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: 45, P2, 50, P3, 55 so acf is 27, 31, 35.
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 1 - 5 house P1 : 12 coins
2. level 6 - 8 house P1 : 51 coins
3. level 9 - 12 house P2: 169 coins
4. 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