Chicago Tribune transportation reporter Jon Hilkevich channels Cecil Adams:
The actual answer is fuzzy, depending on the location, the time of day, vehicle traffic volumes, when the walk button is activated—and luck too.
Many pedestrians refuse to press walk buttons due to suspicions they are a trick or a placebo concocted by the traffic gods to keep walkers calm while breathing fumes from tailpipes as they wait for green lights at busy street corners.
Steve Travia, IDOT's bureau chief of traffic for the Chicago area[, says:] "The bottom line is that if you don't push the walk button, the walk signal may never come up."
Of course, if you're in New York, don't bother, because 80% of their "walk" buttons are disconnected.