I want to build a carnival midway g...

I want to build a carnival midway game similar to the ones where you roll a ball to score points and your horse moves along the track dependent upon how many points the hole was worth. I want this to support 3 players, but require only 2 to start. The target will be a target block hit with snowballs, and the targetblock accuracy will be used to determine how far the "horse" goes. I want the visible width to be no more than 15 blocks wide. We can do redstone behind it and depth isn't a limit, or we can do above or below if needed. I want to use minecarts on powered rails. The minecarts should hold an armor stand so we can put something on and make it look like a horse. More about the finish of the race in the next chat.