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They are civil towards each other. It's the saying, "Keep your friends close and your enemies closer". They are not buddy-buddy friends who meet up at the pub for a drink and swap stories. The Master is canonically a recurring villain/rival of the Doctor who can match his intelligence and wit -- a nice change from the Bang Shoot Kill Destroy methods of the Daleks or Cybermen.

Three: "We're best enemies." (or something like that from The Five Doctors)

The Master is, for lack of a more descriptive term, evil. Examples: he has stolen bodies to survive past his 13-regeneration limit, (including when he chose to kill/steal the body of a loved one of another character ON PURPOSE), kills people with no remorse whatsoever, by various means (notably when he gassed the PM Cabinet in the new series and laughs about it).

I think new fans (a friend of mine is a prime example of this) who are only familiar with the S3 Master don't realize the extent of his character and background. The new series Master was made to counteract the hyper personality of Ten and as a result, IMHO, became far more likable than he would ordinarily be -- I still have no clue why my friend inexplicably likes the S3 Master. I went back to some Classic Who episodes with the Master to get a better feel of his personality and I prefer the toned-down, sinister Master (however camp he may seem sometimes).

A random character pairing would actually make more sense than Doctor/Master. (Not counting Jack/anyone, for obvious reasons. rolleyes ) The Master seems akin to Daleks in villain status. Doctor Who's high-ranking villains tend to not get the love interests unless it's through force/mind control/general deceit/shared evil tendencies (Lucy in S3 comes to mind).

The Doctor is opposed to basically everything the Master stands for.

The Doctor only cares about the Master to the extent that they are the last of their kind and therefore if the Master dies, the Doctor is truly alone in the universe, which is pretty depressing -- and also completely understandable. As Defender put it, "an act of sheer desperation for the companionship of another Time Lord".

An example of how this wouldn't work is Trillian and Arthur Dent from Hitchhiker's Guide to the Galaxy: They are the last two humans on earth, after finding out their planet went KABOOM for a senseless reason. The reason that an Arthur/Trillian relationship makes sense while a Doctor/Master one doesn't is because the first two share such things as a sense of morality and decency, and neither of them turn into a sociopath with a kink for world domination.

As to why "the Master keeps playing games with JUST the Doctor":
1. They're both brilliant geniuses-- but only one has a working conscience.
2. The Master and the Doctor are both Timelords -- they went to the same "school" and share memories of their home and culture -- it's a lot easier to push the buttons of someone you know rather well than a complete stranger.
3. He's not going to start playing mind games with the Daleks or anything, because we all know that's rather stupid.
4. I may very well be the first one here to vocalize this, but I'm calling it out: the Doctor and the Master are akin to Batman and the Joker. Think about it, and then tell me how a Batman/Joker relationship would work. (Hint: it wouldn't.)
5. The Master put the Doctor in pain and made him completely helpless and then forced him to watch the Toclofane swarm down to the planet he holds so dear, and then kill people. Just because he can.
6. Anyone who is willing to die rather than regenerate purely to spite the other person does not care about that other person in any way, shape or form. That's about as cruel as you can get. AND you die. Value of life clearly isn't on the top of his list, even if it's his own. -- Unless he planned the whole thing and will be back, but even Jack doesn't like voluntarily dying/reviving unless it's completely necessary.

The difference between Jack/Ianto and Master/Doctor, other than the "one of these things is not like the other" game, is that one consists of a rather loving relationship (even if it tends to go one-sided) that is clearly shown as such. I'm not going to use the one-is-canon-and-one-isn't angle because that's clearly not a basis for a relationship in this argument.

Sorry to burst your bubble, but what you're talking about sounds like hate!sex between them (it sounds like what it is, guys) and there's more than enough fanfic sites to go around if you want that sort of thing.

I just wouldn't expect to see a lot of Master/Doctor shippers in mainstream DW fandom. Unless it's an AW THEY'RE CUTE LET'S SHIP THEM group (never a good basis for a relationship) or a We're Doing This For The Lulz group that doesn't actually take itself seriously (ie: Caramelldansen and other silly crack-induced versions that make most people laugh and/or facepalm).


*finishes kicking the dead horse and sits down*

The only time I have ever seen the Doctor even mildly yaoi with someone was with Jack. You know, in the episode The Parting of the Ways when Jack kisses Rose and then the Docotor, and the Doctor never seemed to mind Jack's fondness for him, lol. But honestly I believe that the Doctor is completely heterosexual. The whole thing with the Master is simply a companionship. Just like everyone else said the Doctor and the Master are more or less friend/rivals, and when the tenth Doctor was so upset about the Master dying it was all about the whole last of the Time Lords and the fact that the master is all he has left of Gallifrey. So no I see no yaoi there!