Katimavik Bay Building Expansion

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

Common assumptions

  1. the city expansion or the house upgrade is completed day 25, 10 days from now
  2. benefit is calculated over next 3 periods until end of game: periods end on days : 105, 150, 180.
  3. AC number grows such that end of P1: 30, P2, 36, P3, 45 so acf is 27, 31.4, 39.
  4. costs and benefits are in donations
(1)
\begin{align} Protection value = \left[ Citizen Donations \over Active Citizen factor \right] + \left[ Arsenal Donations \over 50 \right] \end{align}
(2)
\begin{align} Danger value = \left[ \left[ Culture value of city + Culture value of Active Citizens \right] \over Protection value \right] \end{align}
(3)
\begin{align} Citizen Donations = ACF x \left[ Culture points \over Danger Value \right] - \left[ Arsenal Donations \over 50 \right] \end{align}
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

  1. level 5 house P1 : 59 / 6 - 59 / 7 = 1.4 resources
  2. level 8 house P2 : 26 x 51 coins / 6 - 26 x 51 / 7 =31 ressoruces = 10 don.
  3. level 12 house P3: 26 x 169 (1/6 - 1/7) = 104 resourcses = 35 don.
  4. level 7 clothes P4: 26 x 59 (1/6 - 1/7) = 36.5 = 12 donations
Level Culture Points Donations
1 0
2 +10 + 1 coin more per resource
3 +10 + 2 coins more per resource
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 + 0.05 donation to the city per lost game
3 +10 + 0.1 donation to the city per lost game

You can play 5 times. This is interesting. It actually pays more to pick1 number out of 6 hoping to win 5 more and loosing 1 resource 5 times. You can play 5 times

Benefit over 1 month: =

  • Betting 1 number: # of players x 30 days x .05 x 4.16 = # of players x 6,24 resources
  • Betting 3 numbers: # of players x 30 days x .05 x 2.5 = # of players x 5.75 resources

With 30 players betting each day 3 numbers 5 times: 172 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

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