I was going to post a similar topic to this.
I feel like the site has done a great job of delving into 2-player strategy at a deep level, but I feel like multiplayer strategy isn't dealt with very much here. I would be really interested to see some more discussion on how multiplayer affects strategy at a deeper level.
At the basic level multiplayer does a few things, that people have already mentioned:
1. Because the amount of regular kingdom cards doesn't vary based on the group size, there is a wider distribution of sought-after cards (4-3-3 or 3-3-2-2 rather than a 5-5 even split). This I would presume effects cards you want a lot of, particularly if you can chain them together (minions, cities, etc.) and they are therefore weakened if other people go also go for the same cards and thus you get fewer of them in your deck. It also hurts if you are trying to build an engine and there is a part or parts that others want also.
2. It affects victory card distribution, particularly in 4-player games. In a 3-player game there still are 4 of any victory card per player in an equal distribution, but it still probably has some effects on the game (though I am not sure exactly what all the effects would be). However, in a 4-player game there are still only 12 victory cards, so now an equal distribution results in only 3 per player, which could lead to games ending faster, particularly if there is a relatively equal distribution of victory cards bought.
3. Attacks that can stack become much more powerful, attacks which might or might not hit become more reliable with multiple chances, and attacks that do not stack become a bit weaker. Attacks like Torturer, cursers, and cutpurse which can a. hit a player multiple times before their turn and b. hit multiple players at once become stronger. Cards that may be poor in 2-player or in general lack reliability because they may not hit (Pirate ship or even Thief) become stronger to at least some degree as with multiple targets the chance of hitting increases. However, attacks that don't stack become at least a little bit weaker such as Militia as there is less to gain by playing it if it has already been played that turn by another player.
4. As said before, three-piling is more likely in multiplayer
5. Dealing with multiple opponents may affect the optimal strategy for the game. If there is one strategy that three players are taking, a different strategy that normally would be less optimal in a 2-player game may become more viable and even the best strategy for the situation.
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However, I think it would be interesting to go more in depth into multiplayer strategy. I don't think anyone would really settle for this level of depth of strategy for 2-player situations. I think what makes the site interesting is the depth to which the discussion, analysis and strategy goes for the game, often even to edge cases. In-depth multiplayer strategy still feels relatively untapped though. I think even a set of card rankings in multiplayer would be interesting to see.