What strategy should I use to win a chess game against a chess computer?
The engine is able to make decisions on an about 3 moves deep search graph.
Please do not say check every move in the next 4 moves...
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There are several important points to know when playing a computer:
Knowing these, a human can try to capitalize by closing the position, simplifying and drying it until the computer has almost no tactical base, and simply makes useless moves. If the human manages to make the computer blunder (because of its horizon it cannot calculate further, but the human clearly sees that his positional advantage will grant him the win) or develops a (positional) plan that simply destroys the computer's position strategically, he most certainly will own the game.
Some famous examples are provided by the top GM Hikaru Nakamura. Here against Rybka you can see how he benefits from the fact that Rybka's programming does not allow it to give a draw when it's up in material (it was two exchanges up and about to arrive to the 50 move rule), and thus blunders several pawns trying to push the game and loses. Here you may look for more information on the match Nakamura (2770 ish) - Stockfish (3300 ish), where the GM had many great closed positions that seemed to end inevitably in a draw, but pushed too hard for the win and ended up losing.
Computers' main strength are tactical positions. So steer into quite positions.
Another good thing to do is to learn your openings well. Why? Computers usually will play the same thing in depth 3 over and over. So you will be able to learn what the computer plays, like studying an opponent's previous games.
Another tip is go to the endgame. The weak calculation power helps you a lot. Try to transpose into King and Pawn endgames, and learn them well.
The last thing to keep in mins is that computers do not blunder. They will play what they think is the best, while humans might not even notice an hanging piece. Try to be attentive, and check ahead.
Remember to practice!
If your computer is so weak to calculate
only 3 moves then you can easily got for trades and play endgame. It will be easier to you to overcalculate him.
Just do not blunder, and hey, you were right, calculate 4 or even more! Practise, practise and practise again!
Would you mind sharing few games of yours? We'd be able to see what kind of mistakes you do and give you a better advice :)
The above answers pretty much cover it. Most moderate chess engines don't really make plans and can't read yours: they are only good at tactical calculations. So avoid double-edged positions, make a solid plan and build up slowly, make sure not to allow any counterplay, and the computer will never know what hit it. Also, for the most part computers are terrible at endings. Such ideas as 'that pawn will queen in 5 moves' - never mind 'outside passed pawn wins' - are all Greek to it.
Also, a program's apparent level will vary a lot between games. If you lose one game, don't assume the computer is invincible - the next time you play, it may be practically be playing suicide chess.
I've read the rest of the answers and I think there is something completely wrong with them:
These answers represent good advice against an ordinary chess computer. Of course the more modern ones will beat you anyway no matter how much you manage to apply those tips, but let's say we are talking about an older/somehow underpowered chess engine. Most of the ideas circle around getting into quiet positions, with not much tactics involve
However, the OP is talking about a very particular type of computer, who "is able to make decisions on an about 3 moves deep search graph." This means this computer is actually very bad at tactics! It won't be able to see what most of the tactical complications of a chess game will return, other than the simplest "I win a piece in two moves" kind of "combination". You could even use sacrifices traps, since the computer will give a high importance to the immediate gain in material, not seeing attacking chances for the opponent that can happen after a few moves.
In short, against this type of "engine", you should definitely go for the tactical complications! This does not mean that positional styles should be disregarded, though. I am pretty sure that, in an endgame, the computer won't be able to see why things like "activating your king" are recomended