Highmoor is an invented but typical 13th-century English stone castle: an outer wall with towers, and behind it an inner ward and a keep. Inside are 100 fighting men and 100 civilians, 4 months of food and one well. Outside, 3,000 attackers have just arrived. Change the castle, play one siege day by day, then run it 1,000 times.
Same settings, new dice every run.
Every simulated day the same things happen in order. Everyone inside eats. We check the well. Sickness spreads a little, faster when people are hungry. Outside, the attackers eat whatever supplies arrive and lose men to camp disease. The trebuchets throw stones of up to about 300 lb (136 kg) (Illumin, USC), the defenders repair what they can, the miners dig, and if there is a gap in the wall the attackers decide whether to charge. If the outer wall is stormed, the survivors fall back to the inner ward and keep and fight on. Then it starts again with new dice.
The castle falls when fewer than 3 men are still fit to fight, or when the last line is stormed. The defenders win when the attackers drop below 4 men for every defender and below half the army they arrived with, too few to keep the siege going. This page runs a JavaScript copy of the episode's simulation (siege.py); with the episode's settings it gives the same results within the normal run-to-run spread.