1. The problem asks to find the experimental probability of rolling a 1 on a fair six-sided die after a million rolls, given the theoretical probability is $\frac{1}{6}$.\n\n2. The theoretical probability for each outcome on a fair 6-sided die is equal, so the chance to roll a 1 is $\frac{1}{6} \approx 0.1667$ or 16.67%.\n\n3. In an experiment where the die is rolled a million times, the number of times 1 appears should be close to the expected value, \n$$\text{Expected count} = 1,000,000 \times \frac{1}{6} = 166,666.66.$$\n\n4. The experimental probability is the number of times 1 actually appears divided by one million. Due to the law of large numbers, the experimental probability will be very close to the theoretical probability,\n$$\text{Experimental Probability} \approx \frac{166,667}{1,000,000} = 0.1667.$$\n\n5. Hence, after a million rolls, the chance to obtain 1 in the experiment approximates the theoretical chance, about 16.67%.\n\nFinal answer: The chance to obtain 1 after the experiment is approximately $\frac{1}{6}$ or 16.67%.