How hard is dominion to learn for AI? Easier than chess? As hard as chess? As hard as Go? Harder?
Harder for sure.
First issue is how you deal with each card introducing its own rules. Arguably, a fully legit Dominion AI would be able to play with a new card without having to re-train the model. That's mega hard, so realistically you probably would just re-train the model.
Some strategies in Dominion need all the components in place or they are garbage, e.g. in some kingdom, if you try to play an engine without +buy it may be garbage, and with +buy the best strategy. You can't really just do random stuff and stumble into a decent strategy the way you can in chess and go. That's a problem because that's how self-play training works.
Dominion has hidden information, most notably your opponent's hand. It's like there's a little bit of poker embedded in the game. AIs can play superhuman poker now, but the techniques used for that are completely different from what's used for other games.
Randomness means search isn't going to help much, unlike in chess and go. Randomness isn't itself such a big problem; IIRC computers were playing superhuman backgammon before superhuman chess. But it does diminish the opportunity to out-calculate humans.
Strategies in Dominion are highly diverse: what's good in an engine is totally different from what's good in BM+X. This is different from chess and go, where, despite some minor variation, you're doing essentially the same thing every game. I can't off-hand think of any game with diverse strategies where computers are superhuman. I don't know if that's because it's hard or just because it hasn't been seriously tried, but it means you're breaking new ground.
I'm not an AI researcher, but if I were trying to develop a Dominion AI, I'd start by making some massive simplifications. Singleplayer only (with the goal being something like buy 5 provinces as fast as possible) and limited subset of cards (maybe just first kingdom). This already sounds pretty hard. Try to get it to discover the
first game engine, for example. (Although that has Militia, so maybe it's not even good singleplayer...)
Starcraft has an astronomically larger decision space than either of those games, and I don't think it was that much harder.
AFAIK, computers are still garbage at the strategic part of Starcraft.