圍城

Sieges are the primary way to capture forts. Sieging forts usually takes lots of time but can be done with minimal losses.

The another way to capture forts are assaults which are faster to execute but result in more losses.

Key elements

• Dice: Random rolls from 1 to 14 are used to weaken and eventually capture a fort.
• Fort level: Higher level forts have a stronger dice roll reduction. Higher level forts also need more units to siege.
• Fort Defense: Increases the interval for dice rolls resulting in slower captures.
• General: Martial skill increases the dice roll. Enslavement efficiency increases amount of captured slaves.
• Army: Every fort level needs 4000 manpower to siege.
• Siege Accumulation: Progress of the siege which increases the dice roll.
• Siege Ability: Reduces the interval for dice rolls resulting in faster captures.

Dice roll

The siege is mostly based on dice rolls. The garrison instantly surrender when the dice rolls a value with 20 or more. Roll modifiers are needed to achieve this because the highest value of the dice is only 14.

Below is a list of outcomes with each dice roll:

• Disease Outbreak (roll 1): No progress, 5% of attackers die.
• Status Quo (rolls 3-4 and < 1): No progress.
• Supplies Shortage (rolls 5 -11): +1 to Siege Accumulation, 1% of Garrison dies.
• Food Shortage (rolls 12 - 13): +2 to Siege Accumulation, 3% of Garrison dies.
• Water Shortage (rolls 14 - 15): +3 to Siege Accumulation, 5% of Garrison dies.
• Defenders desert (rolls 16 - 19): +2 to Siege Accumulation, 10% of Garrison dies.
• Breach (dice 14, all modifiers ignored, higher priority): +2 to Siege Accumulation, +1 to Breach, 5% of Garrison dies.
• Surrender (rolls 20+ or less than 100 garrison remaining, top priority): Siege over.

Below is a list of roll modifiers:

• Dice: 1 - 14
• Siege Accumulation: 0 - 11, increases over time when the fort gets weakened.
• General: 1 for every 5 martial skill.
• Fort level: -1 for every fort level.
• Siege Engineers: 0 - 7, from inventions.

Siege interval

By default, the dice is rolled every 25 days when sieging a fort. Non-fortified cities are instantly captured in 15 days because no garrison.

Fort Defense increases the interval. For example with a +10% Fort Defense the interval is 27 days.

Similarly Siege Ability reduces the interval. For example with a +10% Siege Ability the interval is 23 days.

All modifiers are calculated additively. So a +10% Fort Defense and +10% Siege Ability cancel each other.

Time to capture

Monte Carlo method can be used to simulate the siege system and to estimate how many intervals are required for a capture. 1000000 simulations were ran for each scenario. Capture by garrison running out was extremely unlikely (less than 0.01%).

• Initial: Roll modifier at start of the siege (without siege accumulation).
• Average: How many intervals are needed on average
• Lucky (5th pct): 5 % chance to capture the fort with this amount of rolls or less
• Good(25th pct): 25 % chance to capture the fort with this amount of rolls or less
• Expected (50th pct): 50 % chance to capture the fort with this amount of rolls or less
• Bad (75th pct): 25 % chance to capture the fort with this amount of rolls or more
• Unlucky (95th pct): 5 % chance to capture the fort with this amount of rolls or more
• Disease: Average amount of diseases per siege.
• Assault: Chance that the siege could be ended with an assault (garrison falls below 50% or 75% with a breach).
• Intervals saved: Average amount of intervals saved when assaulting with above conditions.
• Intervals saved (total): Same as above but also includes sieges where assaults were not possible.

Initial	Average	Lucky	Good	Expected	Bad	Unlucky	Disease	Assault	Intervals saved	Intervals saved (total)
-5	28	13	18	24	34	53	75 %	71 %	13	9.3
-4	19	11	14	17	22	33	57 %	51 %	7.0	3.5
-3	15	9	12	14	17	24	43 %	37 %	4.7	1.7
-2	12	8	10	12	14	19	30 %	27 %	3.5	0.95
-1	10	6	8	10	12	16	19 %	20 %	2.8	0.56
0	8.6	5	7	8	10	13	10 %	14 %	2.4	0.35
1	7.4	4	6	7	9	11	0 %	10 %	2.1	0.21
2	6.4	4	5	6	7	10	0 %	6.7 %	1.9	0.12
3	5.6	3	4	5	7	8	0 %	4.2 %	1.7	0.07
4	4.8	3	4	5	6	7	0 %	2.4 %	1.5	0.04
5	4.2	2	3	4	5	7	0 %	1.3 %	1.4	0.02
6	3.6	1	2	3	5	6	0 %	~0 %	1.2	~0
7	3.1	1	2	3	4	5	0 %	~0 %	1.1	~0
8	2.7	1	2	3	4	5	0 %	~0 %	1.0	~0
9	2.3	1	1	2	3	4	0 %	0 %	1.0	0
10	2.1	1	1	2	3	4	0 %	0 %	1.0	0

Above values multiplied by the length of a siege interval results in the total time to capture.

For example a level 1 fort will be captured in ~8 months with the default 25 day siege interval.

Enslavement

After the siege, some pops of the city may get captured and moved to attacker's cities. Captured pops also have a chance to get demoted or even die. Enslavement requires the sieging army to have a general.

Slaves are easier to capture than other pop types. All pops are used to count amount of slaves captured.

Citizens, freemen and tribesmen are harder to capture. Each pop type is considered separately.

 citizens_captured = round_nearest(enslavement_efficiency * total_citizens / 4)
 freemen_captured = round_nearest(enslavement_efficiency * total_freemen / 4)
 tribesmen_captured = round_nearest(enslavement_efficiency * total_tribesmen / 4)
 slaves_captured = round_up(enslavement_efficiency * total_pops)

Each captured pop has a 50% chance to get demoted and a 33% chance to die instead of moving to an attacker's city.

機制