Saturday, December 31, 2011

Quantum Mechanics and Magic AI

Okay, the title is kind of a stretch, but Quantum Mechanics sounds so much cooler than probability...

So what do I want to talk about? One thought that I often have is that the computer has the advantage of perfect memory. If it once views your hand, it can perfectly memorize all the cards in it. It follows that it can say that as long as a card doesn't leave your hand, you still have it in hand. But when the game progresses, things get more vague: You shuffle cards into your library without revealing them before. Here, probability comes into play.

I assume that the computer knows my deck list for simplicity. (It could even use heuristics to guess what cards might be in your deck, but that only complicates the matter.) At the beginning of the game, before even drawing your opening hand, each card in the library has an equal chance of being one of the, say, 60 cards in your deck. For example, in your mono green deck, a card has a 24 in 60 chance of being a forest. These chances don't change as you draw seven cards, at least from the computer's point of view. Even so, the computer can say that the probability of you having a Giant Growth in hand is (# Giant Growth in deck)/(# cards in deck)*(# cards in hand), and it can have "fear" that you might play that card during combat. The greater the probability, the greater the fear.

Now comes the "collapse of the wave function": the computer observes the cards in your hand. (You see, I can even use QM terminology here ;)) Suddenly, the probability of every of the cards in your hand becomes 100% for the card the AI has observed. Technically, as the hand is not a sorted zone, the AI should not remember which card is which. Let's say you have 4 different cards in hand, then the AI can assume that every of the cards has a 25% probability of being any of these cards.

When you now shuffle one card back into your library, nothing really changes, except that there's only 3 cards for a total of 75% per previously observed card.

I hope that it's clear what I'm saying. I have the feeling to make too many words about a simple concept, yet at the same time I feel that all this seems abstract and not very understandable... well, I should have made some images, but I'm too lazy...

Let me end with this: Magic is a game of uncertainty, and luckily the computer has the capabilities to process these. When an AI can make decisions based on what it sees, why not on what it doesn't see? Assigning these possibilities is pretty simple; every card in the game has a total of 100% of being some card from the deck list, and every card in the deck list is represented to 100% among all cards in the game.
The problem is to design the AI to use that information; it's often hard enough to process the known information, so even more the unknown. But in principle, there's no difference. And even if it is too hard, there are some shortcuts: If you have only one Morph card and play a Morph card, the AI knows which it is, even though it's face down. Such probability collapses can happen all the time, and it would be a waste to let them go unconsidered.

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