get lost - very likely in 4 dimensions.
I see your point. If Fred got lost, he would just walk in a straight line to the left or right and he would find his home. If Bob got lost, he would have to use the "always turn left" rule to find his home, which fails if there are any loops in his path. If Emily got lost, she would also have to follow the "always turn left" rule, but since there are 2 more directions to move in, there is a 3x bigger chance of there being loops and the rule failing.
If you lived in the 5th dimension, there would be a 6x bigger chance of you failing than in the 3rd dimension, and for the 6th, there would be a 10x bigger chance.
I think.