A tricky guess

Strange as it seems, the answer to any of the questions improves your odds from a random guess (1/52) to 1/26.  Ask ‘is the card red?’ and once you know the answer, you have to guess one of the 26 red cards, so 1/26.  Ask  ‘is the card a king, queen or jack?’ If yes, you have a 1/12 chance and if no, it’s 1/40. The overall chance, therefore is (1/12 x 1/52 = 1/52 for ‘yes) plus (1/40 x 40/52 = 1/52 for ‘no’)  so 1/52 + 1/52 = 1/26. And finally, ask ‘Is the card the ace of spades?’. There’s a 1/52 chance that it is and a 51/52 chance that it isn’t. If the card is not the ace of spades you have a 1/51 chance of guessing it. So the chance of guessing correctly when the card is not the ace of spades is 51/52 x 1/51 = 1/52. Again, the sum of both possible outcomes is 1/52 + 1/52 = 1/26.