✨ Religious Spread

Once per turn, after every player has moved, each founded world religion rolls its spread chance. On a success it spreads to exactly one city or tribal settlement, picked as described in the next section.

• The chance belongs to the religion, not to a player, and the city it picks can be anyone's: yours, a rival's, or a tribe's.
• Map size adds to it for world religions only: Duel +0, Tiny +0, Small +2, Medium +4, Large +6, Huge +8.
• Every theology the religion has established adds to it.
• Player bonuses add up across all players. Pilgrimage gives +25 to your state religion's chance, and if two players both run it with the same state religion, that religion gets it twice. The target city is still anyone's, so the law also pushes your religion into your neighbours' cities.
• Some religions never roll: every nation's pagan religion, plus Atenism and Hinduism. They spread only through their shrines, improvements and events.

When the roll succeeds, every eligible city gets a score and the lowest score wins. The score starts from the city's distance to the Holy City and has a random part that grows with that distance, so a near city isn't guaranteed to win but a far one almost never does.

1. Distance. Count the tiles from the Holy City to the city.
2. Connection. If the city is on the Holy City owner's trade network (roads, rivers and sea), multiply that distance by 67%, rounded down.
3. Religions already there. Multiply by one more than the number of religions the city already has. Every religion counts, including pagan religions and the owner's state religion. A city with one religion (even just its nation's pagan faith) counts as twice as far away, a city with two as three times as far.
4. The roll. Call the result D. The game picks a random whole number from 1 to D and multiplies D by it, so the score is anywhere from D to D × D.

Tribal settlements join the contest for world religions, but only settlements of the tribes you can do diplomacy with (Gauls, Vandals, Danes, Thracians, Scythians, Numidians, Huns) that have no religion yet. They use the plain distance with no connection test, and they lose exact ties to cities.

A city can be picked only if:

• it doesn't already have the religion;
• the religion hasn't been purged from it (a Purge keeps the roll from bringing it back until it gets back in some other way);
• the religion is a world religion;
• if the city refuses spread (Iconography for all of the owner's cities, or a Dissent project from an event), the religion is the owner's state religion. Under Iconography with no state religion, the roll never picks your cities.

The roll does nothing for a religion that has no Holy City.

Because the random part is multiplied by D, a city's score grows with the square of its distance. Two consequences:

• Twice as far is much worse than half the chance. At distances 6 and 12, the farther city wins 8.3% of the time.
• Some cities can't win at all. A city's best score is D, and the nearest city's worst is D × D. So with a nearest D of 4, no city above 16 can win; with a nearest D of 6, nothing above 36.

The table shows the chance that the farther of two cities wins, for every pair of D values. Apply the connection and religion multipliers first: a connected city at distance 12 is D = 8, and an unconnected city at distance 6 that already has one religion is D = 12.

Every turn, right after the spread rolls, the game checks whether a world religion can be founded, and founds at most one. A city qualifies when the religion isn't founded yet and the city's owner meets every requirement in the table. The founding city becomes the Holy City, which every later spread roll measures distance from.