Mike McCaskill spent years scouring the stock market and betting on long shots. Then he found the opportunity that changed his life—and helped spark the mother of all short squeezes.

Over the course of a few hours on April 20, a guy called Cuddles and eight of his pals from the freewheeling world of London’s commodities markets rode oil’s crash to a $660 million profit.

How automated ‘execution algorithms’ are taking the world’s markets on a wild ride that few economists can even understand, much less control.