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I can find countless quotes like this

In many countries chess is incorporated into the scholastic curriculum. Countless researchers and studies have shown over the years that chess does indeed strengthen a child's mental clarity, fortitude, stability, and overall health. In this technologically driven world, chess helps aid in the synthesis and growth of certain areas in the brain and mind where many children can benefit as they grow older from the game. "It's all condensed in a playful manner in a game format and it's extremely fascinating because first of all I'm in control of my own destiny, I'm in charge. You have to be responsible for your actions, you make a move, you had better think ahead about what's going to happen, not after it happens, because then it's too late. Chess teaches discipline from a very early age. It teaches you to have a plan and to plan ahead. If you do that, you'll be rewarded

These beilefs are so strong that even got a recognition in Wikipedia.

Here is another quote to highlight the gist of my question

Chess has a unique and strong brand attribute, in that it is generally perceived that playing chess and being smart are connected.

I do not ask if chess really improve the mental performance. I am asking Why are they considered unique/unmatched in this respect? Almost any game demands strengthening your intellect for careful planning of your moves. Why other games are less useful?

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Chess is considered "special" due to certain attributes of the game. From "Beyond the 64 Squares: Does Chess Instruction Enhance Children’s Academic and Cognitive Skills? A Meta-Analysis":

Two main explanations have been adduced to support this hypothesis. First, chess requires decision-making skills and high-level processes (such as acquiring and selecting relevant information from a problem) similar to those used in mathematics and reading (Margulies, 1992). Second, since chess is a demanding task involving focused attention and problem solving, playing chess should strengthen these cognitive abilities and thus be beneficial for children's school performance (Bart, 2014).

However, this consideration is only marginally valid. In "Enhancing Creativity in Children by Imparting Chess Training" the increase in mathematical skills from Chess was compared to mathematical instruction and playing the game Go. Although Chess outperformed Go, thus cementing it's "specialness", it did not beat basic mathematical instruction.

In conclusion, Chess is a bit "special" among games in terms of cognitive improvement, however it doesn't beat actually doing a task and it seems unlikely for any other game would be superior.

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    $\begingroup$ +1 But, I cannot concur with the part "it seems unlikely for any other game would be superior". How about simple games? IMO, simple games can go a long way to complement basic mathematical instruction (eg: subtraction games[see Sec. 2 in math.uchicago.edu/~ac/cgt.pdf] to encourage kids to learn multiplication), and may be even used as a way of basic mathematical instruction. $\endgroup$ – Cyriac Antony Jan 25 at 11:42

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