Numbers Game II

You and a friend play a game. Each of you selects an integer from 1 to 100. The player with the strictly larger number wins $1 from the opponent. A tie results in no exchange. But if one player's number is exactly 2 less than the other's, the player with the smaller number wins. If both of you play optimally, a mixed strategy involving selecting a number $ X $ from a certain probability distribution would be optimal. Determine the variance, $ \text{Var}(X) $, of this distribution.

Answer format: round to 3 decimal places.