True RNG can be rough, but changing from percentages to dice won't alter your success/failure rate at all. It is just a means of determining how likely you are to succeed or fail.
Just remember a simple thing: What are the chances of missing a 95% chance swing?
5%.
What are the chances of missing three 95% swings in a row?
Not zero.
The RNG is fine. Working as intended. You might want to sacrifice a goat to Lady Luck, though.
