I regularly play chess against computers on the Internet and the computers SEEM to be analyzing the position in the same way I am, visually. However, that isn't really the case at all. The computer is merely dealing with numerical representations of the position of the pieces on a numerical representation of the board and calculating outcomes based on the dynamic interrelations of those values. In short, it doesn't see pieces or a board visually. It is merely reacting to mathematical inputs and responding by providing a solution via mathematical output. But to the human player it seems otherwise since the mimicry of human thought is so convincing that it is very hard to believe that the machine isn't actually consciously pondering as we are.
Talking about computers and chess... My dad is a chess enthousiast and has loads of specialised chess software which use cutting edge "chess engines", backed by a database of millions of chess games, even going back all the way to documented games of chessmasters of the 1600s. Next to the actual "AI" calculations those engines perform during a game, these engines also cross reference the current game against that entire database. These engines also automatically scale as you add more CPU horsepower to the hardware.
So the dificulty level of playing against the CPU will also be dependent on how fat the computer is that is running the software.
Most of the time, my dad wins. On max level. He is really smart.

But, more importantly (in his opinion, anyway), he is very human.
He always says that "
it's still a computer. It can not think like a human. All it takes for me to beat it, is to think like a human and not play chess like a predictive calculator"
The way he wins against the pc, is (in his own words) by setting up a "human trap" that a machine simply can't see. I'm not sure what that means exactly, but it sounds smart.
It's pretty much in line with the way Garry Kasparov approached his matches against Deep Blue (the IBM supercomputer that played a few chess matches against Kasparov in the late 90s).
If memory serves me right, in total it was about 50/50 for wins vs losses/draws.
But think about that for a second....
A
supercomputer, which was
designed to play chess, didn't manage to whipe the floor consistently with a human. In fact, the supercomputer lost half the time.
This computer was an absolute beast that calculated the outcome of
millions of potential chess moves in a split second.
Off course, that was 20 years ago (wow, I'm getting old...) and I probably wouldn't even last for much longer then a minute against that computer... But the fact that a human actually was able to achieve such a result... It's quite remarkable imo.