You have to get 99 lives
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in my guide it said if you get 99 lives, Mario takes his hat off. lose your 99 lives and he puts it back on.
Run away.
His original hat color is red, but in games like Super Smash bros brawl, and many other games where he can get power ups, his hat can go from light blue, to black, to white, to yellow, and rainbow.
once you reach this point Mario appears without a hat until he looses a life.
This is what is sometimes called an 'easter egg' which does not affect the game in any way but it's just interesting. Mario does away with his cap (not the propeller cap; he needs that!) when he gets 99 lives in New Super Mario Bros. Wii. 99 is the maximum number of lives you can get.