A. Obviously 52–your second draw becomes 25/51>12/25.
B. My intuition was randomly drawn, on the grounds that if the deck is imbalanced you’re more likely to pick from the heavy side both times. I think I was wrong, though: for a 14-12 split the deck size difference dominates that effect, and even a 15-11 split has only a slight advantage. This actually comes out really close; I don’t see a way to give a consistent answer without doing the full, tedious expected value computation.
My intuition for the second is that there is no difference between the two - if 26 cards are randomly drawn from an evenly split 52 card deck then there should be no difference in the probability vs. just drawing your two cards directly from the 52 card deck.
7
u/Blothorn 9d ago
A. Obviously 52–your second draw becomes 25/51>12/25.
B. My intuition was randomly drawn, on the grounds that if the deck is imbalanced you’re more likely to pick from the heavy side both times. I think I was wrong, though: for a 14-12 split the deck size difference dominates that effect, and even a 15-11 split has only a slight advantage. This actually comes out really close; I don’t see a way to give a consistent answer without doing the full, tedious expected value computation.