There is a time period, after which the power of AI has always doubled. I think it is about 7 years. Our brain probably uses its ressources much more efficiently, but will not be able to beat AI pretty soon in anything, where it can be programmed.
Chess bots are not much of Artificial Intelligence. They do what they are programmed to do. Positions on the chess board all have values. Bots go through possibilities and chose the lowest risk move. The fact that they were assigned values by chess masters makes them just programs, not real AIs. They, however, can beat humans.
There is also other kind of bot. The one, which assigns the values to itself independently. They rank much worse than the first kind. But it is only because of limited ressources; They still beat most humans though. Something important about them is they improve themselves. While in Chess, they are still beatable, in Dota 2, a many times more complex game, shadow fiend mid bot was beaten only three times and remains unbeaten since that moment.
The bot improves himself with each defeat. Dying is bad. Taking damage is bad. Dealing damage, pushing tower, denying creeps, killing heroes is good.
Given that, I think it's safe to assume there won't be an AI uprising anytime soon.
As I mentioned before, there are already self-educating bots. Some personalize the adverts on the internet for you or such. But the importance is in them being self-educating. They are only limited by ressources, which double every 7 years. Bots can also be far more focused on one thing and dedicate all their capabilities to it, humans can not. Bots already do beat humans in some activities including trade, advertisement, some games. If they can double their efforts every 7 years, it is highly unsafe to assume this.
Furthermore, there is a term "singularity" used for a bot, which can endlessly improve himself by himself. It is fairly reachable point. Today, humans work on improving bots. Tomorrow, bots may be doing it themselves. At that point, which is definitely not sci-fi anymore, they will be unbeatable at everything.
But I don't know if it is good for humans to create a machine like that. You order it to grow rice, make a mistake in its core and it will kill half the species in the worls, so it can grow more rice...
Yes, bots can handle data faster than humans, but they aren't more intelligent. They can brute force data, not see through to a solution intuitively like humans. I don't think it's good to try to replace humans, as humanity will be replaced...