Maybe I'm missing something, but it seems that if player 2 lands away from one of the extremal tiles in less than $d$ turns, (s)he has lost (since, then player 1 can order player 2 to move n-1 places). 

So wouldn't the winning strategy (for $n>2$ and $d>2$) be $n-1$, $1$, $n-1$?