LAS VEGAS - Ahead of the grand opening of Caesars Palace in August 1966, a flashy advertisement ran in newspapers. "I, Caesar, invite you to an orgy of excitement at my Palace of Pleasure," it read.

Luck won’t have much to do with the outcome of the race, even if it takes place in the city often referred to as “the gambling capital of the world.” The Las Vegas Grand Prix is the last of three ...