Did you know that, at least in my world, only Players "play" the game? it's true. What? You think that's obvious? I don't think so. Bear with me on this.
I think the Dungeon Master's role is to set the stage, know the rules and roleplay the NPC's. His/her job is to focus on the game itself. A "good" DM/GM never plays the game, they observe it, they manage it, they adjudicate it, but they never "play" it.
Only Players "play" the game. By saying they play the game, I mean they are trying to win. They are trying to "beat" the adversaries, conquer the challenges and reap the spoils. In contrast, the GM/DM never makes an effort or "tries" to win or defeat the Players using elements of the game to defeat or kill the PC's intentionally.
Having said that, there is one aspect of the game in which the DM/GM is actively "opposed" to the players, but not as the DM/GM directly. It is in the roleplaying of the NPC's that the Players interact with. To correctly roleplay those NPC's (the monsters, people, enchanted objects with intelligence, etc... the DM must truly roleplay the NPC as if he/she actually were the NPC. The NPC in question has it's own "in game" goals, objectives, attitudes, mindset.
I know some DM's take a sort of a "cheerleader" role because deep down, they are good people and want to see the Players do well. Because of that, they will, when given the option, give the Players a break when it comes to dice results, etc... Then you have the ones who are all about the game and don't give any breaks, to PC's or NPC's alike. Of course, there are the ones who secretly want to have the game win and give the NPC's the breaks and nudges but not the Player's PC's.
I like to think of myself as the Neutral, "it is what it is", kind of DM but to be honest, I end up being a 4th kind of DM in that I like to follow the action, wherever it is. Basically, if I see the dice roll result in something no one expected or in a direction that catches either Player's or NPC's by surprise, I'll go with it just to see what happens and keep the game interesting.
Sometimes following the action ends up in one side or the other getting a break, but well, life's not fair and I tell the Player's don't expect the game to be "fair" either in that same regard. I try to be the "it is what it is" kind of person normally but yes, sometimes my curiosity gets the better of me.