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Tuesday, April 10, 2012

Unexpected Hiatus

I have had a few subscribers email me asking if I'm going to continue the TtA series.  Answer: Yes!

However, I started taking courses offered by Stanford (Game Theory Math and Cryptography).  Game Theory is fun and I enjoy it.

Cryptography is significantly harder, and it has a programming component.  Making it worse, I decided I'd drop the course when I discovered programming to complete sections of the course.  I can write programs, but it is not worth my time to struggle with it when I really wanted a more high level overview.  With a heavy heart I wrote the letter to drop the course and sent it off.

About a week later the teacher replied they reexamined the course completion requirements and had dropped the programming portion, making it "extra credit" instead.  So, I was back to doing Cryptography!  But I had lost two weeks and the first quiz was due in two days  (course requires one quiz every week).  Since then I've been struggling to catch up with Crypto.

I should be caught up by end of this week, and moving onto a more normal schedule.  It is far easier to maintain a workload than to play catch up and be stressed all the time.

So, I hope to be back to a normal schedule soon!  And if your interested in some courses from Stanford, please check them out at: https://www.coursera.org/

Once these wrap up I'm thinking of taking a course in Model Thinking or Automata.  In early June/late May I will take a week off to prepare for my CISM.  One good thing, once I catch up I want to sit and write up a slew of articles, hopefully building up a buffer.

Saturday, March 31, 2012

Through The Ages - Card - Ravages of Time

Forum for this blog is here: Forum
This is a series of blogs written about each card in Through The Ages.  To find more, simply click on "Cards" label.

Ravages of Time

I usually take this time to discuss a Wonder, but today I'm going to talk about something a bit different: Ravages of Time (RoT).

Ravages of Time essentially "destroys" an Age A or Age I wonder.  From that point on the wonder generates 2 culture, but all of its other effects are lost.  one thing I always wondered was "How big of an effect did Ravages of Time have on the game?"

Game Statistics

RoT appears in just under a quarter of games played.  There may have been a game or two when Ravages was played, but it did not "pop" before the game ended.  This greatly eliminates the "threat" of Ravages to only 1 in 4.

What Crumbles?

The chart below graphs the "crumble percentage" of each of the wonders.  The "crumble percentage" is the number of times the completed wonder was both present and chosen to crumble when RoT appeared.  I believe this number is slightly more accurate since not all wonders are built in every game.
From the graph we can see the largest target is Pyramids.  This effectively gains the player 2 points per turn in exchange for a single Action per turn.  Based on our calculations of Average "Culture per Action", this is a great trade off (see Average Scoring per Turn).

The crumbling of any other wonder is not so significant, generating an additional 1 culture per turn, which isn't bad, if the player had prepared for it beforehand by compensating for the loss of their wonder.

Only 6% of players do not build an Age A or Age I wonder by the time RoT makes an appearance, meaning they gain neither a benefit nor a decrease.  More precisely, the player suffers no direct consequences.  The reality is the player needs to make up an additional culture per turn since the other player's culture increases by 1 per turn.

Opinion

Ravages of Time is nowhere as large a threat as I originally anticipated.  In fact, it is probably not an effective danger at all.  Appearing in only 25% of games means it is something to be anticipated, but not overly concerned about.  Second, by the time it makes an appearance, turn 15 or turn 16, the player should have their economy in full steam and any issues caused by the "loss" of the wonder should have little impact on the player.

The two exceptions I can see is St. Peter's Basilica and Hanging Gardens.  Both would negatively impact Happiness, with St. Peter's having a greater impact at turn 15.  Worse case scenario, the player needs to disband two or three structures to resolve the unhappiness, otherwise the nation goes into Civil Disorder. This may seem a large deal, but consider the player should have assigned these two (or three) workers to some other activity through the course of the game, so it is bringing the player into realignment with the other players.

Now, if a player has both Hanging Gardens and St. Peter's Basilica, there is the possibility the player completely ignored happiness generating buildings altogether.  In this case the player may find themselves rushing to reallocate population, spending actions on useless upgrades.  Analyzing games showed this happened only once.  In the other games the player with both SPB and HG had sufficient unassigned workers to "absorb" the loss of one of the two Wonders.

In short, RoT is not as big a danger or as big a threat as I originally thought.  I now believe RoT is a great card for the player with Pyramids as it quickly boosts their culture/action ratio, without benefiting their players as much.  Furthermore, it comes at a time when the player should no longer have an issue with Actions.

Sunday, March 25, 2012

Through The Ages - Card - Winston Churchill

Forum for this blog is here: Forum
This is a series of blogs written about each card in Through The Ages.  To find more, simply click on "Cards" label.

Recently I received the following comment from an anonymous user in response to the "Strategy Science" article:

"Have you considered Churchill as a Science Leader? "

I'll be honest, no I had not.  So, this week I'm dedicating the article to my anonymous user and we will investigate Winston Churchill.

Winston Churchill

"If Hitler invaded Hell, I would at least make a favourable reference to the Devil in the House of Commons." -- Winston Churchill, 1941

History

Sir Winston Leonard Spencer-Churchill (30 November 1874 - 24 January 1965) is considered one of the greatest war time leaders of the 20th Century.  Born into the family of the Dukes of Marlborough, Winston Churchill is of both English descent on his Father's side, and of American descent on his Mother's side.  His Mother was considered one of the most beautiful women of her time.  As was the custom, Winston was raised by nannies and did not play a large role in his early life.  However, they later became good friends and political allies.

Young Winston suffered from a severe stutter which struggled diligently to overcome, through carefully prepared speeches and even prosthetic dentures.  Churchill entered the Royal Military College in 1893, though it took him 3 tries before he passed the exam.  He chose to enter the cavalry specifically because it had lower grade requirements and he would not need to take mathematics.  Despite his father's wishes he remained in the cavalry and did not transfer to the infantry.

From 1895 to 1899 he distinguished himself in many engagements from Cuba to India.  It was his escape from a Boer prison camp which launched him into politics.  In the 1930s he denounced the rise of the NAZI party in Germany.  After many trials and tribulations, Churchill would go on to lead his nation through its darkest days of World War II by serving two terms as Prime Minister.  Winston Churchill's speeches and adroit statesmanship would become critical to bringing the United States into the war and defeating fascism in Europe.

Winston Churchill was a man known for having strong convictions.  He was vapid anti-fascist and a staunch anti-communist.  However, even he knew when to choose the lesser of two evils and he could find the words to say it in such a way it sounded both logical and intelligent without contradicting himself.  

Winston Churchill suffered from severe health problems.  As early as 1941 he had a heart attack.  In 1943 he contracted pneumonia.  Despite these conditions he stalwartly led his country through the war years.  On January 15, 1965 he suffered a stroke, and nine days later he passed away.  The legacy of Winston Churchill lives on in the world which took shape after WWII.  He was a noted author, journalist, statesman, and leader.  Without him it is questionable who would have stepped up to save Great Britain from the despairing days of WWII.

Game Stats
Through The Ages represents Winston Churchill as an Age III Leader with some impressive abilities, all military related.  His defensive capabilities permit him to either quickly build an army in response to declarations of Wars, or make him unassailable to Aggression cards with Defense cards.  At best, these abilities make him a deterrent to being attacked.

From a Science perspective, Churchill reduces the cost of military cards (red unit cards) by 3 science.  Although limited to just military cards, this effectively makes Winston Churchill a "Science Leader", albeit one with limited focus.

Strategies
Winston's war time abilities are only useful if a war is declared on the player with Winston Churchill.  Thus, Winston's abilities do not apply if Winston declares a War on another player.  There are a few great times to play Winston, and a few "gotchas" to be careful of:

Surprise Winston
The Turn immediately after someone declares War on you, play Winston.  Yes, they should have seen it coming if you took Winston Churchill, but for 2 or 3 actions to play, Winston can really boost the military strength.

Attacking with Winston
If possible, Declare War against a player the turn after a player declares a War on you.  Since Winston is in play and a War has been played against you, the reduced costs apply for this turn.  This can greatly increase the military strength to overcome your own War card.

Upgrading Military Units
Winston's ability only works with "New Units", not existing units.  Thus, he provides no resource benefit when upgrading a military unit.  If Winston is in hand, but not played, it may be worthwhile to wait a turn rather than build military units immediately.  This would save some resources, though it would leave vulnerabilities to Aggression cards for a round.

Opinions
Winston Churchill is a great card for deterring the military attacks.  He obviously combines well with Military Technology based cards, but this is limited by his late arrival of Turn 17.  In absolutely ideal scenario, Churchill would bring in Military Technology cards from Age II and Age III, 7 cards total.  This represents a maximum potential savings of 21 science points.

In reality, Winston Churchill was observed to see a maximum gain of 12 Science.  Players only learned military technologies in 29 of the 42 games where he made an appearance.  This comes to an average of just over 1 Science point savings per game that Winston appears.  If planning to use Winston as a science leader, some preparation needs to be applied.

So, does Winston Churchill count as a Science leader?  I have to answer 'Yes'.  Properly applied he can generate a significant amount of science.  However, like many cards, if it is not properly planned his science abilities will fail.

Thursday, March 22, 2012

Through the Ages - Part XXI - Strategy: Science

Forum for this article is located here: Forum
If you like this article, please +1, Like It, and pass it on to your friends.  The more it's read, the better I know we are heading on the right track.

The Leading Indicator

When looking for "Leading Indicators" to determine the good resources which increase the odds of predicting the outcome, the amount of science each player spends is a good place to look.  In fact, the following chart displays the relation between final position and ranking of science output quite clearly:
I have heard this theory several times, particularly when mentioning the importance of Alchemy as a key early technology, but the graph above is the first I know of which supports these suppositions.  The graph shows the relative amount of science spent correlates almost very well with the expected final position.

The first and second highest spender of science account for 89% of the wins. Similarly, those which spend the less in science appear lower in the final position.  To analyze more completely, there are two things to consider:

1) How much Science to spend?,
2) How to Generate the Science?

How Much Science is Needed

The real answer is "more than your opponents".  However, that is impractical and doesn't provide an objective to shoot for, so I offer the following chart which lists the science generated per player's final position:
From the chart above, we can see the lead player needs to spend 90 Science points on average.  This is roughly only 15 points higher than the second place player.  This 90 points provides a target we can use to analyze the various buildings, leaders, and Wonders: How much do they contribute to the Winning player?

Generating Science

Isaac Newton: A Great
Leader
Science really comes from two sources: buildings (Libraries and Labs) and Wonders.  Some Leaders enhance science output, but only with a Library or Lab previously.  Aristotle doesn't require a building, but he does require generating science by taking a tech card from the card row, thus requiring players to spend an action to gain a card.

Wonders

Only 31 people who won the game built a science wonder: Universitas Carolina or Library of Alexandria.  In one game the winner managed to build both science wonders (In this game, the player scored 129 science total, but won by only 2 points).

For those games where Wonders are built, they account for roughly 10% to 21% of the player's total science.  Despite these Wonders, the total amount of science generated by the Winner was not significant (91.8 science on average compared to 89.8).

Science Leaders

Three Leaders in the game provide a science boost: Aristotle (Age A), Leonardo DaVinci (Age I) and Isaac Newton (Age II).  Bill Gates and Sid Meier provide a production and culture boost respectively, but neither increases the science output, so they are not considered in the Science Leader.


The Winning player chose at least one of the Science leader 57% of the time.  The distribution of these is such that there was no significant difference (24% Aristotle, 24% Leonardo, and 26% Isaac Newton).  In only 15% of the games did a player choose two or three science leaders.  Again, the distribution was roughly even among the combination of leaders.

Interestingly, when reviewing games were a science leader was chosen twice, the odds of success seem to drop significantly, from 57% to under 20%.  This leads to the conclusion that players are best off selecting a single science.  On average, Leaders will only generate from 5 to 10 science, but these 5 to 10 science are critical to improving the player's positioning overall.
Another Great Leader:
Just Don't Pair Them

Buildings

Libraries and Labs generate science based on the number of workers assigned to them and the level of the building.  Many of these players build an upgrade for their building as well.  In only a single game (1%) did a player build neither a Library nor a Lab.  This indicates upgrading a lab or library is critical to success.

Which is better, however?  Most winners built Lab buildings (94%) over Libraries (78%), although 66% of winning players built some combination of both types.  In 8% of games the winning player upgraded to only a single Science building.  For this 8%, the distribution was roughly equal between Labs and Libraries, and they were fairly evenly distributed between Age I and Age II, though no Age III Science buildings appeared in this group.

The following Venn diagram displays the mixture of science building technologies discovered by the winning players:
Science Building Upgrade Breakdown
From the diagram we can see the general tendency of players to follow specific upgrade paths.  Many players build the Age I and Age II buildings, but by Age III the exorbitant science and production costs make them unfeasible.

The advantages of the two paths is not readily apparent.  Concentrating on Labs tends to yield no more additional science expenditure than those who choose to build just libraries.  However, fewer Age I libraries (Printing Press) are discovered than Age I Labs (Alchemy).  This indicates the preference to build Labs first, and Libraries second.
Conclusions
The conclusions are easy to draw.  The winning player generally out produces the other player's in science.  The winning player will spend roughly 90 points of science in the course of the game.

The two science Wonders: Universitas and Library of Alexandria, can provide a great boost in the odds of winning the game (roughly 30%).  However, the real boost comes from selecting a Science Leader: Aristotle, Leonardo Da Vinci, or Isaac Newton.  Counter intuitively, it seems better to only choose one science leader in the course of the game, and it doesn't matter which one is chosen!  After analyzing the losing positions against the winner, a player is better off choosing no science leader rather than choosing two or more science leaders, which is really quite surprising.

Like Culture, the majority of Science will come from buildings (roughly 60-75%).  The majority of the science will come from Labs, and the first lab built should be Alchemy.  Libraries are commonly built in conjunction with Labs, but normally later in the Ages.

Summarizing, the advice seems to be as follows:

  • Select only one of either Aristotle, Leonardo Da Vinci, or Isaac Newton
  • The Wonders Library of Alexandria or Universitas Carolina are nice, but not crucial to success.
  • Science Buildings should be discovered in this order:
    • Age I - Alchemy
    • Age II - Journalism
    • Age III - Computers and then Multimedia
  • Computers is often discovered, but rarely built.  Whereas Multimedia is less likely to be discovered, but is more often built.
So, the above four buildings make up 27 of the 90 Science points players will spend.  What technologies do you believe should form the other 63 points?  Let me know your ideas!

Friday, March 16, 2012

Through The Ages - Card - Wonder: The Kremlin


Forum for this blog is here: Forum
This is a series of blogs written about each card in Through The Ages.  To find more, simply click on "Cards" label.
The Kremlin
History
Some Good, Some Bad,
but how Ugly?
In 1147 the Grand Duke of Kiev, Yuri Dolgoruky, had a wooden fort, or kremlin, constructed where the Moskva and Neglina rivers joined.  People flocked to the new fort, which soon became a thriving city.  By the 1300's stone buildings formed up around the city, and in 1326 the Russian Orthodox Church moved its seat to the city of Moscow.  Since that time, Moscow has become the center of Russian culture and politics.  Even when Moscow was not the capital of the Russian state, it remained the cultural center of the nation and was the place where all Tsar's were crowned.

The Moscow Kremlin has been damaged and rebuilt many times during its existence.  In the 1400's the wooden structure was enlarged and replaced with brick and stone.  In the late 1700's Catherine the Great destroyed several surrounding buildings and began another expansion of the fortress.  Napoleon attempted to blow it up for three consecutive days before his retreat from Russia, but despite extensive damage the core structure survived and took decades to rebuild.  Reconstruction was completed in 1851, and the Kremlin remained relatively untouched until the Bolshevik revolution in 1917.

At that time the new regime transferred the government's seat of power back to Moscow from St. Petersburg.  It has remained in Moscow ever since.  Only government officials were permitted until 1955, when parts of it were opened as a museum.  The Kremlin dates back nearly 1000 years from its origination as a wooden fortress.  The many reconstructions of the buildings brought together many architectures and styles of various times: Italian renaissance masters, early Russian style architecture, neo-gothic, and baroque structures all make an appearance.  These unique blends of art set the Kremlin apart from other Kremlins.  Today the Kremlin continues to undergo preservation of its styles, but it continues to function as the central power of the Russian state.
Game Stats
Among the Wonders of Through the Ages, The Kremlin is unique in that it has a "negative" associated with it when built.  All other Wonders have all benefit, but The Kremlin causes 2 Unhappiness upon its construction.  In return, the Kremlin grants an additional Civil Action, Military Action, and 3 culture per turn.  It is the only card, besides governments and Hammurabi, which affects both Civil and Military Actions.

The "Unhappiness" caused by the Kremlin has an interesting effect on the final tally, or bonus points, as I calculate it, it causes the score to decrease by 1 point in final scoring.  Put briefly, the bonus points distribution consists of the "contribution" of the card to the overall Impact points earned, the odds of the Impact card being played, and the average culture gained from the Impact card.  In the case of the Kremlin, the two Unhappiness causes a loss of just under 8 points, while its governmental bonuses add up to just over 6.  Thus, the "final bonus" for the Kremlin is negative by 1 point.

Strategies, Combos and Opinions
Strategies
Military Domination
The Kremlin's additional Military and civil action is nice, particularly for those who are Ore rich, but science poor.  However, the Military action comes late compared to other means, such as government switches, code of laws, or Warfare.  Additionally, most Wonders don't require population, but The Kremlin does require some offset to its Unhappiness.  This means the player building it must build an additional Religious structure, effectively using increasing the cost of the Kremlin by one or two population.

Combinations
Hanging Gardens
Hanging Gardens +2 Happiness directly offsets the -2 Happiness of The Kremlin.  The danger here is the Ravages of Time could destroy the Hanging Gardens, leaving the player with a sudden Unhappiness factor.

St. Peter's Basilica 
Like Hanging Gardens, St. Peter's Basilica offsets the Kremlin's negative Aspects.  It still requires the use of a population to generate a positive culture, but is quite effective.
A rare recommendation for Arenas
(and only just barely)

Arenas (Bread and Circuses, Team Sports, Professional Sports)
I usually do not recommend Arena's over religious buildings.  Arena's increase happiness and Military strength, but normally the Military gain is minimal in comparison and I believe there are far better things to spend science than Arena buildings.  However, for those who want to try to use The Kremlin I do recommend building an Arena first.  A single population placed on the Bread and Circus would cancel The Kremlin's negative aspects.

Opinions
I'll admit that I want to like The Kremlin.  Its culture gain is high, and in fact it ranks near the top 5 culture generators of the wonders (see Culture:Wonders) when built.  However, I would rank The Kremlin as the single Wonder requiring the most Skill and preparation to use properly.  The player must understand how to offset the Happiness loss and have the population and structures in place to make it happen.  It is not a Wonder for the beginning player, and in fact if the game is not gong well, it isn't the Wonder for an expert player.

The additional actions provided by The Kremlin tend to come at a bad time.  Usually the game is 3/4 over by the time it is completed, meaning it will only provide about 5 extra actions in total (see Actions: Generating More).  I will go so far as to say that if The Kremlin does not make an appearance within the first full round of Age II, do not take it from the card row.  There are far better options with far fewer risks available.

What is everyone else's experience with The Kremlin?
Sources
1. Michael C. Paul, "The Military Revolution in Russia 1550–1682", The Journal of Military History 68, No. 1 (January 2004) .
3. Fletcher, Banister; Cruickshank, Dan, Sir Banister Fletcher's a History of Architecture, Architectural Press, 20th edition, 1996.
5. Klein, Mina. The Kremlin: Citadel of History. MacMillan Publishing Company (1973).

Wednesday, March 14, 2012

Through the Ages - Part XX - Strategy: Economics

Forum for this article is located here: Forum

Where to Start
When starting the strategy articles I was puzzled how to begin.  There are so many things to discuss.  Seriously, I started four articles before writing this one.  But each of those articles required a fundamental understanding of "something else" in order to truly grasp the trade offs being made.  This helped me determine the entire game boils down to one item: Economics.  It's a big item.

In order to be successful player must learn to manage the games economies.  Some will say the game is a "Military War Game", and they are correct.  Some will say it is a game of "culture generation", and they are correct as well.  Others will say it is a game of "scientific progress", and they are (also) correct.

But powering all of this is the economies.  Players who want to build armies to make it a military game will need an economy to support them.  Similarly, players that want to construct Wonders and Culture will need economies to support them.

So, to start talking strategy, one must first understand the economies at work.
Food drives Population, which comes from the Population Bank.
But, as the Population bank increases,  Consumption of food
occurs (number in circles is the lost food)
Defining Economics (in TtA)
I define economics for Through The Ages in terms of three resources: Science, Food, and Ore.  All other components of the game derive from one of these resources.  Science is needed to learn better technologies, new units, and better buildings.  Food is required to bring more population into play which may be assigned to new tasks.  Ore is the resource spent to assign workers to tasks: build buildings, become a military unit, construct Wonders.

Without either of these resources, Through the Ages is not possible as the game it is.  Similarly, any other card or group of cards can be removed, and the game "changes", but it is still playable.  Don't think it is possible, remove all the Cavalry cards, Libraries, or Theaters.  The strategies required to win change dramatically, but the game remains playable.  Therefore, it is these resources: Ore, Food and Science we need to understand.

Resource Values
The resources are not weighted equally, and their value will differ depending on actions the player takes.  For example, not building Farms will eventually leave the player "Food short", meaning the player will eventually run out of new citizens, thus limiting the number of building and units the player may build.  Each player must build their economy to meet their demands, but once built the economy becomes more difficult to modify.

Ore loss occurs due to Corruption.
However, Ore loss is based on total Resources taken from
shared pool between Food and Ore
(number in lower left circles is lost Ore)
The problem is a player can only focus on one or two of the resources early in the game.  This is due to a lack of actions, lack of ore, and rapidly increasing costs for bringing in new population.  Science is the only core resource which doesn't suffer a "Production Loss".  Food suffers consumption, based on the population remaining in the "population bank", and Ore suffers corruption determined by the amount of ore produced that turn.  Furthermore, both Ore and Food are "linked" in that they share a common resource Pool.  So, the more Food one produces, the more likely the player will suffer corruption in Ore. (vice versa is not true as Food Production is resolved before Ore production).

Figuring out a starting place point in strategy discussion was challenging, but with the basics of economics reviewed, I feel better about presenting the strategy articles.  Next week: real strategy talk!

Monday, March 12, 2012

Through The Ages - Card - St Peter's Basilica

Forum for this blog is here: Forum
This is a series of blogs written about each card in Through The Ages.  To find more, simply click on "Cards" label.
St. Peter's Basilica
History
Good Culture, Reasonable Cost
Awesome Ability
Unlike the majority of Age I and Age A wonders, records on St. Peter's Basilica are fairly well kept.  From these records we can see construction of the current Basilica began in April 1506, but it began in 324 when the Roman Emperor Constantine I ordered a church built over the grave of the catholic Saint Peter.  After 1200 years of use, it was decided to build an even grander structure, one that required over 120 years to construct.

St. Peter's Basilica is the largest church in Christendom and much of its architecture influenced later churches in the Western world.  The building is 730 feet (220 m) long by 500 feet (150 m) wide.  It rises 452 feet (138 M).  The dome of the basilica is its most notable feature, being visible throughout much of the city of Rome.  Since St. Peter's Basilica is not the seat of a bishop it is not a cathedral, though it is not uncommon for it to be referred to by that term.

The construction of St. Peter's Basilica required massive funding.  To pay for it the Catholic church began selling indulgences, one of the items which became a major point in the development of Luther's 95 Theses which started the Protestant reformation.

Designed and constructed by dozens of renaissance artists, including Michelangelo, the Basilica still stands today.  It has undergone various restorations and modifications to preserve the building.  It stands as testament of the beauty of human art and an example of the majesty of human engineering.
Game Stats
St. Peter's Basilica has great statistics and an even better ability.  With a cost of 8 and requiring only 2 actions to construct, St. Peter's remains affordable and inexpensive.  However, the greatest benefit may come from its ability: "Every Happy Face counts twice".  With this building constructed a player can almost effectively remove Unhappiness and discontent as an issue for their civilization.
Strategies, Combos and Opinions
Strategies
Culture Generation
St. Peter's provides 2 culture per turn, a not insignificant amount of culture gain when viewed from a pure culture perspective.  St. Peter's Basilica provides a nice increase in culture at end of game scoring from the Final Impact cards.
Production Engine
The advantage of St. Peter's Basilica for a production strategy is it frees up workers.  Here it is the savings the player experiences which will make up the benefit of St. Peters Basilica.  First, there is the fact the player will need fewer Religious and Drama buildings to maintain happiness.
Combinations
Hanging Gardens
Hanging Gardens provides 2 Happy faces.  With St. Peter's Basilica, this increases to 4 Happy Faces.  Although one or the other usually becomes the target of a Ravages of Time, this combination is the easiest for even beginning players to see.
w/St Peters Basilica: a
culture machine
Michelangelo
Michelangelo is another obvious combination with St. Peter's Basilica.  Effectively, Michelangelo and St. Peter's Basilica will turn a basic Religious building into a major Culture generating event.  Unfortunately, Michelangelo is an Age I leader and so will die when Age III starts.
Michelangelo and Hanging Gardens
No worries about
Happiness
Requiring a total of 14 culture and 9 actions, these three cards are the trifecta of culture generation.  The player completing these three cards will bring the player 7 culture per turn by themselves.  Fortunately for other players it takes some time to put all the pieces in play, but even so an "average" run of 9 turns would generate a whopping 63 culture by themselves.  Usually this player needs to concentrate on military matters to balance this out, but simply put this combination is known for generating enormous culture.
Theocracy
Theocracy and St. Peter's Basilica is, I believe, an oft overlooked combination.  There are many advantages to this combination.  First, Theocracy is the cheapest government to learn, giving the player quick access to constructing 3 urban buildings at low expense.  Secondly, Theocracy provides 2 happiness, which becomes 4 when combined with St. Peter's Basilica.  Although there may be a lack of Civil Actions at first, a Code of Laws can quickly balance it out.
My choice for most
underused combination
with St. Peters Basilica
Kremlin
Special note of the Kremlin needs to be made with regards to St. Peter's Basilica.  The Kremlin decreases happiness when it is built, though it provides other obvious benefits (+1 Civil Action/Military Action, culture gain, etc.).  It is important to note that St. Peter's Basilica does NOT modify the Kremlin's negative happiness.  Thus, having the Basilica in play should make the Kremlin more attractive as building the Kremlin still results in a a loss of only 1 happiness, but this is easily offset by the Basilica.
Historic Territories I & II
Each of the Historic Territories combines great with St. Peter's Basilica as it doubles the Happiness benefit of the territories.  With both Historic Territories in play Happiness issues should never occur, though getting both may be a bit dangerous given the cost in military unit.  However, even if lost, it cost the other player military units to get them.
Opinions
4 Culture, no population
but the cost is variable
I will admit it: St. Peter's Basilica is my favorite Wonder of them all.  If I could only construct one Wonder in a game, this would be it.  When constructed I can focus on increasing my military, directing most of my workers towards becoming the strongest nation on the block.  I use this military to defend myself from attack, and take Michelangelo if I'm able, or I seed the deck with Territories with the intent to outbid the other players.

Another favorite option of mine with St Peter's Basilica is making Theocracy my government type.  It requires I spend additional science learning civil technologies, but with the science saved from Theocracy and without a happiness problem, it about breaks even science wise.  Furthermore, Theocracy grants me the ability to build 3 lab buildings.  If I manage to get Alchemy in there, I am soon generating 6 science/turn without even trying.  Usually in this case I do not aim to lead in military, but to merely come in a close second.  This prevents players for attacking me militarily, and it yields a bit of flexibility in my plans.  My nation upgrades and learns technologies rapidly.

I believe St. Peter's Basilica provides the greatest benefit of all other Wonders out there.  It combines well  with more cards than any other Wonder, and it provides great flexibility since the player can concentrate on other aspects of the nation.  My biggest issue becomes generating enough food to get the population in play.  But usually I have more population than other players by this time, so it is a good position to be sitting.

Friday, March 9, 2012

Through The Ages - Card - Universitas Carolina

Forum for this blog is here: Forum
This is a series of blogs written about each card in Through The Ages.  To find more, simply click on "Cards" label.
Universitas Carolina (UC)*
* Yes, I know the abbreviation of the real Universitas Carolina is "CU, however I already referred to it as UC in an earlier article so I will continue to use it for internal consistency sake.
History
Universitas Carolina, also known as the Charles University of Prague, is one of the oldest academic institutions in Europe.  The Holy Roman Emperor Charles of Luxembourg had the University built in Prague.  Founded in 1349, it was modeled after the University of Paris.  Unlike the University of Paris, Universitas Carolina has maintained near continuous operations throughout its history...to some degree.

University's older than Charles University exist, but few have played as large a part in European development as Charles University.  It's list of notable alumni is long, but some of the more world famous include: Franz Kafka, Nikola Tesla, and Jaroslav Heyrovský.  But the University played more than just scientific studies in its history.  It has served as an incubator for new religious and social thought.  In the 1400's it nursed the writings of John Wyclife and Jan Hus which would later become the Protestant Reformation.

Today the Charles Unversity of Prague still operates, quite successfully.  It is ranked in the top 2% of educational institutions in the world, and in the Top 100 in Europe.  It educates roughly 51,000 students around the year.
Game Stats
In the game, Universitas Carolina has an elder sister: Library of Alexandria (LoA).  Unlike the Library, the Universitas Carolina provides 2 Science instead of one.  It also doesn't provide the ability to hold an additional military and civilian card.  Perhaps most importantly in comparison, the Universitas Carolina has a random "availability", where as the Library is available from the start of the game.

The "winning odds" the Universitas Carolina benefits again resembles that of the Library.  There is a slight 2% increase in winning the game with UC over LoA, but LoA has better odds of ending in 2nd place than UC.  Overall it is too small to make either a significant deciding factor in the game.
Strategies, Combos and Opinions
Strategies
Science: The Library forms a strong addition for starting a science strategy.  Unfortunately, the Library is subject to Ravages of Time, and has the highest Action cost of all Age A wonders.  Building the Library leads to a greatly reduced economic and military engine.  Ideally this would be offset by the ability to learn technologies quicker than opponents, but this may not be the case.

Combinations
The Library, like the other pure science wonder, Universitas Carolinas, has no card combinations.
Opinions
The Universitas Carolina, like its sister the Library of Alexandria, represents a constant stream of science, a critical component to many strategies.  UC requires 1 fewer action, 3 additional ore, and provides 1 additional science per turn compared to the Library.  In the long run, the UC loses to the Library in terms of culture output, but by only 4 points.  In return, the UC can be expected to generate about 8 more Science than the library.

An alternative to the
Printing Press, Journalism
costs twice as much but
saves on population
If both were built as quickly as possible the comparison becomes more striking with the LoA generating 20 Culture and 18 Science.  The UC would generate 18 Culture, but a whopping 32 Science!  But the UC may be built as late as turn 13, in which chase it would generate only 10 Culture, but still manage 16 Science.

In comparison to other Science/production buildings, the UC holds up significantly better than LoA.  However, the Printing Press still out performs UC since it costs 1 ore less and generates twice the culture.  However, the UC doesn't require population, a critical component to early economies.

From a statistics standpoint, the UC doesn't due much better than LoA.  In fact, building the UC seems to do slightly worse since the odds of coming in 3rd or 4th are slightly raised compared to LoA.  Still, neither seems to improve the odds of winning the game.

Overall, I like the Universitas Carolina.  I prefer it over most other Wonders, especially if I fail to get an Alchemy or have a late arriving Printing Press.  The UC can provide an alternative means of gathering Science.

Thoughts?

Tuesday, March 6, 2012

Through the Ages - Strategy - Overview

Forum for this blog is located here: Forum.

I had an issue over the weekend and an article didn't post.  So, I will speed up the posts a bit to catch up.  There will be an extra card post coming out on Friday.  This should catch us up!

Overview
Among games, I consider Through the Ages very unique.  Often times in games once a player commits to a line of action, they must pursue that course of action to its conclusion, even if halfway through the game it is obvious it is not working.  Furthermore, there are usually only one or two 'optimal' ways to win.  In Through the Ages every player is confronted with the same challenges, but must choose how they will overcome them.  If one method is not working, or becomes impossible, there is time to switch to an alternate method and lose only a little ground.

Be Prepared
That said, it is always better to go into a game with a plan or two in case a critical card doesn't appear when expected, an opponent takes a critical card, or an event changes the game.  Generally, the cards may determine an initial starting condition precluding jumping into a strategy, but usually there is something players can due to mitigate it.  In general, every player suffers the following issues to plan for:
  • Civil Actions,
  • Population (Farming) and handling Consumption,
  • Production and handling Corruption,
  • Colonizing Territories,
  • Generating Culture,
  • Building your Military,
  • Maintaining Happiness,
  • Managing the Card Row,
  • Generating Science,
  • Planning for Events,
  • Final Scoring.
This next series of articles will discuss specific strategies around each of the items mentioned above.  It is nearly impossible to focus on all the various items.  However, it is possible to focus on a few and let the rest handle themselves.  In some cases, handling one issue will resolve a second issue...or exacerbate it.

We will handle each one individually and discuss strategies around resolving them.  Which issues to ignore and which to focus on are up to the player to decide, but hopefully there are some nuggets of information in the talks.

I recommend trying some of the strategies in your games.  Besides adding variety to your games, it improves play to by providing real life insights into the game's mechanics.  Not every strategy is successful, and some are more critical than others, but situations arise where knowing a particular strategy helps to pay off.

Lastly, I recommend everyone contributing to the discussion if possible.  Everyone's insight is unique and there is no one "correct" way.  The more is shared, the better everyone's game will improve.

Friday, March 2, 2012

Through The Ages - Part XVIII - Military: Aggression and Wars

Forum for this blog is located here: Forum

Sorry for the late post.  Writing this article took much longer than anticipated as analyzing the various Military statistics and required more in-depth study than it initially seemed.  Enjoy!
Aggression and Wars
Military options in Through The Ages are very limited.  At the start of every player's turn that player has the option to perform a single political action: either a Pact/Treaty or an Aggression/War.  Pact cards are few and from our analysis account for little in way of culture.  Aggression/Wars do generate significant culture, being the third largest source of culture after buildings and Wonders.

A Popular War:
War over Culture
Aggression and Wars differ significantly.  Aggression cards resolve immediately and only the defender is at risk.  Furthermore, the defender of the Aggression may play Defense Cards to try to meet or beat the attacker.  Wars resolve the turn after they are announced, Defense cards may not be played by neither attacker nor defender, and both players are at risk to lose.

Aggression and Wars also differ in timing.  Prior to Age II, only Aggression are available.  During Age II only 3 Wars exist, and during Age III 7 Wars exist.  Given that Age III is the shortest Age, there are fewer Wars than Aggression cards.  One thing both have in common is a Military Action "cost" to play.  This is critical only when one realizes by playing an Aggression/War, the player will have fewer Military Actions with which to build units/replacements.  In a 4-player game this can become critical as a player who has current military domination may see an opponent overtake them if they continue to use their military actions to declare War or Aggression cards.
Popularity of Aggressions & Wars
The chart below shows the overall breakdown of Aggression and Wars.
Overall, through the 100 games played, there were a total of 808 Aggression or Wars played.  This implies players should expect to see 8 military conflicts in a typical game.  The largest number of conflicts recorded was 16, and the smallest was 2.

The other item the chart above tells us is when the conflicts take place.  During Age I most players focus on their economy, and so military conflicts are rarer in Age I.  As time goes on, military conflicts become increasingly common.  In general, the breakdown of military attacks in a typical game for each Age are as follows:



Our first chart also shows the "popularity" of the different conflict cards.  More Raids and Plunders exist than other cards, so seeing them high in the play list is not surprising.  Next on the high list are the two "Culture Stealing" cards: Armed Intervention and War over Culture.  Although War Over Culture exceeds Armed Intervention in number of cards in the deck, War Over Culture suffers in number of plays because it may not be played on the last round, whereas Armed Intervention is playable on the last round.
Success of Aggression
Declaring an Aggression or War is one thing, being successful at it is something else.  Since Wars and Aggression cards have different outcomes we will look at the two differently.   As long as the attacking player doesn't sacrifices troops to increase the attack, there is very little risk in initiating an Aggression.  At most, the Aggression costs some Military Actions, but that is essentially it.  Looking at the following chart we determine the ability of an Aggression or War of succeeding.

From the diagram we can see the odds of a military action succeeding is just under 60%.  The odds of success do differ depending on the Age of the attack, however.  All Age I attacks have less than 50% odds of success.  During Age II and Age III the odds of success increase to just above 55%.  However, during Age IV the success rate increases to 70%

A Popular Aggression:
Raid
These discrepancies are easily explainable.  During Age I the players' military strengths are all relatively close together, being within 1 or 2 points.  Spending a Defense card, or even sacrificing a military unit to make up the difference is not to terrible a loss.  By Age II the player's begin to differentiate themselves both economically and militarily.  Tactics come into play which greatly influence strength.  Similarly, more advance units are researched and built which increase the military strength further.  Lastly, the cost of replacing units puts a tax on the player's economy, so player's are less likely to sacrifice military units in defense if replacing the unit will cost more than the player would lose from letting the attack succeed.

This last item is particularly true when it comes to Armed Intervention.  Armed Intervention takes 7 points from the defending player and gives it to the attacking player.  However, by the time Armed Intervention comes into player most players are making more than 7 culture per turn.  Looked at over an entire game, the loss of 7 culture is roughly equivalent to losing a single game turn.  Most players are willing to accept this loss if it means their economy remains untouched and can be increased on following turn.
Success of War
Wars carry significantly greater risk.  First, the outcome takes a turn to determine and greatly impacts the uncertainty of the outcome.  First, the attacker must have a clear numerical majority in units as the act of declaring war will decrease the number of available actions to build more units for the attacker the War.  Second, the defender has a turn to play a combat changing Tactic, research an improved unit, or build more military units.  Third, although defense cards may not be played, the defender has a clear advantage in deciding if sacrificing units is a feasible option or not to reduce the Wars effects.  Lastly, Wars go "both ways", the attacker loses something if the Defender succeeds.
For our discussion of "success" in wars, we will consider wars which were Won by the player that initiated the War.  This yields the following chart:
The high success rate of Wars follows from the above discussion: there is so much at risk for the attacker Wars are only initiated when the player believes victory is certain.  Still, roughly 1 out of every 5 Wars will not succeed for the two most popular Wars: War over Culture and Holy War.  The losses of these Wars come from three primary sources: Defender Military Jump/Leader Loss, Acquisitions, and Scavenging.
Gandhi is a leader which doesn't
cause a Military Jump, but
ends Wars immediately and
protects from them in the future.
Defender Military Jump/Leader Loss
This scenario occurred in roughly half of the losses.  Basically, the defender managed to play a tactic, build a unit, or place a leader which greatly increased the military of the defender of the war to the point the War.  In 4% of the cases the defender achieved parity with the attacker rather than exceeding the attacker's strength, counting as a 'loss' for the attacker, although neither side gained nor lost any resources.

A similar situation occurs if an Age ends after a War is declared but before it resolves.  Usually the attacking player's leader was Napoleon Bonaparte and his loss resulted in a dramatic loss of military strength, making the construction of military units capable of overcoming the attacking forces.
Acquisitions
Acquisitions involve a territory coming up for bid after a player has declared a War.  The scenario may seem relatively rare, but accounts for a little under one-third of War losses:
  1. The War Initiator declares a War,
  2. During some other players turn a Territory appears as an event,
  3. The War Initiator wins the bid for the Territory and must sacrifice military units,
  4. The lost military units cost the War Initiator the war!
It is hard to determine if the War Initiator forgot a War was going on at the time the Territory bid came up, but the fact this accounted for a third of losses means the player made a decision which said the Territory was worth more than the war.
Scavenging
The last scenario where player's lost wars I refer to as "scavenging".  This scenario takes account of the multi-player aspect of Through The Ages.  This scenario is complex and seems difficult to pull of, but it goes as follows:
  1. Player A declares War on Player B.  Player B has a smaller military than Player A.
  2. Player C then declares an Aggression against Player A.
  3. To defend from Player C, Player A must sacrifice units to defend from the Aggression.
  4. This weakens A to the point where Player B then wins the War.
"Scavenging" involves attacking
a player just after they declare a war.
Consider the Tactic above, the loss of even
a single 3-point unit results in a loss
of 16 points of Military Strength!
In this circumstance usually Player C and Player A are close militarily, although often times Player C was not as strong as Player A and may sacrifice units to boost the attack.  Interestingly, the lead player rarely had a Defense card in hand to defend from this, usually because being in the lead means the Defense card is taking up space another, more useful card would occupy.  The only other last note was many times the Aggression card played was a card which attacked Player A in a significant economic or military way, such as the following:
  • Annex,
  • Assassinate,
  • Sabotage,
  • Raid.
Rarely did the second player attack with Armed Intervention, which directly steals culture, or Plunder which reduces resources.  The point here is the second player is forcing the War player to either lose critical infrastructure or weaken themselves to the point where they may lose the War.  Depending on the War played and the potential infrastructure lost, the War player is placed in a Lose-Lose situation.
Observations
Aggression, Wars and Military Strength form a major component of Through the Ages.  Overall, Aggression cards form the majority of military attacks.  Part of this is there are more Aggression cards than War cards.  Timing is critical for both, however.  Wars are more likely to succeed than Aggression cards, but both are more likely to succeed in the later Ages the card is played.  An Aggression will fail just a little over half the time, but Wars will succeed upwards of 80% of the time.  However, the attacker in Wars needs to be careful of timing to avoid end of Ages, how close the second player is to them in military strength, and be aware of the military cost of bidding for territory cards if a card is drawn.

This concludes the Military section of Through the Ages.  There are a few Odds and Ends to wrap up, but now we will begin to discuss various Strategies to improving the play.  Yes, many of these articles touched on various aspects of Strategy, but now it is come time to put them all together into a cohesive whole!

Saturday, February 25, 2012

Through The Ages - Card - Great Wall

Forum for this blog is here: Forum
This is a series of blogs written about each card in Through The Ages.  To find more, simply click on "Cards" label.
Great Wall
History
Construction on the Great Wall began around 770 BC, when six Chinese states arose and warred with each other.  To defend their individual kingdoms, each began construction of thick walls along their various borders.  Eventually the state of Qin rose above the other 6 states around 300 BC to 220 BC despite the walls.  The first emperor of China ordered the Northernmost walls become joined to defend from the Mongols, while the other internal walls were dismantled.

Construction and maintenance of the Wall varied throughout the remaining dynasties.  Some dynasties maintained the wall, others expanded it, and some simply let it fall into disrepair.  In fits and starts the Wall continued to grow and shrink in length.  At one time it was nearly 6000 Km in length, but later eroded away to under 3300 Km.  However, it was up to  Ming Dynasty (1368 to 1644) to finish the Great Project.  Prior to the Ming Dynasty the Wall had a length of around 3200 Km , upon its completion the Wall was just short of 8,852 Km (5500 miles).

The Great Wall stands as a testament to human sufferings and efforts.  The wall took millions of lives to construct.  Despite failing to prevent the Mongols from invading China, the Wall did preserve Chinese culture and architecture in its design.  Today the Great Wall still stands, but it once again begins to shrink in size due to erosion, natural causes, and human use.
Game Stats
The Wall does not provide a huge culture benefit, but most people probably build it for its secondary benefit: increased Military Strength for every Infantry and Artillery unit.  The other benefit of the Great Wall is an increase in Happiness.
Strategies, Combos and Opinions
Strategies
Military Domination
The Great Wall combines easily with the Military domination strategy.  If used in this regard, the player should most likely construct Infantry and Artillery units, and supporting Tactics: Fortifications, Defensive Army, Fighting Band, Legion, and Entrenchments.
Combinations
St Peter's Basilica
St. Peter's Basilica doubles the Great Wall's happiness benefit.  Although it is rare to be able to build both, it can be done.  Out of the 40 games involving the Great Wall, this was accomplished once.  However, the player only achieved third place.

Michelangelo
Michelangeo as a leader provides an extra Culture for every happiness on the Wonder.  This doubles the Great Walls' culture benefit while Michelangelo is in play.
Opinions
I find the Great Wall a useful Wonder, although not the best Age I wonder.  If I am going for an Military Strategy I try to include it.  I find having the Great Wall in play permits me to focus my science and resource efforts more narrowly.  If I manage to get the Great Wall, I forego Cavalry technologies and aim for one of the Tactics indicated above.  This reduces science costs by removing cavalry from the equation.  Similarly, it saves population and resources which can be put to other uses in increasing the economy.

Sources
1: http://www.chinahighlights.com/greatwall/history/
2: http://whc.unesco.org/en/list/438
3: http://www.travelchinaguide.com/china_great_wall/history/
4: http://geography.about.com/od/specificplacesofinterest/a/greatwall.htm
5: http://www.nasa.gov/vision/space/workinginspace/great_wall.html

Thursday, February 23, 2012

Through The Ages-Part XVII - Military: Tactics Progression

Forum for discussion located here: Forum

Military
Military forces in Through The Ages require units, which come from the population.  At first, only warriors are allowed but through civil actions and science, players may increase the strength and type of military units available.  The strength of military units is entirely based upon their Age, as show in the table below:

What makes the different types of military units important are the Tactics, which are found in the Military/Events deck.
Tactics
Tactics represent how the player's nation organizes is military.  Unlike civil cards, where the player has some control on choosing if a military technology can be learned, Tactics cards are drawn at random (see The Numbers Game).  Still, players can make plans around these tactics cards and determine which ones they wish to keep/upgrade, and which to discard.  Given the requirement in science resources, military actions, civil actions and population requirements, players prefer an "efficient" progression of tactics.  The following chart displays the units, the cost to build, and the strength (for those tactics with antiquated strengths this is displayed in parenthesis).

Drawbacks of Advanced Tactics - Flexibility
Overall, the more advanced tactics provide a greater increase, but there is a drawback to them beyond their cost.  Since a tactic has no effect if a single unit is missing, attempting to control territories can become "more expensive" for those with tactics requiring more units, especially if forced to sacrifice a unit.  This is a common occurrence when bidding for territories.

Consider this as an example: Two players, Alicia and Brutus have four military units each of the same type and strength - 2 Infantry and 2 Cavalry (both minimal Age for maximum gain).  Alicia has Medieval Army giving a total strength of 10 ( (2[infantry x2] + 4 [knights x2] +4 [Tactics: 2 sets of Medieval Army] = 10) ).  Brutus has Conquistadors giving a total strength of 14 ( (3[infantry x2: One is Age I for maximum Tactic effect] + 4 [knights x2] + 5 [Tactics] = 12) ).

The next political phase a Territory appears which both players want to bid on.  In this scenario, Alicia can bid an Infantry and Knight for a combined strength bid of 5.  Alicia's final strength is reduced to 5 if she wins ( (1[infantry x1] + 2 [knights x1] +2 [Tactics: 1 set of Medieval Army] = 5) ).

Brutus' best bid would be 3 (both infantry) or 4 (Age II infantry and a Cavalry).  If using the Age 3 unit, Brutus' strength drops from 14 to 4( (0[infantry] +  4 [knights x2] = 4) ). If using Age 2 Units for a bid of 4, his strength drops to 3 ( (1[infantry:Age A] +  2 [knights x1] = 3) .  In the latter case, Brutus could simply build a Knight to gain partial us of the tactic, but this only yields 8 ( (1[infantry x1: Age A ] + 4 [knights x2] + 3 [Tactics] = 8) ).

The difference seems minor, but to restore their armies to their original strength will require more resources for Brutus than for Alicia.  Alicia's smaller unit requirements on her Tactics card gives her a small advantage in Bidding wars for territory.  Although a single bid doesn't seem to make much difference, two or three territories over the course of two rounds can cripple a player with larger unit requirement tactics as they consistently spend additional resources to restore their military.  This is a topic I hope to return to later as it is a strategy I have used effectively in several games to keep "military suppressed" by simply seeding territory cards when in a weak position.
Tactic Popularity
The final discussion for this article will be the "popularity" of the various tactics.
The results really don't come as much of a surprise.  The earlier Age techs are more popular, with the exception of Heavy Cavalry and Light Cavalry.  Most of this is due to the effects of Age I Events, and the fact Cavalry technologies are not available immediately.  Except for Conquistadors, which is a natural progression from both Medieval Army and Light Cavalry, there is a significant drop in the popularity of the various Tactics.  They still remain popular, but not overwhelmingly so.

I attempted to draw results on the final position of  a player and their chosen tactics, but the results were all the tactics were evenly spread out among the various Tactics.  Out of 100 games (400 players), only 4 chose not to play any Tactics cards.  Although not conclusive, it is interesting to note their final results were also evenly spread out.

In short, it is not "which tactic you choose", but "how you choose to use it" which makes a difference in Through The Ages.

The next article will cover the various forms of Military Aggression and Wars, bringing the Military portion of the blog to a conclusion.

Edit: Corrected the military tree image after Harald Korneliussen recognized I'd left off two arrows.  Good job of keeping me honest, Harald!