Question: What is the probability of getting a 5-2 split, and after making two purchases, getting ANOTHER 5-2 split, with both of your purchases on the bottom of the deck? (Ignoring things like Nomad Camp, Noble Brigand, etc.)
Answer: 1 in 2376.
I swear a 5/2 followed by a 5/2 doesn't seem that rare to me. I know I have had it happen before on a few occasions.
These posts can be reconciled by the following observation: many games when you start with a 5/2 split, you make only one purchase and buy nothing on the $2 hand. In your next shuffle the chance that the single card purchased is on the bottom is 1/11, which is much higher than the 1/66 chance if you purchase 2 cards. Therefore, two 5/2 splits is likely to be substantially more common than the 1 in 2376 calculation suggests.
Edit: in addition, the exact situation where you get a 5/2,
purchase two cards, and get another 5/2 is even rarer than 1 in 2376 games because in many of the 5/2 openings, you only purchase a card on the $5 hand.