Okay, we'll go with limiting them to 2 since it makes things easier. I ran some numbers, and chances of 1 event: 35.66%, and chances of 2 events: 22.38%, which are really close to jonts numbers.
We're looking for one specific event.
Odds of it happening in a 1 event game times odds of a 1 event game = 4.7% * .35 = 1.67%
Odds of it happening in a 2 event game times odds of a 2 event game = 9.5% * .22 = 2.1%
Add them together, and you get the odds of a specific event occurring in any game = 3.77%
Odds of any two kingdom cards occurring in the same game: 90/55460 = .16%
Multiply them, and you get .00611792% or
1/16,399This is a lot closer to your method's result, Accatitippi.
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I'm probably still messing up, but at least it's fun.
Real answer:
MANY MANY GAMES