A mission is issued according to its score. The mannor in which it is, is not documented. Therefore we don't really know when or how a mission is issued. However, I have my theories. My leading theory is that each supported mission type has a formula to calculate its score based on the parameters. At the start of every factions turn the game calculates the score of each mission, if the faction currently has no current missions issued already (excluding crusades). Then the game selects and issues the mission that has the highest score. However, in play testing I found that when you eliminated all missions except the Gift mission and eliminated the exclude duration that the mission wasn't issued every turn. Sometimes it would be issued back to back, sometimes even three turns in a row. Then other times it would be issued every other turn. There even were some gaps lasting 10 turns without the mission being issued. When I turned on the exclude duration, the mission appeared much less frequently. It rarely appeared twice within 10 turns.
This leads me to believe that not only does it take the highest score, but that score also has to exceed a certain threshold. In order for that to work, the score would have to be calculated and added to the previous turns score every turn. And in the end, I am still really confused on how exactly missions are issued based on the score. The only known right now is that higher score means higher chance of being issued.
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