This posted today on the Guardian newspaper website.

https://www.theguardian.com/science/2021......f-spades

Mike

That first question is one of those infuriating puzzles that you do not want to believe the answers even when they were explained. I worked out 1 + 2 but still cannot believe 3!
A Keeper

(3) seems so unbelievable because a "yes" answer is so improbable (1/52) that, in the vast majority of cases (51/52), the probability of guessing correctly is 1/51. It's hard to believe that the unlikely scenario when the card is actually the Ace of Spades can change matters so dramatically so that the overall probability is 1/26.

Intuitively it would seem even more implausible if a random number between 1 and 1000 was selected and you then asked "Is it 482?" But the theory remains the same and a Monte Carlo type simulation should confirm that the probability of guessing correctly in this case is 1/500.

Mike

Chess engines can now use monte carlo simulation to coalesce around the best move