I personally spent some time a few years ago teaching elementary-schoolers chess in a club after school. A lot of them weren't good students, but all of them took a lot of pride in getting better at chess. I think it would be really worthwhile if we had a tool to get the pleasure of self-improvement into kids' heads.
I used to play a bit online, and as well as improving my chess just through more play, the pressure of playing under time limits really forced me to develop a strategy, something I'd never realized, despite playing many games over the years.
Playing on-line, self-improvement should be pretty clear, just from watching your number of wins and rating gradually improve.
I began to practice somewhat obsessively and I got to the point where I could regularly beat most of my co-workers within a year. It could be argued I have an inclination for something like chess, but the connection between practice and payoff was more apparent playing chess than just about anything else I've ever done.
Chess has also taught me to think ahead a few moves and to realize that sometimes a short-term loss is worth it for a long-term gain. All things I see as essential for entrepreneurship.
In my youth, I used to just think people were just "good" at something, and there was little they could do to influence it. I did software because I was "good" at it. Over the years, I've realized that an inclination or talent is important, but relentless years of honing one's craft are more important. I've watched a couple of my "smarter" friends waste away due to lack of focus and other people shine seemingly in spite of themselves.
Please read the section about her early life.
Edit: In case it's not clear:
Judit Polgár and her two older sisters, Grandmaster Susan and International Master Sofia, were part of an educational experiment carried out by their father László Polgár, in an attempt to prove that children could make exceptional achievements if trained in a specialist subject from a very early age. "Geniuses are made, not born," was László's thesis. He and his wife Klara educated their three daughters at home, with chess as the specialist subject.
And yes, I agree that a sample size of three + massive survivor bias makes for tricky interpretation :) But I think the Polgar story is fascinating; Laszlo had a theory about how to develop genius, and he (rather creepily!) decided to test it out.
From Bounce [0]:
Realizing that the only way to vindicate his theory was to test it out on his own future children, he started corresponding with a number of young ladies, in search of a wife... A young Ukranian named Klara was one of those women. "His letters fizzed with passion as he explained his theories of to produce children with world-class abilities," Klara, a warm and gentle lady, a perfect counterpart to her husband, tells me. "Like many at the time, I thought he was crazy. But we agreed to meet."
What's more, Laszlo would take issue with saying his daughters were born geniuses.
As Polgar puts it: "If they had seen the painfully slow progress, the inch-by-inch improvements, they would not have been so quick to call Susan a prodigy."
[0] http://www.amazon.com/Bounce-Federer-Picasso-Beckham-Science...
That said, chess is simply not an inherent skill. But small differences in native ability can lead to large differences in interest, hence time spent, hence results achieved.
My co-founder joined our start-up after spending a year traveling through Asia, and brought back with him Chinese Chess. The pieces are incredibly similar to traditional chess, with slight movement variations. We adopted the game as our 3am work-break for a while, and were able to build up a record over a few weeks. Unlike traditional chess in which my win rate would be near-absolute, he was able to win approximately 25% of Chinese games, with his win rate stable over time as we both developed our knowledge of the nuances of the game.