We had rehabbed a century old house from the Addams family house to a museum piece, only to have a mouse breakout happen in our yard. Then they started to get in the house, and that was a serious problem. I tried traps, but I could literally set 10 around the back steps, and in an hour they would all be sprung, with about half of them with a dead mouse.
He were starting worry about it, when a stray cat showed up at our house, and decided it was a nice place, with nice people, and the added bonus of a yard full of mice to kill. Fun!
He was such a sweet guy, but he had the heart of serial killer. Within a couple of weeks, we weren't seeing any mice, and I couldn't walk across the backyeard without finding a headless mouse corpse. After he had things under control, he decided the place was good enough now, and invited his beautiful Siamese girlfriend and their three kittens to live with us. No humans were consulted in any of these decisions.
So if you've got mice around your house, a cat is your very best extermination strategy.