Dominating Two

You and the friend play the following game: You and your friend each select an integer in $[n] = \{1,2,\dots,n\}$, where $n \geq 3$. The winner is the person who picks the strictly larger number OR who picks exactly $2$ below the larger number. For example, if your friend selected $75$ and you selected $73$, you would be the winner. If the two numbers are equal, nothing occurs. The winner receives $€1$ from the loser. Assuming both you and your friend play optimally, the optimal strategy is a mixed strategy where you choose your value according to some appropriately selected random variable $X$. Find $\mathbb{E}\left[ X \right]$ when $n = 100$.