Designer: Andreas Seyfarth

Year: 2002

Artist: Harald Lieske, Franz Vohwinkel

Publisher: alea, Ravensburger + 12 more

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The questions of interest here are:

  1. Is there any clear difference in game results for going first (or second, or third)
  2. How do games end? Of the three victory conditions, which ones are triggered most commonly (or rarely).
  3. Which buildings seem to be most used in practice. Are there any buildings which are hardly ever used?
  4. Is there a clearly optimal choice of actions in the first turn?
  5. If a player is very bad at the game, does this provide an advantage to the players to their immediate left and right?

The experiments reported below use a variety of `intermediate’ agents, with an increasing computational budget per decision. As we provide more time to make each decision, we expect the agents to get better. The budgets used are 0.04, 0.2 and 1.0 seconds per decision (or, 40, 200 and 1000 milliseconds). We term these agents ‘intermediate’ as they have a short-to-medium range planning horizon, and hence do not usually adopt a strategy that uses the large victory point buildings - and in practice a skilled human player can beat them. Work is in progress to repeat this analysis with agents that focus on the end-game victory point bonuses.

200 games were run for each of these different budgets.


Effects of player order on winning

Firstly a graph of the correlation between starting position of a player and their final position in the game.

This varies as the quality of the players increases, but in general the first player has a lower probability of winning than the players in 3rd or 4th position.

Budget 40ms

Budget 200ms

Budget 1000ms

Budget 5000ms

Victory Condition triggers

A summary of the game-end conditions as one of the three possibles:

It is possible for more than one of these to apply to any given game. The table below shows that the majority of games finish due to the exhaustion of victory points, with very few games (beyond three players) finishing due to a player completing their town spaces.

This is naturally linked to the intermediate nature of the agents. We would expect this result to be different once longer-term agents are also used.

Budget 40ms

Games out of 100 that finish with every combination of end conditions
Town Trigger VP Trigger Colonist Trigger 3 4 5
No Yes No 24 44 82
No No Yes 41 33 8
No Yes Yes 5 20 10
Yes No No 16 0 0
Yes No Yes 8 0 0
Yes Yes Yes 3 1 0
Yes Yes No 3 0 0

Budget 200ms

Games out of 100 that finish with every combination of end conditions
Town Trigger VP Trigger Colonist Trigger 3 4 5
No Yes No 43 69 90
No No Yes 35 14 2
No Yes Yes 6 16 8
Yes No No 6 0 0
Yes No Yes 4 0 0
Yes Yes No 3 0 0
Yes Yes Yes 2 0 0

Budget 1000ms

Games out of 100 that finish with every combination of end conditions
Town Trigger VP Trigger Colonist Trigger 3 4 5
No Yes No 62 76 90
No No Yes 20 10 4
No Yes Yes 12 13 6
Yes Yes Yes 2 0 0
Yes No Yes 2 0 0
Yes No No 2 0 0
Yes Yes No 1 0 0

Budget 5000ms

Games out of 100 that finish with every combination of end conditions
Town Trigger VP Trigger Colonist Trigger 3 4 5
No Yes No 66 74 96
No No Yes 19 12 0
No Yes Yes 12 13 4
Yes Yes No 2 0 0
Yes No No 1 0 0
Yes Yes Yes 0 0 0
Yes No Yes 0 0 0

Buildings

Then a table of the buildings constructed (on average, plus the min/max values) by the end of the game.

Apart from end-game victory buildings (the Residence, City Hall, The three buildings that are least used across the board are:

Budget 40ms

Mean and Max number of buildings at end of game for each player count
Building Players-3 mean Players-3 max Players-4 mean Players-4 max Players-5 mean Players-5 max
SMALL_INDIGO_PLANT 2.68 3 3.94 4 4.00 4
SMALL_SUGAR_MILL 1.95 3 3.54 4 3.92 4
INDIGO_PLANT 2.33 3 2.98 3 2.99 3
TOBACCO_STORAGE 2.04 3 2.44 3 2.08 3
SUGAR_MILL 1.45 3 2.17 3 2.23 3
SMALL_WAREHOUSE 1.59 2 1.96 2 2.00 2
HACIENDA 1.47 2 1.97 2 2.00 2
SMALL_MARKET 1.48 2 1.96 2 2.00 2
CONSTRUCTION_HUT 1.48 2 1.96 2 1.99 2
HOSPICE 1.42 2 1.71 2 1.62 2
COFFEE_ROASTER 1.23 3 1.22 3 0.64 3
LARGE_MARKET 0.67 2 0.61 2 0.29 2
OFFICE 0.46 2 0.58 2 0.26 2
FACTORY 0.50 2 0.36 2 0.17 2
GUILD_HALL 0.70 1 0.19 1 0.04 1
HARBOUR 0.60 2 0.20 2 0.09 1
FORTRESS 0.68 1 0.14 1 0.04 1
CITY_HALL 0.66 1 0.06 1 0.02 1
RESIDENCE 0.58 1 0.12 1 0.01 1
CUSTOMS_HOUSE 0.49 1 0.11 1 0.03 1
LARGE_WAREHOUSE 0.36 2 0.14 2 0.06 2
UNIVERSITY 0.26 2 0.12 2 0.01 1
WHARF 0.13 1 0.04 1 0.00 1

Budget 200ms

Mean and Max number of buildings at end of game for each player count
Building Players-3 mean Players-3 max Players-4 mean Players-4 max Players-5 mean Players-5 max
SMALL_INDIGO_PLANT 2.75 3 3.94 4 4.00 4
SMALL_SUGAR_MILL 1.84 3 3.33 4 3.86 4
INDIGO_PLANT 2.56 3 2.97 3 3.00 3
TOBACCO_STORAGE 2.30 3 2.47 3 2.06 3
SMALL_WAREHOUSE 1.65 2 1.98 2 2.00 2
SMALL_MARKET 1.45 2 1.94 2 1.99 2
SUGAR_MILL 1.43 3 1.98 3 1.87 3
HACIENDA 1.31 2 1.92 2 1.99 2
CONSTRUCTION_HUT 1.28 2 1.93 2 2.00 2
HOSPICE 1.47 2 1.67 2 1.54 2
COFFEE_ROASTER 1.48 3 1.04 3 0.72 3
HARBOUR 0.90 2 0.34 2 0.09 1
LARGE_MARKET 0.52 2 0.38 2 0.20 2
FACTORY 0.54 2 0.30 2 0.15 2
OFFICE 0.36 2 0.36 2 0.12 2
GUILD_HALL 0.64 1 0.16 1 0.03 1
FORTRESS 0.42 1 0.06 1 0.02 1
CUSTOMS_HOUSE 0.36 1 0.05 1 0.02 1
RESIDENCE 0.38 1 0.04 1 0.00 1
CITY_HALL 0.36 1 0.03 1 0.00 0
LARGE_WAREHOUSE 0.16 2 0.01 1 0.01 1
UNIVERSITY 0.05 1 0.04 1 0.01 1
WHARF 0.07 2 0.01 1 0.00 0

Budget 1000ms

Mean and Max number of buildings at end of game for each player count
Building Players-3 mean Players-3 max Players-4 mean Players-4 max Players-5 mean Players-5 max
SMALL_INDIGO_PLANT 2.86 3 3.95 4 4.00 4
SMALL_SUGAR_MILL 1.73 3 3.16 4 3.78 4
INDIGO_PLANT 2.62 3 2.98 3 2.99 3
TOBACCO_STORAGE 2.44 3 2.63 3 2.16 3
SMALL_WAREHOUSE 1.80 2 1.99 2 1.98 2
SMALL_MARKET 1.31 2 1.88 2 1.98 2
SUGAR_MILL 1.33 3 1.92 3 1.78 3
HOSPICE 1.51 2 1.82 2 1.64 2
HACIENDA 1.06 2 1.84 2 1.95 2
CONSTRUCTION_HUT 1.04 2 1.86 2 1.94 2
COFFEE_ROASTER 1.32 3 0.92 3 0.54 3
HARBOUR 1.06 2 0.28 2 0.12 2
FACTORY 0.53 2 0.22 2 0.16 2
GUILD_HALL 0.66 1 0.14 1 0.03 1
LARGE_MARKET 0.34 2 0.30 2 0.12 2
OFFICE 0.14 2 0.20 2 0.14 2
FORTRESS 0.33 1 0.04 1 0.03 1
CUSTOMS_HOUSE 0.30 1 0.04 1 0.02 1
RESIDENCE 0.25 1 0.04 1 0.01 1
CITY_HALL 0.20 1 0.01 1 0.00 0
WHARF 0.09 2 0.01 1 0.01 1
LARGE_WAREHOUSE 0.06 1 0.01 1 0.00 0
UNIVERSITY 0.03 1 0.01 1 0.00 0

Budget 5000ms

Mean and Max number of buildings at end of game for each player count
Building Players-3 mean Players-3 max Players-4 mean Players-4 max Players-5 mean Players-5 max
SMALL_INDIGO_PLANT 2.94 3 3.98 4 4.00 4
SMALL_SUGAR_MILL 1.77 3 3.19 4 3.78 4
INDIGO_PLANT 2.67 3 2.99 3 3.00 3
TOBACCO_STORAGE 2.56 3 2.52 3 2.07 3
SMALL_WAREHOUSE 1.86 2 2.00 2 2.00 2
HOSPICE 1.79 2 1.86 2 1.58 2
SUGAR_MILL 1.24 3 2.10 3 1.75 3
SMALL_MARKET 1.19 2 1.94 2 1.97 2
HACIENDA 0.86 2 1.88 2 1.95 2
CONSTRUCTION_HUT 0.84 2 1.74 2 1.89 2
COFFEE_ROASTER 1.15 3 0.80 3 0.46 3
HARBOUR 1.14 2 0.29 2 0.14 2
FACTORY 0.57 2 0.18 2 0.13 2
GUILD_HALL 0.62 1 0.10 1 0.03 1
LARGE_MARKET 0.24 2 0.26 2 0.12 2
OFFICE 0.14 2 0.16 2 0.07 2
FORTRESS 0.32 1 0.02 1 0.00 0
CUSTOMS_HOUSE 0.18 1 0.05 1 0.01 1
RESIDENCE 0.22 1 0.00 1 0.01 1
WHARF 0.07 2 0.03 1 0.00 1
CITY_HALL 0.07 1 0.01 1 0.00 0
UNIVERSITY 0.04 1 0.02 1 0.03 1
LARGE_WAREHOUSE 0.06 2 0.00 0 0.01 1

Buildings built by round

The graphs below are a summary of when the different types of building are built. For each building type they show how many are built in each round of the game, so there is a large spike in the first turn for building Indigo plants.

Budget 40ms

Production

Commercial

Victory

Budget 200ms

Production

Commercial

Victory

Budget 1000ms

Production

Commercial

Victory

Budget 5000ms

Production

Commercial

Victory

First Actions in Game

The graph and tables below show the percentage of games in which the first (second, third…) player selects on their first move.

There is a very clear order of:

This is clearest for the largest computational budget agent (The most `intelligent’ one that spends most time thinking about the implications of its move, and what the later players will do on their turn).

Budget40ms

Role selection in 3-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 3 40 1 40 18 15 8 6 9 4
Players 3 40 2 33 15 11 4 12 8 16
Players 3 40 3 2 13 2 8 15 6 55
Role selection in 4-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 4 40 1 46 26 10 4 8 6 1
Players 4 40 2 32 18 10 4 5 6 26
Players 4 40 3 4 16 7 2 24 4 42
Players 4 40 4 5 8 10 20 33 6 19
Role selection in 5-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 5 40 1 49 28 10 4 4 4 0
Players 5 40 2 28 14 11 6 9 2 30
Players 5 40 3 9 11 7 5 28 6 34
Players 5 40 4 3 10 6 26 31 4 20
Players 5 40 5 7 19 8 30 22 5 9

Budget200ms

Role selection in 3-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 3 200 1 66 15 13 2 2 2 0
Players 3 200 2 24 7 4 1 2 0 62
Players 3 200 3 0 5 1 0 60 1 33
Role selection in 4-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 4 200 1 74 22 5 0 0 0 0
Players 4 200 2 23 6 0 0 0 2 69
Players 4 200 3 1 4 1 0 67 1 26
Players 4 200 4 0 2 0 64 28 2 4
Role selection in 5-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 5 200 1 80 18 2 0 0 0 0
Players 5 200 2 19 6 0 0 0 0 75
Players 5 200 3 0 2 3 0 76 0 18
Players 5 200 4 0 2 0 73 18 1 6
Players 5 200 5 0 49 24 21 6 0 0

Budget1000ms

Role selection in 3-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 3 1000 1 96 2 2 0 0 0 0
Players 3 1000 2 4 0 0 0 0 0 95
Players 3 1000 3 0 1 0 0 94 0 4
Role selection in 4-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 4 1000 1 90 10 0 0 0 0 0
Players 4 1000 2 10 0 0 0 0 0 90
Players 4 1000 3 0 0 0 0 90 0 10
Players 4 1000 4 0 0 0 90 10 0 0
Role selection in 5-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 5 1000 1 92 7 0 0 0 0 0
Players 5 1000 2 8 0 0 0 0 0 92
Players 5 1000 3 0 0 2 0 92 0 6
Players 5 1000 4 0 0 0 92 6 0 2
Players 5 1000 5 0 62 30 6 2 0 0

Budget5000ms

Role selection in 3-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 3 5000 1 92 0 8 0 0 0 0
Players 3 5000 2 8 0 0 0 0 0 92
Players 3 5000 3 0 2 0 0 92 0 6
Role selection in 4-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 4 5000 1 80 11 8 0 0 0 0
Players 4 5000 2 17 0 2 0 0 0 80
Players 4 5000 3 2 5 0 0 80 0 12
Players 4 5000 4 0 0 0 80 13 0 6
Role selection in 5-player games in the first turn (percentage of all games)
PlayerCount budget Player BUILDER PROSPECTOR SETTLER CAPTAIN CRAFTSMAN TRADER MAYOR
Players 5 5000 1 82 8 10 0 0 0 0
Players 5 5000 2 16 2 1 0 0 0 80
Players 5 5000 3 2 8 0 0 80 0 10
Players 5 5000 4 0 0 0 81 13 4 2
Players 5 5000 5 0 46 34 12 4 0 3

Sitting next to a bad player

For three player Puerto Rico, we then run a number of additional games in which we insert a Random player in each game. This player will, as the name suggests, act completely randomly. The question is then whether this helps the player to their left (who takes the next turn), to the player to their right (who took the previous turn).

As the results below show, there is a clear advantage to the player who sits downstream (to the left) of this very bad player.

Percentage of games in which the player to the left of random comes 1st, 2nd or 3rd (the columns are for each budget)
40 200 1000 5000
1 50 66 64 64
2 48 34 36 36
3 2 0 0 0
Percentage of games in which the player to the right of random comes 1st, 2nd or 3rd (the columns are for each budget)
40 200 1000 5000
1 52 42 40 40
2 46 58 60 60
3 2 0 0 0