CHICAGO — As a kid rooting around in the attic of his boyhood home, Allan Calhamer stumbled across an old book of maps and became entranced by faraway places that no longer existed, such as the Ottoman and Austro-Hungarian empires.

That discovery and a brewing fascination with world politics and international affairs were the genesis of “Diplomacy,” the board game he would create years later as a history student at Harvard University in the 1950s. After its commercial release in 1959, the game earned a loyal legion of fans in the U.S. and elsewhere that reportedly included President John F. Kennedy, Henry Kissinger and Walter Cronkite, among others....