Oh wow, and here I was thinking I'm rolling a red cube against Lady Luck's white cube all this time. I saw the required stat type after the dialogue, but was the exact number needed specified somewhere? Or is it more of a intuition thing?
You picked the dialogue based on your assumption on which stat it was linked to - and then it showed you which stat the dialogue actually was. I think if I got above a 6 for that stat it passed - but that was never shown explicitly.
You nailed on how the dice and dialog options work! The options are spread between 3 and 7 on their particular stat, with some options being higher and others lower.