She's not very good at math, is she. Unless the game randomizes the hole every time you stick a sword in, and can choose holes that are already filled, you do increase the probability each time.
I think this is just a case of poor word choice. I think she meant to say "The chances of you selecting the right hole on any turn is equal." It's true that the probability of a player picking the right hole increases as the holes get filled up, but the player's chances of winning stay the same since you also have to take into account the probability of the previous picks being wrong.
Probability of the first sword being right = P(A) = 1/24
Probability of the second sword being right = P(A') * P(B|A') = 23/24 * 1/23 = 1/24
etc...
The point the character was trying to make was that you may feel like your chances of winning are increasing but overall it actually stays the same.
last edited at May 7, 2014 8:28PM