Does it hurt to draw after the lottery than to draw first?

Don't suffer. Suppose that all four people participating in the lottery are ABCD, and A draws the lottery first, then his winning probability is 1/4. B is the second person to draw lots, so this prize may have been drawn by A. The probability of A winning is 1/4, which means that the probability of A not winning is 3/4. And if A doesn't take the prize money, then the probability of B winning the prize increases to 1/3, and then the overall probability of B winning the prize is 3/4 times 1/3, which is equal to 1/4. Obviously, like A, the probability of B winning the prize is 1/4. Therefore, the probability is the same whether it is first or later, and there is no loss.