On the philosophy question, one problem is that nobody agrees what consciousness is anyway. Despite that, I think the prevailing view is that, at least in principle, a sufficiently powerful computer could simulate the human brain and such a simulation would be as much conscious as a human is, whatever that means. Not everybody even agrees on that point, though.
Which is probably not needed, reminds me quote that machines start thinking when airplanes start having feathers.
Back of topic to solve problem computer/human needs to have enough skill. Every problem skill can be divided to knowledge and intelligence part. A knowledge part is that somebody solved same problem before and wrote article/algorithm with optimal solution. Intelligence part comes when you come to novel situation and you want good solution.
Most board games are mainly knowledge based, there are psychology studies that show that being good on board games is mainly determined by how one has good spatial memory. That is natural, if it would be mainly intelligence based then smartest person on world could win 50% of games versus stef despite being complete newbie.
Main obstacle why computers are not better is that its easier to write strategy article for human than to computer as you could easily evaluate fuzzy concepts while computers have trouble with pattern recognition. Second problem is how to integrate conflicting information which is also hard for humans.
A question here is if you could write good bot reasonably cheaply, where you need add equivalent of intelligence. If cost was not concern its possible without needing to add much intelligence to bot.
Hire 1000000 chinesse programmers. Each gets a three-card kingdom, plays it for year to learn how handle presence of attack, trashing, three piling... then writes best possible bot when these three cards are in kingdom.
Bot itself would use supercomputer that would on turn take all pairs (A,B) of triples present in kingdom, then run 1000 A versus B matches with feasible hand/discard pile combinations, compute nash equilibrium of that matrix and choose strategy according to it.
Then human could have advantage only on boards where best strategy is four+ card combo. These should be rarer than probability than human makes mistake so bot would win in more than 50% cases.