In Death Race 3, the Wayland corporation suffers a hostile takeover by some very rich and evil guy, but because he's also very smart he's got a British accent. He wants to turn Death Race into an international series of races at a bunch of prisons all over the world.
Meanwhile Frankenstein is one victory away from gaining his freedom. But Niles (that's the new guy) changes the rules of the game. If Frankenstein wins, he dies. Niles moves Frankenstein and his crew to South Africa where the next multi-stage race will take place. The jail there is some sort of working mine as well.
During the first couple of stages Frankenstein indeed decides not to win, but for the final one he'll have something up his sleeve.
The races themselves are alright, we see lots of interesting scenery and the racers will have to deal with the locals as well as missiles that Niles shots at them whenever he feels like it. There are plenty of fights and lots of neat explosions, but dialogue is something the director can't and won't deal with. Not to mention that at the times the script is pretty painful to have to listen to.
This is one of those movies where at the end you get a recap of how the solution was accomplished. It's interesting but because you don't really care about any of the characters, including Frankenstein, it's almost like it doesn't matter. There is a story here, lots of action, lots of cleavage but only a split second of nudity, the director just doesn't manage to get us involved in any of it.