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Bottom line: view the games as fun and a way to pass some time, but nothing more. From the Atlantic:

The Myth of the Brain Game

Over the past decade, digital brain-training games have emerged as the newest way to sharpen memory skills. They’re often touted as having a wide range of benefits, from helping people remember names and childhood stories to possibly staving off dementia and Alzheimer's disease.

In October, Stanford University’s Center for Longevity and the Max Planck Institute for Human Development in Berlin asked a group of more than 70 neuroscientists, cognitive psychologists, and academics to share their views on these games. “There is little evidence that playing brain games improves underlying broad cognitive abilities, or that it enables one to better navigate a complex realm of everyday life,” the group wrote in a consensus report.

The validity of brain games has been a point of debate ever since the first iterations of them launched in the early 2000s. What’s notable about the Stanford/Max Planck report is its deliberation and scope, offering insight collected over the course of a year from experts based at 40 institutions in six different countries.

The report questions the “pernicious,” “exaggerated,” and “misleading” claims made by brain-game manufacturers and stresses that wide-reaching positive results are “elusive.” The signatories don’t call out any specific types of brain-training software, but their language is often damning. “Many scientists cringe at exuberant advertisements claiming improvements in the speed and efficiency of cognitive processing and dramatic gains in ‘intelligence,’” they write.

Brain training is projected to be a $3 billion industry by 2015. Its target demographic is vast, from kids lagging behind in school to seniors who’d love to be able to remember things more efficiently. Most people, in fact, would appreciate the opportunity to feel like they’re getting the most out of their brains, and when a particular product is advertised as being both educational and backed by science, it can be hard to resist.

That there’s a need for scientists to issue a signed letter like this one only goes to show how popular brain games are and to what extent experts feel the public may have been seduced by the promise that they’re endorsed by science. The letter is both a word of caution to the public and the signatories’ way of distancing themselves from the commercial products. 

In 2013, two researchers at the University of Oslo and University College London conducted a meta-analysis of 23 different brain-training studies. What they saw was what every skeptic has seemed to notice. “Memory training programs appear to produce short-term, specific training effects that do not generalize,” they wrote. That is, training with games helped people get better at the games they were playing, but not much else.

Brain games aren’t a complete waste of time. They provide mental stimulation, the kind that doctors advise the elderly to get from crosswords and other mind games. They are fun, engaging, even competitive. They show how we can train the brain to get better at a task with repeated practice. But these are fairly obvious results given what we know about the brain's plasticity. 

All that said, the things that do help shape a healthy brain are the things that have been tried and tested for years. Physical fitness forces more blood to flow into the brain, allowing for more neural connections. So exercise works, as does conventional training in reading and language skills for children with reading-comprehension and oral language difficulties.

Also helpful are curiosity and engagement with the world around us, and the body’s lifelong subconscious effort to keep the brain active. The report's summary is perhaps the biggest indictment of any pop-a-pill brain-game philosophy. “The promise of a magic bullet detracts from the best evidence to date,” they wrote. “Cognitive health in old age reflects the long-term effects of healthy, engaged lifestyles.”