Games Computers Lose
There is a very simple game called Go, which involves placing pebbles on a grid. The rules are very simple and can be taught in a few minutes. So far, no one has managed to write a Go-playing computer program that can beat a moderately skilled human player.
The human brain is excellent at applying heuristics to a situation and very good at parallel processing. A computer tries to create a set of all possible games and steer the human toward one in which the computer wins.
Unfortunately, the space required to calculate this is huge. Consider an even simpler game, Connect 4. The set of all possible orders of putting counters in a Connect 4 game is just under 4 x 10^83. Assuming that each game could be represented in 64 bytes (one character indicating the column into which a piece was played), this would take over 2 x 10^73 TB of storage space—far more than exists in all of the computers in the world.
So it is impossible for a computer to create a complete set of all possible games for anything much more complicated than tic-tac-toe. Instead, it has to make assumptions or guesses. Each of these assumptions must be individually programmed. Some can be inferred as a result of watching humans play, but this can be very time-consuming.
Computers are also not as good as humans at pattern recognition. Detecting the expression on a human face, for example, is very difficult for computers to do. Even something as simple (for a human) as reading text requires a significant amount of processing power. Games that take advantage of this are hard for computers. One trivial example is the idea of the capcha—a blurred or morphed image of text that is used as a requirement for creating an account with some systems. A human (with working vision) can easily read the word; a computer finds it much harder however.