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# Tree Diagrams

## Multiply probabilities along the branches and add probabilities in columns

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MEMORY METER
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Checkmate!

Credit: Stefan Powell
Source: http://www.flickr.com/photos/duchamp/9844794/

Have you ever played chess? Have you ever played chess against a computer? When you play against a person, you and your opponent think through each move with the hope of winning the game. How does this work with a computer? Is the computer "thinking" through each move?

#### Why It Matters

The computer can't think, but it can look for patterns and count outcomes. That is how a computer plays chess. The computer records the possible moves for each chess piece. Then when you move, the computer registers your move and calculates which move it should make.

Credit: Laura Guerin
Source: CK-12 Foundation

The tree diagram above shows how the computer counts and records all of the possible moves for each player. The tree diagram shows the outcomes. When you move your pawn or your bishop, the computer tracks your move, compares it with the outcomes for winning and moves its piece next.

It is difficult for people to figure out how to beat a computer because of all of the possibilities for future moves. But even the computer can't hold all possible future moves in its memory. The computer looks for patterns of outcomes for the next 10 or 15 moves and then plays accordingly. Can you imagine if you could hold 10 future moves in your head?

#### Explore More

Read the article at the first link below for more on how computers play chess. Then try your own hand at playing chess against a computer opponent!

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