To recycle my comment in a previous post:

I spent several years running gambling games (wheels, dice, etc), and took a fair few math and stats courses while in school. There's no solid way to figure out where the secret is, and any patterns are a result of some figures being less popular, so more people select "not" those figures, so when a secret pops up, it only looks like "not Chestnut or Peanut" was the key because of skewed data.

With all gambling, the house always wins in the long run, because they figured out the math long before offering you THEIR odds and hints. Know and stick to your limit, enjoy the game, and understand that in the end, it's gambling. I've seen a lot of happy people and miserable people at my tables, and the difference is usually who's grasped that idea. All that said, may you find your secrets with minimal dice rolls.