First Mover on the Number Line

Three contestants take turns publicly committing to integers. Contestant A goes first, naming any integer from 1 to 100. Contestant B, having seen A's number, names a different integer in the same range. Contestant C, having seen both, names a third distinct integer from 1 to 100. A referee then draws a target $R$ uniformly at random from 1 to 100, and whoever's number lies closest to $R$ wins; exact ties in distance are settled by a fair coin. If B and C both play optimally, what should A announce to maximize the chance of winning?