I had this game. I wished I still did. I also had two other horseracing games. One was a straight track with lanes for like 6 or so metal horses. The tracks moved at random speeds, so you never knew which would win (picture found here). I bought it at the old FAO Schwartz location (across the street — south — of where it is now). I was probably ten years old. The other game was at my grandmother’s house. It was made up of plastic horses all named the big names of the day for when she bought it (Tim Tam, Citation, Whirlaway, etc.) You basically spun a wheel to see how many spots ahead on the board you’d move. Pretty basic, but I spend HOURS playing it.
I LOVED all these games.