I didn’t quite understand the verbal arguments well enough to confidently evaluate them directly (though argument 2 seems to hit the correct applause buttons), but I diagrammed out the options on a spreadsheet and got the same answer as argument 2.
Essentially the reason argument 1 is wrong is because in enumerating the different possible outcomes compatible with the response given, the hand with 2 aces should receive half the weight of the other hands containing the ace of spades, since it will only yield a “yes” half the time, and therefore has a 50% chance of being excluded from scenario 2.
So instead of 3 1 possibilities (of which one has a 2-ace hand), there are 2 1 possibilities with one ace plus 1 * 1⁄2 possibilities with 2 aces.
I didn’t quite understand the verbal arguments well enough to confidently evaluate them directly (though argument 2 seems to hit the correct applause buttons), but I diagrammed out the options on a spreadsheet and got the same answer as argument 2.
Essentially the reason argument 1 is wrong is because in enumerating the different possible outcomes compatible with the response given, the hand with 2 aces should receive half the weight of the other hands containing the ace of spades, since it will only yield a “yes” half the time, and therefore has a 50% chance of being excluded from scenario 2.
So instead of 3 1 possibilities (of which one has a 2-ace hand), there are 2 1 possibilities with one ace plus 1 * 1⁄2 possibilities with 2 aces.