Monday, January 2, 2012

Through The Ages-Part VIII-Culture:Giving Final Scoring Its Due

Forum for discussion located here:
Brief Review
Before moving on to Culture Generation, it is necessary to give Final Scoring, or "Impact" cards (from their wording: Impact of...), a more in-depth look.

In the previous article it was mentioned Impact cards cause a change in player position order roughly 60% of the time.  In other words, in 3 out of 5 games played a player will overtake another player in culture through Impact cards.  However, in less than 5% of games (or 1 in 20) does this affect the player enough to eventually be the final winner.  (full article here: )
Culture Bonuses
The following chart provides a breakdown of the highest scores in twenty games. Included is the "average" of all the games:
In all the cases, the majority of the points are formed before the end of Age IV.  In fact, this is the case for all the pl
ayers.  Within the range of games, there may be several Impact cards played, or few.  The more cards, the greater the relative score increases, but overall the pattern remains unchanged.
Impact Card Popularity
The following chart lists the appearance of the Impact cards in the sample games.  Overall, the probability most cards will make an appearance in a game is between 35%- 50%.  Only three cards should not be counted on to make an appearance:

  • Impact of Colonies: 30%
  • Impact of Science: 30%
  • Impact of Technology: 20%

Culture Gain
Perhaps more important than the appearance of the Impact cards is the amount of culture a player can expect to gain.  The following chart shows several Culture related statistics for games played.

  • Maximum Gain - Maximum recorded gain in Culture between the player who benefited the most and the player who benefited the least.
  • Most Common Gain - The Mode of the maximum culture gain  the player who benefited the most and the player who benefited the least.  Most common maximum Culture gain found in games.
  • Average Gain - The average culture difference between the player who benefited the most and the player who benefited the least.
  • Net Gain - The gain in Culture between the player that benefited the most and the player who benefited the second most
  • Average Net Gain - Average culture benefit between the player that benefited the most and the player that benefited the second most.
These last two statistics are probably the most important of the set.  Although the other statistics show the maximum potential benefit a player may receive, the last two show the gain against the next best player.
Impact of Industry (IoI)

A single game accounts for the majority of the Impact of Industry's high score.  In this game, IoI scored 45 points, and the second highest player scored only 10.  If the game is removed from the statistics, IoI's average rating falls from 7 Culture to around 4 Culture.
Most Profitable Scoring Cards
Of the Final Scoring cards, Impact of Progress and Impact of Technology will affect a player's score the most (on average).  Technology is significant because it is the card played the least, but when it does make an appearance it could result in a huge increase in culture. 
From the previous article we determined the Impact of cards are unlikely to bring a player into victory.  This article goes to assist in proving this point.  For the majority of the cards, the culture gains are roughly equal, or at most within 5 points of each other.  Therefore, if the every player plays logically, the various Impact Of cards effectively cancel each other out as every player plays a card which maximizes their gain and minimizes their opponents.

Overall, the best use of this knowledge may simply be as a mental exercise.  If Final Scoring cards affect the outcome so little in regards to the eventual winner, the above is simply an observation and a potential explanation.  Players should still play their cards to maximize their benefit and minimize their opponents.

Any other thoughts on the "Impact Of..." scoring cards?
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