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Would cards like Lich's Mastery, and Door to Nothingness effect each other at all? Or Platinum Angel for that matter?

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    A very similar question was asked a while back, with no clear answer: boardgames.stackexchange.com/questions/34844/… – John Jan 6 at 21:02
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    That question is very specific to multiplayer games and rule 104.3h. Interestingly, it looked like two official answers were given to the same question, one from WOTC Customer Support and one from the Rules Manager. The question was whether one Platinum Angel could save multiple players in a limited range of influence game. This question avoids the ambiguity of that one by not involving multiplayer at all. – CALEB F Jan 6 at 23:40
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In general in Magic: the Gathering, "can't beats can":

101.2. When a rule or effect allows or directs something to happen, and another effect states that it can’t happen, the “can’t” effect takes precedence.

So Lich's Mastery and Platinum Angel prevail against Door to Nothingness. To win the game, you first need to get rid of the opponent's permanent. Or, in the case of Lich's Mastery, have a card that states that you win the game, like Battle of Wits. Lich's Mastery has a ruling below the card in Gatherer:

While you can’t lose the game, your opponents can still win the game if an effect says so.

and that's the reason why Platinum Angel separately states "your opponents can't win the game".

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    How does "you can't lose the game" without "your opponent can't win the game" work? If they win, but you can't lose? – David Heyman Jan 7 at 15:00
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    @DavidHeyman good question, but I guess the answer is just "because the rules state so". – Glorfindel Jan 7 at 15:12
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    @DavidHeyman It's a causal relationship: The game ends when either player wins or loses (or both players tie). The other player then experiences the opposite. So, if your opponent manages a condition whereby they win without having to (for example) reduce your live to 0 or exhaust your deck, then the game is over - and Lich's Mastery / Platinum Angel are no longer in effect. This means you can (and do) then lose. The normal way to win the game it to first make your opponent lose, but here you would need to reverse that order. – Chronocidal Jan 8 at 13:51
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As a supplement to Glorfindel's answer:

104.3a A player can concede the game at any time. A player who concedes leaves the game immediately. That player loses the game.

In other words, even if you control a "can't lose the game" effect like Lich's Mastery or Platinum Angel, you can still lose by conceding.

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    doesn't "cant' beats can" override this too? you concede and leave, you can't lose because of that, then... not sure what happens. in a fun world that would force the other player to remain at the table because the game isn't over and they can't do anything but concede themselves to end the game since there is no opponent to play against. – OganM Jan 8 at 21:58
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    @OganM 800.4a: "When a player leaves the game, all objects (see rule 109) owned by that player leave the game and any effects which give that player control of any objects or players end." 901.10: "When a player leaves the game, all objects owned by that player except abilities from phenomena leave the game." 104.3a: "A player who concedes leaves the game immediately. That player loses the game." When you leave the game, Platinum Angel leaves the game immediately, and you can lose again, just in time for 104.3a to tell you to lose. – Patrick Stevens Jan 9 at 7:36
  • I have yet to work out formally what happens if my opponent controls and owns an effect that says I can't lose, but I bet it works correctly. – Patrick Stevens Jan 9 at 7:38
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Gideon of the Trials

No game effect can cause you to lose the game or cause any opponent to win the game while Gideon’s emblem is in effect. It doesn’t matter whether you have 0 or less life, you’re forced to draw a card while your library is empty, you have ten or more poison counters, you’re at your Glorious End, your opponent casts a second Approach of the Second Sun, or so on. You keep playing. (2017-04-18)

Other circumstances can still cause you to lose the game. You will lose a game if you concede, if you’re penalized with a Game Loss or a Match Loss during a sanctioned tournament due to a DCI rules infraction, or if your Magic Online® game clock runs out of time. (2017-04-18)

So a Gideon of the Trials emblem functions like Platinum Angel and stops both winning and losing, both Door to Nothingness as well as Approach of the Second Sun.

However, Lich's Mastery doesn't stop your opponents from winning, it only prevents you from losing. So even if you have a Lich's Mastery, an opponent can still win with Approach of the Second Sun. This is simply because winning is different from losing.

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