We examine here the cost / benefits of expanding each type of city building as well as houses.

# Common assumptions

- the city expansion or the house upgrade is completed day 25, 10 days from now
- benefit is calculated over next 3 periods until end of game: periods end on days : 105, 150, 180.
- AC number grows such that end of P1: 45, P2, 50, P3, 55 so acf is 27, 31, 35.
- costs and benefits are in donations

Initial | P1 | P2 | P3 | P4 | |
---|---|---|---|---|---|

Day | 60 | 105 | 150 | 180 | |

Duration ( Days) | 60 | 45 | 45 | 30 | |

Duration (weeks) | 8.6 | 6.4 | 6.4 | 4.3 | |

AC | 30 | 36 | 45 | 54 | |

ACF | 27 | 31.4 | 39 | ||

Expansion cost | 54 | 63 | 78 | ||

Arsenal donations | 217 | 225 | 225 | ||

TOtal culture points | 100 | 200 | 300 | ||

Danger value | 18 | 20 | 22 | ||

Protection Value | 5.5 | 10 | 13.6 | ||

# of donations to protect 1 CP = ACF/d | 1.5 | 1.5 | 1.56 | 1.77 |

Note that some are constant whiles others are proportional to the number of players who achieve criteria

# House

Upgrade | Culture Points | Cost | benefit |
---|---|---|---|

5 to 8 | 40 / ACF | 21r + 66c = 32r = 11 don | 0.7 don / week |

8 to 12 | 89 / ACF | 46r + 169c = 74 r = 25 don. | 0.7 don / week |

Cost/Benefit | Initial | P1 | P2 | P3 | P4 | Total |
---|---|---|---|---|---|---|

Duration (weeks) | 1 | 6.4 | 6.4 | 4.3 | 17.1 | |

culture points | 6.4 | 6.4 | 4.3 | 17.1 | ||

Cost 5-8 | 11 | 2.2 | 2 | 1.8 | 0 | 17 |

Benefit 5 - 8 | 0 | 0.7 | 4.5 | 4.5 | 3 | 12.7 |

Cost 8-12 | 25 | 5 | 4.5 | 4 | 0 | 40.5 |

Benefit 8 - 12 | 0 | 2.8 | 4.5 | 3 | 10.3 |

Upgrading from Level 5 to 8: NET LOSS: -4.3 donations

Upgrading from Level 8 to 12: NET LOSS: -30.2 donations

# Arsenal

Level | Culture Points | Donations |
---|---|---|

1 | 0 | |

2 | +7.5 | + 5 donations to the City Guard every 2 days |

3 | +7.5 | + 5 donations to the City Guard per day |

Cost/Benefit | Initial | P1 | P2 | P3 | P4 | Total |
---|---|---|---|---|---|---|

Cost | 54 | 11.2 | 11.7 | 13.3 | 0 | 80.2 |

Benefit | 87 | 135 | 135 | 0 | 357 |

NET BENEFIT: 276 donations

# Town Hall

Level | Culture Points | Donations |
---|---|---|

1 | 12.5 | 12 Gold per week to distribute |

2 | +12.5 | 24 Gold per week to distribute |

3 | +12.5 | 36 Gold per week to distribute |

Cost/Benefit | Initial | P1 | P2 | P3 | P4 | Total |
---|---|---|---|---|---|---|

Duration (weeks) | 5 | 6.4 | 6.4 | 4.3 | 17.1 | |

# of donations to protect 1 CP = ACF/d | 1.5 | 1.56 | 1.77 | |||

Cost | 54 | 19.5 | 19.5 | 22.1 | 0 | 116.1 |

Benefit | 0 | 20 | 25.6 | 25.6 | 17.2 | 88.4 |

NET cost: -28.2

# Library

Assume 70% AC win 3 games a week 40% win 5 games a week

Level | Culture Points | Donations |
---|---|---|

1 | 0 | |

2 | +10 | A player who has won 3 games per week receives 1 additional gold |

3 | +10 | A player who has won 5 games per week receives 1 additional gold |

Cost/Benefit | Initial | P1 | P2 | P3 | P4 | Total |
---|---|---|---|---|---|---|

# of donations to protect 1 CP = ACF/d | 1.5 | 1.56 | 1.77 | |||

Cost | 54 | 15 | 15.6 | 17.7 | 0 | 102.3 |

70% AC / 3 | 7 | 7 | 8.4 | 10.5 | ||

Benefit | 0 | 35 | 44.8 | 44.8 | 36.1 | 160.7 |

NET Gain: 58.4 for level 2

NET cost: -11.3 for level 3

# Bank / Coin trader

### Assumptions

- level 1 - 5 house P1 : 12 coins
- level 6 - 8 house P1 : 51 coins
- level 9 - 12 house P2: 169 coins
- level 7 clothes P4: 59 coins

Level | Culture Points | Donations | level 6 - 8 | level 9 - 12 |
---|---|---|---|---|

1 | 0 | |||

2 | +10 | + 1 coin more per resource : 1 coin is .0238 cheaper | 51 x .0238 x 40 = 48 res = 16 donations | 168 …. = 53 donations |

3 | +10 | + 2 coins more per resource: 1 coin is .01765 cheaper |

Cost/Benefit | Initial | P1 | P2 | P3 | P4 | Total |
---|---|---|---|---|---|---|

# of donations to protect 1 CP = ACF/d | 1.5 | 1.56 | 1.77 | |||

Cost | 54 | 15 | 15.6 | 17.7 | 0 | 102.3 |

Benefit | 0 | 1 | 20 | 35 | 12 | 68 |

Net cost: -34 don

# Market Square

Level | Culture Points | # of Merchants |
---|---|---|

1 | 0 | 3 |

2 | +15 | 4 |

3 | +15 | 5 |

Cost/Benefit | Initial | P1 | P2 | P3 | P4 | Total |
---|---|---|---|---|---|---|

# of donations to protect 1 CP = ACF/d | 1.5 | 1.56 | 1.77 | |||

Cost | 54 | 22.5 | 23.4 | 26.85 | 0 | 126 |

Benefit | 0 | 0 | 0 | 0 | 0 | 0 |

Net cost 126 donations.

# Assembly Hall and Park

Upgrading Assembly Hall or Park increases number of expansion donations for placing in top 10 for Catan dice game or Riddle Game

Level | Culture Points | # of resource donations for city levell expansion |
---|---|---|

1 | 0 | (55 - 5 x place) / 100) x 2 x Active Citizen Factor |

2 | +10 | ((110 - 10 x place) / 100) x 2 x Active Citizen Factor |

3 | +10 | ((160 - 10 x place) / 100) x 2 x Active Citizen Factor |

**Benefit over 1 month:** = (1.1 - 0.1 x place) x ACF

For 6th place and ACF of 27 = 0.5 x AACF = 0.25 expansion levels =

13.5 donations or 40.5 resources

For 1st place : 0.5 expansion levels

Gold to players = ( # players (1-10) x 3 + # players (11-25) x 2 + # players (26-50) +

# Bath House

You can play a dice game where you have even odds of winning. Choose 3 numbers to have 1 in 2 chance

Level | Culture Points | # of resource donations for city levell expansion |
---|---|---|

1 | 0 | 0 |

2 | +10 | + 0.075 donation to the city per lost game |

3 | +10 | + 0.15 donation to the city per lost game |

You can throw the dice 5 times and you have to guess what the result will be:

- 1 guess: 1 in 6 chance, you win 6 resources (including resource you bet),
- 2 guesses: 1 in 3, you win 3,
- 3 guesses 1 in 2 you win 2.

In the long run you break even but you can easily have a 5-6 resource losing streak

This is interesting. It actually pays more to make 1 guess because you lose 5 in 6 but win 6 when you win. Here you can easily have a 20 resource losing streak and then win 18 resources 5 turns.

I think the only reasonable way to play this is with 3 guesses.

**Benefit over 1 month:** =

- Betting 3 number: # of players x 30 days x .075 donations x 3 resources x 5 times x 1/2 losses = # of players x 16,875 resources
- Betting 1 number: # of players x 30 days x .075 donations x 3 resources x 5 times x 5/6 losses = # of players x 28.125 resources

For each level of the bathhouse:

With 15 players betting each day 3 numbers 5 times: 253 resources a month.

With 15 players betting each day 1 number 5 times: 421 resources a month.

# City Wall

Level | Culture Points | Donations |
---|---|---|

1 | 0 | 0 |

2 | +5 | + 20 % per donation to the City Guard made by the citizens |

3 | +5 | + 40 % per donation to the City Guard made by the citizens |

4 | +5 | + 60 % per donation to the City Guard made by the citizens |

**Benefit over 1 month:** 2 donations x 20% x (# of citizens donating) x 3 resources

For 30 citizens: 36 resources