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discounts

Madrid doesn't go in for this sort of thing (luckily, there are all those free days at the major museums). There is one pass, called the Paseo del Arte (€7.50), that grants you admission into all three major art museums: the Prado, Reina Sofia, and Thyssen-Bornemisza, but it only saves you money if you do all three.

My advice: enjoy the the Prado and Reina Sofia on their free days, and just pony up the €4.80 for the Thyssen alone (though yes, it isn't free, it'd be a shame to leave Madrid without seeing this outstanding formerly private collection of art ranging from the 12th to the 20th centuries and featuring such names as Duccio, Holbein, Caravaggio, Bernini, El Greco, Tintoretto, Van Gogh, Mondrian, Picasso, Degas, Monet, Hopper, Rothko, de Kooning, and Dalí).

There is the Madrid Card.