The Problem

Alpha doesn't know which square he's in. In order to find himself, he has two tools: he can move, and he can sense whether there are walls around him or not.

Unfortunately for him, he can neither move nor sense the walls reliably. 80% of the time he can move where he wants to, but 20% of the time he will move 90 degrees from where he wants to; if the grid spot in that direction is invalid, he will fail to move at all.

His wall sensors work similarly; 75% of the time they return the correct mesaurement in any given direction, but the other 25% they fail. Since he can measure walls in the north, east, south, and west directions, he will only get a completely correct measurement of his current situation about 32% of the time.

Use the arrow keys to play with moving him around a bit, and you'll see how he often fails to move and how his sensors are often wrong (indicated by a red measurement):