Compute value of card guessing game

Consider the following gambling game with a standard deck of 52 distinct cards (4 suits × 13 ranks):

1. The deck is thoroughly shuffled; all $52!$ permutations are equally likely.
2. Cards are turned face up one at a time from the top of the deck until all 52 cards have been revealed.
3. Before each card is turned over, you must guess the exact identity of that card (rank and suit).
4. If your guess is correct, you earn $1. There is no penalty for incorrect guesses.
5. You are allowed to use any strategy, and may base each guess on all information observed so far (i.e., all previously revealed cards).

Assume you are risk-neutral and want to maximize your expected total winnings.

Questions:

1. What is the maximum possible expected number of correct guesses (and hence expected winnings in dollars) under an optimal strategy?
2. Based on this expectation, approximately how much would you be willing to pay to play this game once (i.e., what is a reasonable approximate fair entry price)?

Explain your reasoning and any probabilistic arguments you use.