There are many good examples of complexity emerging from simplicity. (Supposedly it may have been Aristotle who first pointed out this phenomenon.) The way complicated multicellular creatures arise when cells all have the same genome is amazing. And programs that play Chess or Go well have strategies that their own creators do not understand.
Another excellent example is the boardgame 'Go', which is particularly popular in Japan.
The rules are incredibly simple, and there's only a handful of them. But the games that are played by those rules are so difficult to predict that, long after chess computers reached the point where they could routinely win against grand masters, Go playing computers are unable to beat the top human Go players.
I believe your information is out-of-date. As late as the 1990's, most computer scientists thought that expert Go play was a long ways away, but that Game has also succumbed to DeepMind's methods. Here's a 90-minute documentary on the program called Alpha Go.
[YOUTUBE]WXuK6gekU1Y[/YOUTUBE]
Alpha Go defeated the top professional player in Europe, but could it defeat Lee Sedol, the best human player in the world? Many, including Lee Sedol himself, were confident that that would be impossible. A five-game match was arranged in 2016, man vs machine.
Lee was stunned to lose the first three games. In one game Alpha Go shocked the world by playing a shoulder hit on the fifth row, a play no professional would ever make. By the fourth game, with Alpha Go ahead 3-0 and certain to win the match, humans were almost in tears; even those on the computer side seemed to be hoping Lee would win a game.
Ninety minutes is a long watch for all but avid Go fans. You can skip to 1:05:50 if you wish, to see the crucial position in Game 4. Lee Sedol thinks for several minutes, and at 1:06:52 in the video he plays a wedge tesuji. Alpha Go hadn't seen this coming, starts making bad news, resigns. Humans celebrate in the streets. The final match score was 4-1, with Lee Sedol (who'd been confident he'd win 5-0), now proud that he didn't lose 0-5. A few years later, knowing that computers could only get better and that, at best, he could only hope to remain the top
human player, Lee Sedol retired from the world of professional Go.
In the following Youtube, you can see the humans laughing at Alpha Go's 5th-row shoulder hit. Alpha Go won that game.
[YOUTUBE]HT-UZkiOLv8[/YOUTUBE]