That's a micro-optimisation that's absolutely worthless. Even if you do pay the cost of indexing an array every single time, that's just a single instruction to fetch the address. The compiler is absolutely capable of caching the indexing for you, either in a register or on the stack, if it deems it worthwhile.
One reason you might want to use a separate variable would be to prevent indexing mistakes, like using i instead of k by mistake in a context where i is a nested loop's counter. But apart from this and other "to make it easier on the human" reasons, there's no point in caching that in a variable. Now, if you were writing Python on the other hand...
Question regarding index access: There are tons of for loops with player[k] occurrences and similar. Personally I would create a local variable and prevent further index-retrievals.
Is this worthwhile or would a compiler optimize the array-index access away? Or maybe subsequent uses of the same index are cached by the cpu? Does someone know?