And that game was Namco's Ace Driver.
First released in 1994, Ace Driver doesn't look terribly exciting. It's got that mid-90s texturing effect, an atrocious menu system and fairly shocking collision detection.
Two things counted heavily in its favour. The first, at our local arcade (within walking distance of our high school), it was only AUD$1 per turn, when most other games were AUD$2. The second, and more important, was the rubber-banding.
Think Mario Kart, only worse. It was almost guaranteed that, come the final lap, whoever was coming first wouldn't be there by the end, and whoever was languishing near the back of the back had a very good chance of making the podium.
We all knew this, so races descended into a fascinating game of tactical slowness, each of us struggling to balance the need to pass checkpoints to stay in the race with a desire to drive as slowly as possible so we'd be at the back when the final lap kicked in.
For a broken mechanic, it made the game a blast. And now that I'm thinking about it again over fifteen years later, it sounds like one hell of a premise to build an entire game around.