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Subject: Isotropic Log Analysis, Take Two rss

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Jacob Davenport
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Innovation Analysis, Again

Methodology

All games recorded by Isotropic's logs between 2013-07-18 and 2015-10-09 were examined, striking aborted games and solo games. This left 380,670 games for analysis. However, an insufficient number of three and four players games was played to make many conclusions from them. 99% of the games played were two player games.

For each game, I pulled out each player's actions as Achieve, Dogma, Meld, Forecast (activate from forecast after melding), Share (draw a card after a shared dogma), Inspire, Fade, Endorse, melds (as in meld a card as part of a dogma), and tucks (as part of a dogma). The I counted how many times those happened, the value of games with that action for the acting player (value is the players achievements divided by total achievements, thus giving more weight to winning by more achievements), and the win ratio of the acting player (a simpler measure). Both the value rate and win rate are interesting, but they tend to correlate highly.

The spreadsheet from which I took this data has been uploaded to http://www.playagaingames.com/wp-content/uploads/2015/10/inn... in Open Office format and http://www.playagaingames.com/wp-content/uploads/2015/10/inn... in Excel format. If you really want to see what's happening, download the spreed sheet and follow along.

All cards are listed at http://innovation.isotropic.org/cardz.

Terminology

After the name of each card, I'll give the age and the statistics I'm looking at. So Clothing(A:1 DV:60% DW:63%) means that Clothing, which is an age 1 card, gave player who ran its dogma an average game value of 60%, and that 63% of the time it was associated with a winning game. Abbreviations are:

A: card age with the set (nothing=base, e=echoes, f=figures, c=cities)
V: mean value of games with this action.
W: mean win percentage of games with this action.
D: Dogma action
M: Meld action
F: Forecast card melded and activated dogma
I: Inspire a figure
E: Endorsed dogma action
m: melded as part of another card's dogma
t: tucked as part of another card's dogma

Results

Base Game

Ignoring several Age 9 and Age 10 cards, the best card in the game based on dogma effects is Clothing(A:1 DV:60% DW:63%). Mobility(A:8 V:54% W:63%) and Lighting(A:7 V:55% DW:63%) were also strong, but if you ignore Age 7 and up, the next best cards are Gunpowder(A:4 DV:56% DW:61%), Pottery(A:1 DV:57% DW:58%), and Metalworking(A:1 DV:56% DW:57%). Perennial favorites The Wheel(A:1 DV:50% DW:51%) and Mathematics(A:2 DV:50% DW:56%) and Sailing(A:1 DV:48% DW:48%) are not nearly as good as players think, being activated 3rd, 4th, and 5th most often. If you don't ignore Age 10 cards, Self Service(A:10 DV:66% DW:85%) is the best card in the game by either measure, but it's not usually activated in any specific game, were as Clothing often is, and is often activated repeatedly.

The value of melding versus dogma was calculated on the belief that this might reflect the value of the icons, but this did not show anything interesting in the base game. Equally, melding as a dogma effect is always better than just doing a meld action, but that showed nothing interesting. When sorted by value to tuck a card in the base game, it's nearly sorted by age, which is what we like to see.

As expected, Achieving is a winning move, and is increasingly a winning move going through the ages. 63% of the players who achieved Age 1 won. Monument is the most common special achievement due to Masonry, leading to a 62% chance of winning. Universe is the least common but leads to a 70% chance of winning, probably because both ways of achieving Universe require having a strong board and thus gaining Universe is both symptomatic and causal.

Drawing a card is a 44% action, not as bad when drawing an age 1 card, terrible when drawing an age 10 card. This corresponds to most players feeling that a draw is a last resort if no other action appears better.

The worst card in the game is Fission(A:10 DV:39% DW:26%), followed by Statistics(A:5 DV:39% DW:33%), Services(A:9 DV:42% DW:34%), Anatomy(A:4 DV:39% DW:36%), and Feudalism(A3: DV:40% DW:36%). Code of Laws(A:1 DV:43% DW:41%) is the worst Age 1 card, and Tools(A:1 DV:44% DW: 44%) and Writing(A1: DV:44% DW:43%) are not much better.

Age 2 cards are very balanced, with Currency(A:2 DV:56% DW:57%) and Mathematics(A:2 DV:50% DW:56%) being mild outliers. Note the difference between value and win rate for Mathematics. Running the dogma for Mathematics led to victory 56% of the time, but the victories must have often been close, because the value was only 50%.

Clearly there are times when your best move in a game is to activate the dogma of a card that is shown to have a very low value, but on balance melding Code of Laws and activating it is not worthwhile.

Echoes Game

Self Service (A:10 DV:69% DW:87%) is still the best card in the game. Ignoring Age 8 through Age 10 cards, notables are Clothing(A:1 DV:60% DW:62%), Almanac(A:3e DV:58% DW:66%), Gunpowder(A:4 DV:57% DW:62%), and Katana(A:3e DV:56% DW:62%). Echo cards are generally better than base cards, as expected.

The value of meld from forecast was calculated, but the number of games melding cards from forecast for each card is not high enough to make many predictions. For what it's worth, playing nearly any card from your forecast is a winning move, except for Fission(A:10 FV:45% FW:48%). Don't activate Fission, except maybe as a joke.

In Age 1, Echoes cards other than Noodles(A:1e DV:57% DW:58%) are not better than 51%. Comb(A:1e DV:45% DW:45%) and Plumbing(A:1e DV:45% DW:42%) join Oars(A:1 DV:45% DW:42%) and Code of Laws(A:1 DV:44% DW:44%) as the worst cards.

Age 2 is still balanced, except Crossbow(A:2e DV:43% DW:37%). Currency(A:2 DV:53% DW:52%) and the ever popular Mathematics(A:2 DV:52% DW:58%) and Linguistics(A:2e DV:51% DW:55%) are among the best, but none beat Katana(A:3e DV:56% DW:62%) and Almanac(A:3e DV:58% DW:66%) in the next age.

Some Base cards improve when played with Echoes. Tools (46%, +3%) is not awful anymore, while Pottery (54%, -3%), Currency (53%, -3%) and Medicine (44%, -3%) become a bit worse.

The worst echoes cards are Typewriter(A:7e DV:44% DW:38%) and Crossbow(A:2e DV:43% DW:37%. Fission(A:10 DV:38% DW:26%) is still the worst.

Sharing is still not a great move, but least costly in Age 1. Drawing an Age 10 card actually led to a 52% win rate, but that's not as good as nearly all Age 10 dogma effects.

Achieving is much the same as before. World was the least commonly achieved base card and only led to victory in 55% of the games. Wealth (77%) and History (76%) are, like Universe (71%) symptomatic of already doing well.

Figures Game

Self Service (A:10 DV:68% DW:89%) is still the best card, but was only activated 612 times in 12,181 games. Ignoring Age 10 and Age 9 figures, Shivaji(A:5f DV:57% DW:69%) and Fu Xi (A:1 DV:53% DW:57) and Huang Di (A1: DV:52% DW:51%) are best figures to dogma. But dogma is not a good measure of figures.

Figures improves Statistics (45%, +6%) but it's still not good. Archery (52%, +6%), Machinery (56%, +5%), and Physics (47%, +5%), Oars (50%, +4%) all improve, enough that some are worth playing. Figures makes Clothing (55%, -5%) worse but still the best Age 1 base card. Gunpowder (52%, -4%) also drops.

Figures are valuable if they are melded and their effects are in play. The most valuable figures below Age 7 are Johannes Vermeer(A:5f MW:57% IW:59%), Tigernmas(A:1f MW:57% IW:62%), both of which are better than many Age 9 and Age 10 figures.

The worst figures are Isaac Newton(A:5f MW:34%), Ruth Handler(A:10f MW:35% IW:29%), Alex Trebek(A:10f MW:38% IW:48%), Grace Hopper(A:9f MW:38% IW:9%) (which is particularly sad for me because Grace Hopper is my hero), and Gilgamesh(A:1f MW:38% IW:45%). But let's not read too much into these, because they haven't been played that often.

Figures are valuable to fade as well, usually in inverse proportion to their effectiveness as a leader.

Echoes and Figures Game

Most people who play Figures play Echoes also.

Self Service(A:10 DV:69% DW:93%) still is the best card, ignoring a few cards that were only activated in 6 or fewer games. Also ignoring Ages 8 to 10 cards, Almanac(A:3e DV:58% DW:67%) and Rubber(A:7:e DV:55% DW:67%) are the best cards, but otherwise the top 40 cards are all Age 8 and above. The other cards at Age 3 and lower which are strong are Machinery(A:3 DV:54% DW:60%), Katana(A:3e DV:54% DW:60%), Sunglasses(A:3e DV:53% DW:59%), and Construction(A:2e DV:53% DW:57%).

Sneferu(A:1f MW:55% IW:57) becomes the best early leader, as Tigernmas(A:1f MW:53% IW:52%) is not the powerhouse that he was without Echoes. The worst Figures here are Ptahhotep(A:1f MW:38% IW:36), Isaac Newton(A:5f MW:39% IW:33%), and Daedalus (A:1f MW:39% IW:51%).

Anatomy (46%, +5), Statistics (47%, +5), Navigation (45%, +4), and Societies (47%, +4) are the Base cards that Figures improves the most, but they are still below 50% cards.

Soap (51%, +2%), Plumbing (47%, +2%) and Comb (47%, +2%) are Age 1 cards that improve with Figures, but only marginally. Most Echo cards don't improve much, or don't improve enough to make them good cards. Crossbow (46%, +3%) is still not worth playing.

Clothing(A:1 DV:51% DW:51%) is much worse from either the base game or game with Echoes. Apparently Echoes and Figures fix Clothing.

Cities Game

The value in cities is melding them. Berlin(A:6c MW:70%) is the best below Age 8. Delhi(A:3c MW:60%) is the best early age city.

The worst cities are Thebes(A:1c MW:45%), Santiago(A:9c MW:44%), Calicut(A:4c MW:44%), and Chicago(A:8c MW:44%).

The best cards to endorse below Age 8 are Perspective(A:4 EV:64% EW:73%), Lighting(A:7 EV:61% EW:76%), and Gunpowder(A:4 EV:60% EW:73%). Clothing(A:1 EV:57% EW:61%) is the best Age 1 card, still.

That said, many base case change in value with cities, maybe because to activate a dogma without endorsement is inferior. Invention (54%, +4%) and Philosophy (48%, +4%) improve, but to activate the dogma without endorsement of Clothing (50%, -10%), Pottery (48%, -9%), Currency (50%, -6%), or Mysticism (46%, -6%) is a mistake.

Cities and Echoes and Figures Game

Although some people played Cities without Echoes, or without Figures, there were not many games of these types to make broad conclusions.

Because cards are valued by their melding, their dogma action, their endorsed dogma action, and their value from the forecast, it's not straight forward to figure out which are the best cards.

The best card to dogma or endorsed dogma that's not an Age 8 card or higher is Industrialization(A:6 EW:79% EW:65%), followed by Rubber(A:7e EW:78% DW:63%) and Photography(A:7e EW:75% DW:62%). Almanac(A:3e EW:69% DW:53%) is too powerful for its age, as are Linguistics(A:2e EW:69% DW:53%) and Katana(A:3e EW:67% DW:60%), all because endorsing them makes them much more powerful. The worst to dogma is Crossbow(A:2e EW:34% DW: 31%), Medicine(A:3 EW:37% DW:40), Agriculture(A:1 EW:37% DW:40%), and lastly Plumbing(A:1e MW:34% DW:37%), perhaps because Plumbing's intended to be effective as an echo, not a direct dogma. Corporations(A:8 EW:50% DW:36%) and Machine Gun(A:7e EW:47% DW:39%) are notable weak cards for their ages.

The most popular card to dogma was Mathematics(A:2 EW:62% DW:55%), and while it's a good card, it's not a win-the-game card. Almanac(A:3e EW:69% DW:56%) was the most popular Echo to dogma, and it's probably too powerful.

Cities are very balanced, slowly gaining value as the ages increase. But there are a few outliers. Delhi(A:3c MW:58%) is an Age 3 city stuck in the middle of Age 5 and Age 9 cities. Babylon(A:1c MW:52%) is the best Age 1 city, but not unreasonably so. Sparta(A:2c MW:46%) is worst city, perhaps because those early industry icons aren't useful.

The worst card to meld is Sargon of Akkad(A:1f MW:35% IW:33%), but in none of the 25,707 games played did Beethoven enter play, so maybe he is worse.

The Age 1 base cards are very balanced, perhaps because they aren't very good anymore compared to Echos, Figures, and Cities. Even Clothing(A:1 EW:52% DW:43% MW:46% mW:50%) is not awesome like the base game. Flute(A:1e MW:53%) is the best Echo to meld and the worst is Plumbing(A:1e MW:47%) but that's not too much of a range. Perhaps in this game, the first meld is not as critical as it was in the base game.

In general, the special achievements give the best chance of winning, since they don't cost an action and they don't grant your opponents a free figure. Further, the five achievements one can get with figures are all generally losing moves to take since they kill your hand. Players who achieved Expansion won only 48% of their games, and those who achieved Rivalry won 39%.

Fission is the worst card in the game. Only 22% of the time that people active it do they win.

Conclusions

Playing with all sets fixes many of the problems in the base game. Rather than modify cards to fix the base game, expert players will appreciate a balanced game using all expansions. As such, the following cards seem most important to fix:

Almanac: perhaps remove “one higher than” will return this card to earth.

Katana: perhaps changing “top two” to either “two” or “top” will make this card less powerful.

Crossbow: it's too unlikely that the opponent has a card with a bonus, and if he does he often draws an echo as a replacement. I'm sure the reason this weak effect is to make up for the
3 point icon on the card, but it's insufficient to make it worth melding. Adding something like “If no cards were transferred as a result of this demand, draw a 2” would make this card work, and be more fun to play.

Plumbing: Give it a dogma effect, like “tuck a 1”.

Statistics: Simplify and empower it with “I demand you transfer the two highest cards in your score pile to your hand.”

Societies: Change from “a top” to “the top” and it's a strong card.

Sparta: Would do much better with a + and one industry, not two.

Mathematics: No change. Much to everyone's surprise.

Fission: Everyone likes a good laugh. But if your removed two top cards, it might actually be worth it.

Achievements: First, special achievements should grant opponents a figure, just like standard ones. Standard achievements are really well balanced, since they take an action to get (usually) and grant opponents additional compensation. Second, because the Figures achievements are such losers to take, and furthermore can be stolen, they should only cost your leaders to take, not your entire hand, and I would even go so far as to not allow them to be stolen. You may allow another player to activate someone else's Figures achievement, but not be able to take it away.
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Sean McCarthy
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Quote:
The I counted how many times those happened, the value of games with that action for the acting player (value is the players achievements divided by total achievements, thus giving more weight to winning by more achievements), and the win ratio of the acting player (a simpler measure).


So just to be clear, let me confirm. "Clothing: DW: 63" means this:

Look at each time the Clothing card was dogmad, and record either a 1 (win) or a 0 (loss), depending on the eventual outcome of the game for the Clothing user. Divide this by the total number of times Clothing was dogmad. (And multiply by 100 to get the percent.) So for example, if we play one game in which I dogma clothing 3 times, then you steal it and dogma it twice, and I win that game, and that's the whole dataset, then I would write "Clothing: DW: 60".

Is that right?
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Sean McCarthy
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Thanks for providing your spreadsheet. I was curious about the value of having a card melded onto your position either by a direct action or by a card effect. Here are my findings. (Only for base game 2p games.)

1) "Age 3 is the worst"

If I tell you that I melded paper in a game, then you should predict that 47.2% of the time, I win. And paper is the top card by this measure in age 3. Feudalism, at 41.6%, is the worst. The mean for all age 3 cards is an abysmal 44.7%. You might ask: how can melding any age 3 card be that bad? Doesn't almost everyone HAVE to meld one? But what these statistics are saying is that the more age 3 cards you meld, the worse you do. Here are the average values for all the ages:

Age 1: 50.5%
Age 2: 48.5%
Age 3: 44.7%
Age 4: 46.6%
Age 5: 46.9%
Age 6: 49.3%
Age 7: 48.5%
Age 8: 51.0%
Age 9: 54.8%
Age T: 68.4%


The other two decks that are a step down from the previous age deck are age 2 and age 7. Not really a surprise to me.

2) The top cards of each age

Clothing: 56.1%
Mathematics: 53.6%
Paper: 47.2%
Gunpowder: 53.3%
Coal: 50.5%
Machine Tools: 51.2%
Lighting: 52.3%
Quantum Theory: 54.8%
Computers: 60.6%
Self Service: 72.8%


3) Bottom cards of each age, a.k.a yellow is terrible

Writing 47.0%
Canal Building 47.0%
Feudalism: 41.6%
Anatomy 42.9%
Statistics 44.1%
Vaccination 45.7%
Sanitation 45.8%
Mass Media 48.5%
Fission 48.7%
A.I. 65.4%



4) The best 20 cards relative to their age's mean (* indicates card not ranked first in its age, values given are card specific % divided by age %)

Gunpowder 1.143
Clothing 1.112
Computers 1.106
Mathematics 1.106
*Satellites 1.091

Lighting 1.078
Coal 1.075
Quantum Theory 1.074
*Metalworking 1.072
*Empiricism 1.071

Self Service 1.063
Paper 1.057
*Genetics 1.057
*Optics 1.047
*Bicycle 1.047

*Combustion 1.047
*The Internet 1.046
*Mobility 1.040
Machine Tools 1.039
*Evolution 1.035


5) How about the 10 worst cards relative to their age, by that same metric?

Code of Laws 0.940
Physics 0.939
Statistics 0.939
Specialization 0.934
Feudalism 0.932
Writing 0.931
Vaccination 0.927
Anatomy 0.919
Services 0.902
Fission 0.888


6) Finally, how about the best and worst cards to meld in an absolute sense?

The ten best are: the age 10 cards! OK, that's kinda dumb. How about the worst, though?


(3) Feudalism 41.6%
(4) Anatomy 42.9%
(3) Compass 43.2%
(3) Alchemy 43.4%
(3) Engineering 43.5%
(3) Translation 43.7%
(4) Colonialism 44.0%
(5) Statistics 44.1%
(5) Physics 44.1%
(4) Navigation 45.0%


Grats again to age 3 for being awful!
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Rees Sloan
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Really interesting stuff, thanks for the stats!
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Jacob Davenport
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SevenSpirits wrote:
So just to be clear, let me confirm. "Clothing: DW: 63" means this:

Look at each time the Clothing card was dogmad, and record either a 1 (win) or a 0 (loss), depending on the eventual outcome of the game for the Clothing user. Divide this by the total number of times Clothing was dogmad. (And multiply by 100 to get the percent.) So for example, if we play one game in which I dogma clothing 3 times, then you steal it and dogma it twice, and I win that game, and that's the whole dataset, then I would write "Clothing: DW: 60".

Is that right?


Exactly.
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