Updating my calculation from yesterday: we're going to be playing with a lot of landmarks/events on average after Empires.

Using the recommendation of a 2 event/landmark limit, the negative binomial approximation to the negative hypergeometric distribution, and assuming 55 total events/landmarks and 260 total kingdom cards (which I believe assumes 24 kingdom cards in Empires)

Chance of 0 events/landmarks: 14.7%

Chance of 1 events/landmarks: 25.6%

Chance of 2 events/landmarks: 59.7%

Average events/landmarks: 1.45. The chance of any given event/landmark appearing is 1.45/55 = 2.6%.

The 2 event/landmark guideline matters quite a bit: if there was no limit, 35% of games would have more than 2 landmarks/events and there would be an average of 2.11 events/landmarks.

Cross-posting from the other thread; this does not use the approximation, should be exact.

Without limiting to 2, I get:

Chance of 0 Events/Landmarks: 14.230%

Chance of 1 Events/Landmarks: 25.661%

Chance of 2 Events/Landmarks: 25.070%

Chance of 3 Events/Landmarks: 17.541%

Chance of 4 Events/Landmarks: 9.816%

Chance of 5 Events/Landmarks: 4.657%

Chance of 6 Events/Landmarks: 1.940%

Chance of 7 Events/Landmarks: 0.727%

Chance of 8 Events/Landmarks: 0.249%

Chance of 9 Events/Landmarks: 0.079%

Chance of 10 Events/Landmarks: 0.023%

Chance of 11 Events/Landmarks: 0.006%

Chance of 12 Events/Landmarks: 0.002%

Chance of 2+ Events/Landmarks: 60.109%

Chance of 4+ Events/Landmarks: 17.499%

A limit of 4 total and picking 0-4 as 20% each is actually not a bad approximation, if you don't feel like shuffling 315 cards...

To answer the Colony/Dominate question: The probability of Colony is 25/260 (~9.6%); the probability of Dominate is about ~2.7% (limiting to 2 total Events/Landmarks), ~3.8% (without limiting).