Playing Monopoly I strongly believe is superstistion that in order to win you must play the piece that you are in order to win. We feel that if we don't have the right piece that we can't win and lose our focus because it isn't our piece.
I like the hat for it reminds me of being a Mad Hatter as in Alice in Wonderland as I study my opponets. The strategy of the game is always mind blowing and to be one step ahead. To be calculating is a intricate talent that only a person with a mind of genuine uniqueness can understand and wn.
Don't not think more of what the hat offers, it is not the top hat of that jolly mustached man on the box, no it is the mad hatter who knows all to well.