I think you missunderstand the underground completly. When you enter the Underground the correct hole is randomly chosen from the start.
Its not like a 50% chance for every hole to be the correct one.
There are 4 sections in the underground. The correct hole is randomly in only one of those sections. If you know the correct hole is on the northern section you know its either the top right or the top left section -> 50% chance to get the correct hole IF you have a tier 3 hint which tells you exactly what hole to use.
If you dont have any other hints than "Northern section" you pretty much have a 12.5% chance (1/8) because every section has 4 holes.
Collect as many hints as you can and put them together to know what hole is the correct one. Sometimes the hints can leave you with a very small chance to get the correct hole and sometimes you know the correct hole for sure.