Maybe they would also kept 1 versus a team of 2 or 3 or something like that...
Personally, I would say about the same minigame types as the other Mario Party games before the 9th one, to say Duel, 1 vs. 3, 2 vs. 2, 4 players and battle. However, I wouldn't mind that much to see the same game types as the previous ones.
Since Mario Party 3DS has boards in where you reach the goal before others, I think it's possible that they'll have types similar to Wii Party. Meaning that we'll see 4-Player and 1-VS.-3 Mini-Games. I don't think we'll see a lot of 2-VS.-2 Mini-Games if that's the case, unfortunately.
I'd love to see 2-vs-2 mini-games return from their absence in Mario Party 9. Non-luck based battle min-games should be in it instead of them being just 4-player mini-games. Boss battles that are better than Mario Party 9 should be included as well. I'd like to see them create a brand new type if possible.
I haven't played Wii Party so I'm not sure what mini-game types can be in this Mario Party if it's going for it's gameplay.
I expect plenty of 4-player mini-games and 1-vs-3 mini-games regardless though.
So far, all I've seen was just a VS space, so who knows what's going to happen when you land on those.
If there's 4-player minigames after every turn, it could either be a Duel or 1vs3 like how Wii Party had it set.
Otherwise, I don't expect any other kinds of minigame types to be included, other than a few Extra or Single-player Minigames.
And I highly doubt there will be Boss Battles in this game due to the board layouts so far (since at the end of the space board it was a finish line with some Lumas and Rosalina cheering, not something like a Bowser Gate)