If jill is playing a game with a single die (singular form of dice), what are the chances she would throw any one number twice in a row?

The answer would be 1/6.

A common mistake made on problems like these is to say the answer is 1/12.

The only roll that really matters in this problem is the second one. This is because the first role only determines what the second role must be. Therefore, you only take the probability of rolling one fixed number in one roll, which would be one in six.

I appreciate the fact that you said die in your question, instead of dice.