>>12598563To help not get tripped up on the "going first when being dealt cards" issue:
Remember that after the deck is shuffled, the aces are locked in place and do not move. That is, imagine the deck is shuffled, and the first ace is 6 cards down. It does not matter what the first 5 cards before it are, because the 6th card will always be an ace dealt to the 6th person, no matter what. It's set in stone who is getting the ace, you just don't know yet.
Deal the cards backwards now, starting from the last card to the last person who would have received the last card.
The 6th person still gets the 6th card = ace.
As soon as the deck is shuffled, the position of the ace is fixed and it is "decided" who it goes to and being 8th or 1st or 52nd does not matter, because the ace has an equal chance of landing in the 8th, 1st, or 52nd slot when the shuffle is finished, with no preference as to what position in the deck it is (that is, its equally likely to land in the middle of the deck as the first part of the deck as the last part of the deck).
The big key is that you don't know which cards are dealt before it gets to you. If you did, that *would* change the probability of you getting an ace, but NOT because the position changed in the deck, but because now you have more information than you did before (whether the first cards were aces or not).
What you will find, however, is that if you play 10000 games, your OVERALL chances of getting an ace are the same (4/52) whether you know what the cards dealt before you are or not, because the aces are fixed once shuffled. It's just that you can use the new information (say, 6 people before you show that they did NOT get aces) to inform your chances of receiving the ace for that particular game, in the same way you would know your chance of getting an ace is 100% if you were dealt the ace. But your chance originally is 4/52.
I
