I have recently just gotten into playing it, so I can contest to this question. As a beginner, I have realized that I start real strong, making good moves maybe even better than what I do playing regularly, but as the game goes I feel extremely fatigued, and start making silly errors, such as confusing what color what bishop travels on. Nonetheless it's extremely fun and after starting have realized that my sense of direction has increased by quite a margin.
Can the average person learn to play blindfold chess?

If you can visualize things with your eyes closed, you can learn to play blindfold chess easier, also if you have a very good memory, you can play blindfold chess easier. Artists that can conceptionalize ideas in their minds only, also have it easier if they want to learn blindfold.
Imagine the board in your mind, close your eyes, repeat the squares from left to right bottom to top with the square color, and letter/number.
Do this until it is burned into your memory. Then start adding the pieces to the board, then think about certain opening, and the move orders of those pieces, and see them in your mind. Then just start replaying whole games in your mind, if you really want to learn to play blindfold. Good luck

Natalia, what do you mean by good? At least 1900, 2000+???
Surely, you dont think a 1600 can play blindfold chess. If a guy is going to be hanging pieces with his eyes open what kind of game will he play with his eyes shut?
I know!!! Like a GM knows what they're talking about!!.........
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You have to memorize all the board squares, once that's done it gets much easier to play blindfolded. @the_johnjohn I don't think repeating the whole game helps, maybe you're doing something wrong. One should be capable of seeing the position normally

If you can visualize things with your eyes closed, you can learn to play blindfold chess easier, also if you have a very good memory, you can play blindfold chess easier. Artists that can conceptionalize ideas in their minds only, also have it easier if they want to learn blindfold.
Imagine the board in your mind, close your eyes, repeat the squares from left to right bottom to top with the square color, and letter/number.
Do this until it is burned into your memory. Then start adding the pieces to the board, then think about certain opening, and the move orders of those pieces, and see them in your mind. Then just start replaying whole games in your mind, if you really want to learn to play blindfold. Good luck
Thanks for the tip.

An AVERAGE person "can" play blindfolded but only to a point ( maybe ten moves)? I went that far Then I was check mated. Does that count?

Blindfold chess is a good exercise but the play demands more mental strength and that's why it is not only tiring but hazardous to health if played for longer. Simply imagine, what happens to a computer when it is given commands more than it's processor and ram's strength.

Before blindfold chess can be achieved I believe you must become extremely familiar with chess notation, and be well-into associating squares with other moves from other games, creating as many connections as possible to your chess memories and notation.
I have practiced OTB with a NM this blindfold practice technique, but it is pretty hard at first. Meet somewhere quiet! Pull out a chess board, leave it empty. One player finds some tactics puzzles that are WELL below the other player's non-blindfold level (500-1000 points lower to start). The player attempting the blindfold tactical feat will stare at the empty board while the other player repeatedly tells him where all of the pieces are. I prefer to hear where all of the pawns are first, then the kings, the queens, the rooks, and then the minor pieces. Often I will ask him to repeat it again and again, until I am confident in the position and then I will verify that I know where all of the pieces are (this can take 10+ minutes just to get the position right). We have only done this 4 times I think. With myself only getting through 3-4 puzzles before my brain feels like jelly. It is EXHAUSTING, but feels like it is INCREDIBLY valuable. Also I would recommend only picking positions with less than 8 total pawns/pieces on the board to start
There are some mental exercises that are fun that are short of full blind-folded chess ---- and which even beginners can try. For example, like calling out two squares and asking for knight path from one to the other. I don't know if this help with real chess, but it is a way to entertain kids on a car trip. Of course, you need adult supervision (or another kid with a board).
Any person able to play chess blindfolded is certainly not an average individual. I could play chess everyday until doomsday and I wouldn't be able to do it.
Guys, I played an entire game blindfolded when I was 1500 points about 5 years ago. I was so good in fact that I challenged people to play against me while I was blindfolded, although it is remarkably hard to visualize the bishop and knight combinations on the board.