Random Selection Game And Mixed Strategy Nash

Question

I came across this question in QuantGuide:
You and your friend play a game where you both select an integer 1−100. The winner receives $1 from the loser. The winner is the player who selects the strictly higher number. If there is a tie, then nothing happens. However, a player can also win by selecting a value exactly 2 below the larger integer. For example, if you select 80 and your friend selects 82, you are the winner in this case. Assume both you and your friend play optimally. The optimal strategy here is a mixed strategy, where you select a random value X from some appropriately determined distribution. Find Var(X).
My Approach: I was thinking of evaluating specific cases of equilibria but was unable to do so.