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Mission chance of success depends on either Happiness or Familiarity. Local Happiness is basically how much the village likes you. Familiarity is how much you know about the village. Familiarity can only ever go up, while Happiness often goes down.

First contact missions work differently. See this page:

Main article: Native Civilization/First Contact

The formula works as follows. Let's take the False Flag Operation. To get the success chance of that mission you have to halve the village's familiarity score, so in the table it says the chance is based on Familiarity, and the formula is x0.5.

Some missions have a minimum and or maximum success chance. They are still based on the formula in the table, but if the formula causes the success chance to exceed the maximum or minimum, you take the maximum or minimum instead.

Some missions will only appear if you have over or under a specific Happiness or Familiarity score. I'm still working on figuring the exact numbers out, but I've put the data I do have in the table under Prerequisite for Availability.

It seems the game ignores Happiness penalty from Health when calculating whether missions are available, but not when calculating mission success chances. This means that for example The Shield will still be available if your base Happiness is over 75, even if that Happiness score is reduced to next to nothing because of a high Happiness penalty from Health.

After making first contact with a village, you have a Familiarity score of at least 5% with them. That's why the minimum score for a lot of missions is 5, half of 5, or double of 5. If you can find a way to decrease familiarity score you might be able to get lower than that.

Sometimes the formulas are 1% off. This is because it then rounds up or down differently.

Failing a Mission will result in a 1% increase in familiarity.

Mission Based on Times Minimum Maximum Prerequisite for Availability
A Knife in the Dark Familiarity x0.5 2 (? 38-50) ?
A Longer Table Happiness x1 0 90 -
Alien Abduction Familiarity x1 5 80 -
Annihilation Happiness x1 0 50 -
Bio-Weapon Familiarity x1 75 100 Village doesn't suffer from Plague yet
Bombardment Happiness x1 25 100 Infrastructure Level is not Stone Age
Death on the Wind Familiarity x1 75 100 Village doesn't suffer from Plague yet
Decimation Familiarity x1 75 100 -
Exposed Happiness x1 75 100 The Shield
False Flag Operation Familiarity x0.5 2 50 -
In Memoriam Familiarity x2 10 95 ?
Inside Perspective Happiness x1 0 95 -
It Belongs in a Museum Familiarity x1 5 90 -
Ivory Towers Familiarity x1 5 80 Happiness over 25
Occupation Happiness x1 25 100 -
Open Communication Familiarity x1 5 100 -
Peace in our Time Happiness x1 0 100 (105 due to bug in version 6.35) -
Protection Money - - 95 95 -
Reconnaissance Happiness x2 0 95 -
Sabotage Familiarity x0.5 (? <5) 50 The Shield
Something Special Familiarity x1 5 100 -
Tainted Water Familiarity x0.5 2 50 -
The Cure Happiness x2 + 10 10 90 Village suffers from Plague
The Grand Tour Happiness x2 0 100 -
The Pen is Mightier Familiarity x2 10 90 -
The Shield - - 90 90 Hab Dome researched. Happiness over 75.
Things Fall Apart ? ? ? 100 Peace Treaty
Trade Treaty Happiness x1 (? <59) 90 Happiness over (? 55-60)
Trail of Tears Happiness x1 0 50 -
Uplift Happiness x1 (? <33) 90 Infrastructure Level is not Industrial.

Happiness over 30 (?)

Word from on High Familiarity x0.5 2 50 -
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