So I was thinking about how often cards from one game seem to reappear in the next. This is obviously more often with less cards. In fact, the probability of any two games using only base cards having distinct sets (no kingdom card appearing in both games) is:
(15 * ... * 6)/(25 * ... * 16) ~ 0.09%.
Even if you're playing with 50 kingdom cards, it's still surprisingly low:
(40 * ... * 31)/(50 * ... * 41) ~ 8.25%.
Currently on Isotropic, there are 130 kingdom cards in use. In that case, the likelihood of any two games having distinct cards is:
(120 * ... * 111)/(130 * ... * 121) ~ 43.57%.
And then there was Hinterlands. Fast forward to October, and 26 new cards will be thrown into the mix, bringing the total to 156 kingdom cards, including promotionals. This will bring the probability of having 2 entirely distinct games to:
(146 * ... * 137)/(156 * ... * 147) ~ 50.50%.
And so with the addition of Hinterlands, for the first time in Dominion history, any new game will more likely than not be completely different from the previous game.