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dose that mean that the machine can now play chess better than what was expected when it was being designed ?

This is The text

On the other hand, other AI researchers have achieved spectacular results in getting particular aspects of human behaviour from machines. A good example would be chess playing. Certainly, when work started in this area in the 1950s it was seen as a good example of intelligent human behaviour. In a tournament in 1997 a computer called Deep Blue beat the World Chess Champion, Gary Kasparov. That machines can now play chess very well has been established.

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The sentence means that we know that machines can now play chess very well. You can think of it as meaning

The fact that machines can now play chess very well has been established

or

We have established the fact that machines can now play chess very well.

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