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?

If the second player were drawing from a full deck, he would draw each of the $13$ ranks with equal probability. The only change when he draws from the $51$-card deck that remains after the first player’s draw is that the rank of the first player’s card becomes less probable; the other $12$ ranks remain equally likely. Thus, given that the game is decided in this round, the second player’s probability of winning is the same for both decks, namely, $\frac12$. The only effect of not replacing the first player’s card is to decrease the expected number of tied rounds before the game is won or lost.
