I've recently come across a new driving game for mobiles, it's called Real Race: Asphalt Road Racing and it's nearly like a simulator with arcade gameplay. Racing around deserts and steppes, avenues and roads, it's like Need for Speed Carbon or Most Wanted, and actually the latest edition, NFS: Rivals. 
On a scale of 1 to 10 I'd give it a strong 8. Selection of features is almost overwhelming, and so is its replayability. Outrunning the leaderboards really entangles you and you are directly pulled in. It trully reminds me of Asphalt Overdrive. Above all it's a great, challenging free game. 
There are no pursuits with the police, but maybe it is for the best as multiplayer asphalt gameplay gives great opportunity to prove your cool underground drag racing skills. 
On-screen immense velocity gives a feel of literally being there and hurrying with top drivers as seen in TV. Stress rushes are numerous. 
It has  really state-of-the-art AI and I'm playing it already 8 times successively or so and it's still amusing and engaging. It is kinda kewl to drive and defeat other racers on six or so maps. App feels like race with GT cars like lamborghini or dodge viper.