early do people build Age A Wonders. Pyramids and Library tend to be built as early as possible, which means delaying the 2nd Philosophy. 1 CA is better than 1 Science later in the game. However, this early in the game, Science might be slightly better, or at least equal. 1 turn earlier into any Age I technology can have a compounding effect that snowballs your economy. Combining with other benefits from Library makes it somewhat more powerful than Pyramids built at the same time.
Thus, maybe we should stop rushing to complete Pyramids. I know, it is a tempting package deal to get that CA early, delay population growth and get 1 extra food. But maybe it's not worth delaying the extra Science production.
I don't think that in the long run, Pyramids' ability is weaker. I looked at the statistics of how early do people build Age A Wonders. Pyramids and Library tend to be built as early as possible, which means delaying the 2nd Philosophy. 1 CA is better than 1 Science later in the game. However, this early in the game, Science might be slightly better, or at least equal. 1 turn earlier into any Age I technology can have a compounding effect that snowballs your economy. Combining with other benefits from Library makes it somewhat more powerful than Pyramids built at the same time.
Thus, maybe we should stop rushing to complete Pyramids. I know, it is a tempting package deal to get that CA early, delay population growth and get 1 extra food. But maybe it's not worth delaying the extra Science production.
Age I Wonders.
Stronger players do not build Age I Wonders more often than weaker players. However, except for the Great Wall, all other Age I Wonders seem to win a lot. The interpretation here requires a bit more steps. Recall that if we use Age III cards to predict the game result, Wonders performs exceptionally well. That does not mean those cards win the game. They simply "indicate" that the player has enough CA, science and resources to complete a big Wonder. Leveraging those into other developments probably wins the game, too.
We did not have to consider this "post selection" effect for Age A Wonders, because everybody starts at roughly the same condition. For Age I, we should ask whether there could be significant differences in infrastructure, which determines a player's ability to build a Wonder.
That does not seem to be the case to me. Even if someone upgrades Iron early, it will take 3 rounds before an upgraded mine to generate a net resource gain. During the prime time to build Age I Wonders, a few timely Yellow Cards probably give you more resource advantage, and that is not much. Thus, it seems like these Wonders are really contributing to victory, instead of just "indicating" someone's exiting advantage. Furthermore, if that were the case, Great Wall should have been an equally good "indicator", but it is not.
Thus, I again conclude that Taj Mahal, University, and Basilica, are under-valued by good players. Investing your early resources and CA in them seems to be a good deal, compare to other things you might have done. This is probably because all other ways to use resources require population and science. You are likely in shortage of either or both during Age I-II transition.
Code of Law vs Warfare.
Good players value them almost equally. However, CoL appears to perform significantly better. I again do not see an alternative explanation here. They have the same number of cards, and the science costs differ by only 1. Thus again, good players seem to over-value Warfare. Probably a bit paranoid and trying too hard to prevent early aggression. I won't say that's wrong. If you are indeed the better player in a game, then the most likely way for you to lose is probably a devastating early aggression. It is a good circumstantial strategy to be slightly paranoid about that and go with the mediocre Warfare. As long as a stronger player do not suffer from an early aggression, she can count on later moves to cover the lost ground.
Knights vs Swordsmen.
Good players value them almost equally, but Swordsmen performs better than Knights. This, even to me, is a surprise. Knights open up more Age I tactics, but Swordsmen are easier to discover and build. At Age II, such difference is almost gone. I would have expected them to perform equally well. My only explanation is that on average, people do spend 15% more CA to take Knights from the card row, and that is bad enough to undermine Knights' record.
Any chance of compiling all particles into one page, for printing/eBooking?
ReplyDeleteHi Wil. I don't think the quality of this article deserves eBooking yet. :P
ReplyDeleteIt's really just some random thoughts and observations, for casual reference.
Very interesting series! I am not a great player but I also suspect that Swordsmen might have an undervalued benefit in terms of tactics, opening up the 2x infantry/1x artillery and similar tactics which don't rely on cavalry. Without Swordsmen, those tactics only give the lesser bonus, and it's possible to save on science and make use of Legion and Fighting Band until then.
ReplyDelete