In the Wild Area near the Day Care Center are two characters called the Digging Duo. For a price of 500 W, they give one or more items, the quantity and type of which is (or seems) random, varying depending on which of the two is chosen. These items can be found, for example, here on serebii.net.
Having spent now over 50,000 W, I have gotten most of the items in large quantities, except for Gold Bottle Caps, which leads me to believe that every type of item has its own odds of getting rewarded.
Has datamining revealed what the odds for the Digging Duo are, both for items and quantity mined?