Okay I’ll dispense with draw order entirely. Imagine if instead of asking them if they had an ace, ask them if they had an ace and mentally select one of their aces to be the primary ace at random.
They don’t tell you what it is or give any other information. So the first question on my tree is what is their primary ace, and the second question is what is their other card.
Their primary ace still has a 50:50 chance of being either (if they only have one ace, it could have been either drawn from the deck, and if they have two then it is selected randomly by the person with the cards). If you guess that their primary ace is one of the aces then the other cards are drawn from a pool of three possibilities.
I see what you’re doing, but I still think you’re making a mistake: Just because there are three possibilities, doesn’t mean that those possibilities are equally likely. It’s similar to flipping a fair coin twice; you could get two heads, two tails, or one of each. There are three possible outcomes, but the ‘one of each’ option is twice as likely as either of the other two.
Okay I’ll dispense with draw order entirely. Imagine if instead of asking them if they had an ace, ask them if they had an ace and mentally select one of their aces to be the primary ace at random.
They don’t tell you what it is or give any other information. So the first question on my tree is what is their primary ace, and the second question is what is their other card.
Their primary ace still has a 50:50 chance of being either (if they only have one ace, it could have been either drawn from the deck, and if they have two then it is selected randomly by the person with the cards). If you guess that their primary ace is one of the aces then the other cards are drawn from a pool of three possibilities.
Does this clear what I am getting at up for you?
I see what you’re doing, but I still think you’re making a mistake: Just because there are three possibilities, doesn’t mean that those possibilities are equally likely. It’s similar to flipping a fair coin twice; you could get two heads, two tails, or one of each. There are three possible outcomes, but the ‘one of each’ option is twice as likely as either of the other two.