1 on a D6

[Seven]

The odds of rolling 18 are 0.5%.
The odds of rolling under 16 are 4.7%.

Those seems like decent odds for a failing a simple task for which one has innate abilities.
For the average character, like a thief doing a constitution check, the odds will be around 40-60% assuming the character doesn't have low stats.

[daryen]

Another common rule is that rolling an 18 is always a failure. Or rolling a 17 is a failure and rolling an 18 is a critical failure. Rolling a 3 is never an automatic success, though.

[Seven]

Alternatively, if the goal is to produce an effect on an object, than the roll is really for the object, not the character. So, if a 2 is rolled, the character who needs a 1 has failed, but the character who needs 1-3 will automatically succeed. And vice versa.

It's totally different from, let's say, a roll to remain standing when a rift hits an unseen rock.
In that case, each roll will affect each character independently.