Everybody Wins!...at the clown game

Today, Middle S played a paper version of the Clown Game, that many of us have played at carnivals, fairs, Luna Park and the Royal Melbourne Show.
First, we established, that when a ball is placed in the clown's mouth, it rolls into one of (usually) 6 slots. To do this we rolled a dice and an even number meant we moved a counter to the right on our game board. An odd number moved the counter to the left, till we reached the bottom. We then discovered, that the majority of balls (or in our case, counters) end up in the three middle slots.

Why would the game operators do this?
Would it affect where they allocate their most valuable prizes?
Is it just a game of chance or is there a mathematical 'secret' behind it?