I have a casino rental company that is outfitted with all kinds of standard games. I'm looking to create a new version of the "Big 6" or "Horse Racing" wheel games you may see from time to time.
Basically, the theory is I would have a wheel like this
split into 32 segments with 7 different colors representing different horses. You can see they are unevenly represented, to represent horses with different odds.
The idea is that players bet on a Horse to win and the operator spins the wheel. Whichever Horse is on the outside will move ahead 3 spaces on the game board. The middle horse will then move 2 spaces and the inner horse will move 1. Then the operator will repeat. Whichever Horse crosses the finish line (7 spaces away) first will win, and we will pay out.
My math is basic enough to figure out EV of each color horse for how many spaces they are likely to move per spin, but I can't figure out the math for what percentage of time the Red horse, or Blue horse, for example, will win the race.
Keeping in mind the complicated scenario of if the Orange horse is at position 6 and Blue is at position 5 and they move 1 and 2 spaces respectively, Blue will win because his move is resolved first.
Any help or insight would be greatly appreciated. Thanks