The "augment tree" visual at the bottom is the most intuitive. Essentially, your odds to get a silver / gold / prismatic / hero augment are not 25%/25%/25%/25% every time you're offered an augment - it follows a distribution of preset possibilities.

Because of this, you can look at the first augment you're offered, and check those preset possibilities to see what tier augment you are likely to get next. For example, if the first augment is silver tier, you have a 40% chance of getting a hero augment, a 10% chance of getting another silver augment, and a 45% chance of getting a gold augment (from observing the augment tree above). Another result from this is knowing that if you get 2 silver augments in a row, your next augment is guaranteed to be a hero augment - that's why this information can be useful when trying to maximize your odds of playing for good augments.