Mind's Desire and a tiny deck

[the Thin White Duke]

Hey folks, so last night I'm goldfishing my Azami EDH deck (my wife has refused to play against this deck...) and as I often do I find myself going off out of nowhere (Magically speaking of course). So I'm digging and digging, looking for Mind's Desire to pull off a truly epic storm. After 28 spells and Mana Severance somewhere in there, I finally find and play Desire and I count out 18 cards in my library. A hint of doubt popped in to my head, but I don't lose because I can't rfg cards to all the storm copies, right? I'll lose on my next draw, but I don't lose right away from the stormage, right?
Thanks for listening.
Happy holidays!

[cdr]

Hey folks, so last night I'm goldfishing my Azami EDH deck (my wife has refused to play against this deck...)

Gee, I wonder why.


I'll lose on my next draw, but I don't lose right away from the stormage, right?

104.3c. (http://yawgatog.com/resources/magic-rules/#R1043) If a player is required to draw more cards than are left in his or her library, he or she draws the remaining cards, and then loses the game the next time a player would receive priority. (This is a state-based action. See rule 704.)

[the Thin White Duke]

But Mind's Desire does not make me "draw" cards, it makes me "exile" those cards. So are the two synonymous?

[Nightmare]

No.

If you Desire for your whole deck, and are not forced by any means (including, but not limited to the draw step) to draw a card before you would win, you win.

[the Thin White Duke]

Thank you guys! That saves me some embarrassment.
And thank you Nightmare for turning me onto Azami.