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Thursday, January 5, 2012

Through The Ages - Part IX- Culture: A Typical Game

The forum for discussion of this topic is located here: http://gamesstrategyandtactics.freeforums.org/strategy-analysis-f6.html
"Average" Scores
Having eliminated Final Scoring as the potential for a deciding factor in the majority of games, we now look at how the game generates culture.  Averaging the results of the sample games we derive the following picture:

Note that these are averages of each player's score at the end of every Age.  The highest final score encountered was 331 culture, and the lowest winning culture was 88.  The lowest scoring players varied from 26 to 175 culture.  The important point from the chart above is the comparative growth of the players' culture.
Milestones
From the average game above and reviewing the games played, the following milestones may be used
as benchmarks to determine how a player is doing against the best player of an "average" game:



Average High Low
Age I 11 27 3
Age II 39 80 11
Age III 108 186 61
Age IV 146 225 74
Final 211 331 88

A breakdown of the culture generated in an "average" game by player is shown below:

During the first two Ages it is difficult to determine major differences in scores.  Indeed, at the end of Age I the players are effectively tied.  Even during Age II they are close enough to potentially overtake each other.  Indeed, the Second Place player is often trailing the other players through the first two ages, only to overtake all but the eventual leader in Age III.

As a final note, each player generates close to the same amount of Bonus ("Impact") scoring.  Only 19 points separate the bonus points generated by player 1 and player 4.

Another view is to look at the percentage of a player's culture generation by Age:

What is not shown is the length of each Age compared to the amount of culture it generates.  Age I, for example, lasts the longest (8 turns), but generates the smallest amount of culture.  Similarly, the Age IV lasts only 2 turns (at most), yet it accounts for 18% of the winning player's culture, as much as the first 14 turns of the game!  The charge shows over half the winning player's culture is generated in the last 6 turns of the 20 turn game.  This clearly demonstrates the "culture acceleration" as the game progresses.
"Constant" Culture Generation
Another way to look at the above information is to view the game as a "constant" culture generation.  Since a game lasts 20 turns, but a player may only score on 19 of them and the average target value is 146 culture at end of Age IV, a player should generate:  146/19 = 7.7 Culture per turn starting on Turn 2.  This target number is impossible to achieve early in the game, but easily achievable later.  Similarly, using the Actions generation from previous articles, we arrive at the following table of target values by Age:
Total deltaCulture Turns Culture/Turn Actions Culture/Action
Age I 11 11 7 1.6 32 0.34
Age II 39 28 6 4.7 36 0.78
Age III 108 69 4 17.3 28 2.46
Age IV 146 38 2 19.0 14 2.71
Overall 146 146 20 7.3 114 1.28

From the table above, any action which would generate more than the target "Culture per Action" or the average "Culture per Turn" could be deemed a "good" action/turn.  This is useful for ranking and measuring the various benefits of cards.  Unfortunately, this only looks at the "short term" problem of action generation and not the strategic picture.  However, it does provide a useful ranking system for measuring overall effectiveness of cards in comparison to each other.
Conclusions
The conclusions here are simple:
  • Player's relative "final position" is difficult to determine, even by the end of Age II,
  • A Player should always generate the same, or more, culture as that of the previous turn,
  • Players' need to think "Long term" on their Culture Generation Engine as it isn't until Age III that the engine really begins to make a significant difference among players.
Lastly, we established a baseline for comparing to determine how "effective" players are based on their culture generation at the end of an each Age.

*Edit: I fixed the chart which was not showing properly.
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