Which player is most likely to win when drawing cards? Two players each draw a single card, in turn, from a standard deck of 52 cards, without returning it to the deck. The winner is the player with the highest value on their card. If the value on both cards is equal then all cards are returned to the deck, the deck is shuffled and both players draw again with the same rules.
Given that the second player is drawing from a deck that has been modified by the first player removing their card, I'm wondering if either player is more likely to win than the other?
Does this change as the number of players increases?

All orderings of the cards are equally likely. It follows that the probability the first player wins is equal to the probability the second player wins. 
