sssssssssS      B

×Horizontal preference is turns 0-4, 10-14, 20-24; vertical preference is turns 5-9, 15-19, 25-29 on the clock.

With horizontal preference, this snake will keep going.

             B                        B
ssssssssS                 ssssssssS

With vertical preference, this snake will turn.

             B                   S    B
ssssssssS                 ssssssss

×For example, if you have a snake moving east with horizontal preference, and Beethro steps SW of its head, the snake wants to use its horizontal preference to move west. But it can't because its body is there. So it turns north. In the same situation, a snake with vertical preference would use that preference to turn south.

In this diagram, the snake has horizontal preference and Beethro takes one step west.

                      S
ssssssssS      ssssssss
        B            B

×Stash the roach at (1).
Get the snake to (2), moving west.
Get Beethro to (3).

I'm assuming you're having trouble getting the snake into position with Beethro up top, instead of off to the east side?

Oh, and remember that the roach moves before the snake.