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1 Nigerian Finance Bureaucrat: How are we going to make sure you win the million dollar prize, Finance Minister?
2 Nigerian Finance Minister: You sit in the audience with an encyclopedia and cough when I say the right answers in my deliberation.
3 Nigerian Finance Bureaucrat: Isn't that cheating?
4 Nigerian Finance Minister: It's a test of intelligence, isn't it? We're just clever enough to be thinking in terms of the metagame!
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A metagame is the overall context in which a game is played. In many situations, this can lead to insights or strategies that one could not come up with by considering the game itself in isolation.
For example, the game of chess is apparently self-contained. Your best move in any situation is dependent only on the current board position, and nothing else. But in reality, there is a metagame associated with chess, involving the personalities and playing styles of the pool of opponents. If you are playing chess against someone who has a distinctive playing style, you may be able to use that to your advantage by making moves designed to counter that style, rather than simply just taking into account the board position.
Metagaming is the term used to describe the action of attempting to take advantage of a metagame. In some situations, metagaming actually becomes very important to one's overall chances of winning the game itself.
For example, the card game Magic: The Gathering involves players constructing decks of cards from a large pool of different cards with different capabilities. In a tournament situation, you come across several players who have all constructed their own decks in an attempt to have powerful decks. If the card pool contains a strategy that is very powerful, then that strategy will become popular. In this case, it can be advantageous to construct a deck not to be powerful in its own right, but specifically powerful against the popular deck. Many of your games will be against some version of the popular deck, and so you will gain an advantage.
Of course, this leads to the popular deck becoming less popular, and other decks designed to counter the deck that you have built. So at any given time you need to use your overall knowledge of the entire playing environment to make a judgement as to what decks will be popular in the general population, and build your deck accordingly. To many people this metagame aspect is an important and enjoyable part of the overall game experience.
There are other places where metagaming is frowned on. For example, in a role-playing game, one's actions are generally supposed to be dictated by the fictional events occurring around the character you are playing in the game. When fleeing a goblin, you should decide whether or not to jump a pit based on whether your character is confident he can safely make the distance or not. It would be metagaming to consider your character's Strength and Dexterity scores, cross-reference them against the Jumping Distance Table, determine that you have a 45% chance of making the jump, and that if you fail you will fall 30 feet and take 3d6 points of damage, which you can survive since you have 23 hit points.
In any given mathematical system, there are mathematical statements that are true, but which you cannot prove are true within the formulation of that system. However you can metagame the system and think outside it, adding extra rules that allow you to prove the statement.
The problem with this is that, as Gödel proved, the metagame-level mathematical system contains new statements that are true, but which cannot be proven to be true within the metagame-level mathematical system. You can add another meta-metagame level of mathematics and prove those, but you inevitably set the stage for statements which are true at the meta-metagame level but unable to be proved at that level.
And so on.
Turns out Kurt Gödel was the ultimate metagamer.
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