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 (how can Excel not have a built in negative hypergeometric distribution!), and assuming 47 total events/landmarks and 262 total kingdom cards (I'm not sure we know how many kingdom cards and events will be in Empires):

Chance of 0 events/landmarks: 19.2%

Chance of 1 events/landmarks: 29.2%

Chance of 2 events/landmarks: 51.6%

Now that we know we have 13 new Events, and based on the previous estimate of 24 new Kingdom cards (likely 9 Split and 1 Victory, to account for the art and total card count), we'll have 260 Kingdom, 34 Events, and 21 Landmarks. 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...