I agree. The problem is logic.
The correct answer is not immediately obvious. It is just the same with the two-coin puzzle -- first you'd think 50%. Also, quite similar to the Month Hall problem or the scene in the movie 21.
Alan, you keep saying stuff like, "Enough! Just prove to me it's 1/11. No games or spreadsheets etc. Just prove it!" [Not verbatim.] And that's exactly what we're constantly doing....but, you are unable to see the truth. You can lead a horse to water but you can't make it drink.
Just try the experiment.