From Presh Talwalker:

In poker tournaments, everyone gets a fair shot at holding the dealer position as seats are assigned randomly.

In home games, an attempt is also made to assign the dealer spot randomly. There are many methods to choosing the dealer. One of the common methods is dealing to the first ace. It works like this: the host deals a card to each player, face up, and continues to deal until someone receives an ace. This player gets to start the game as dealer.

The question is: does dealing to the first ace give everyone an equal chance to be dealer? Is this a fair system?

Answer:  it’s not.  Presh goes through the full analysis, but here’s a simple way to see why.  Suppose you have 5 players at the table and you are dealing from a deck of 5 cards with 2 aces in it.  Every time you deal there will be two people with aces.  But the person who gets to be dealer is the one who is closest to the host’s left.  If the deal went in the other direction, someone closer to the host’s right would be dealer.

It can’t be fixed by tossing a coin to decide which direction to deal because that would disadvantage players sitting directly across from the dealer.  You need to randomly choose the first person to deal to.  But if you have a trustworthy device for doing that, you don’t need to bother with the aces.