Four statisticians are playing bridge. One of them says, "I have an ace." The chance that she's holding more than one ace is 5359/14498, which is less than 37 percent.
Later the same player says, "I have the ace of spades." Strangely, the chance that she has more than one ace is now 11686/20825, which is more than 56 percent.
Why does specifying the suit of her ace improve the odds that she's holding more than one ace? Because, though a smaller number of potential hands contain that particular ace, a greater proportion of those hands contain a second ace. It's counterintuitive, but it's true.
That is so deeply counterintuitive that I couldn't explain it to myself. Had to search the web, and found a discussion at Reddit. I feel a little more comfortable now, but counterintuitive things are always particularly hard to digest.
See also these pages in Martin Gardner's Hexaflexagons and other Mathematical Diversions.
