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The chance of rolling a double is 1/36. https://stackoverflow.com/questions/32313428/understanding-the-probability-of-a-double-six-if-i-roll-two-dice

The chance of rolling any given double (e.g., as in your link, a double 6) is indeed 1∕36. There are, however, six doubles to choose from, so the total probability is in fact 1∕6 of rolling any double.

The chance of rolling a single is 1/6 ⁓ but two dice thence double the likelihood of instances to 1/3

Alas, adding probabilities does not work that way. In effect you've counted the outcome of a double twice. The chance of rolling at least one of a given number with 2 dice is, in fact, 1−(1−1∕6)²=11∕36.