13 Things You Might Not Know About `Super Mario Bros. 3´ – This is the bit that really got me:

9. It doesn’t matter which chest you choose in Toad’s bonus game. Speaking of Mario 3‘s bonus games, prepare to have all your childish illusions shattered. Turns out, the chest you pick in the “Pick a Box” game makes absolutely no difference. The power-up you get is determined when you enter the mushroom house, and all three chests contain the same thing. I don’t know what to think about anything any more.

Indeed.