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I'm an intermediate-level amateur chess player. How would I go about learning how to accurately play a complete game of chess, blindfolded? What skills are needed, and how are they practiced?

In particular, how can I maintain an accurate representation in my head of the board state over time? Whenever I've tried this, I get a dozen or so moves in, and it all starts to fall apart. Are there specific techniques or representations to help with this?

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Do lots and lots and lots of chess problems :) Not only is this the fastest way to get better, but as you get to more and more difficult problems, you'll have to keep track of more and more moves in your head. Besides that, play lots of games - after so many hundred games, you get used to knowing where each of the pieces commonly moves to, and what squares it attacks from there, without even having to think about it. –  BlueRaja - Danny Pflughoeft Oct 26 '12 at 7:19
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I think you have to take a closer look at mnemotechnics. Probably Memory Palace technique in particular. You can read about it here, for example.

Here is a discussion about techniques used with Chess games. Mainly about memorizing them. A book called How to develop a perfect memory is suggested reading.

If you know Derren Brown (he's British mentalist, a "mind-reader", if you like), he has done a bit about playing 9 simultaneous chess games with top English players. You can watch it on youtube with explanation on how he did it.

Of course, he only had to remember 8 moves at a time, but it's still pretty tricky not to get confused. If you are interested, you can read Derren's book Tricks of the Mind, it has whole section about Memory.

Best of luck!

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