The cars on both sides actually win a majority of the time because sometimes, both cars to win the same race. But the right side does win more often. From the data from the guy who has riden it over 10K times, the left side wins about 51.5% of the time and the right side wins about 54% of the time (a statistically significant difference).
In my non scientific experience, it's more like 90% of the time the right side wins. It's a running joke in our family. As soon as we see the car ahead of us go to Ramones, we all groan. And we always lose.