Odds of drawing a good hand at the start of the game

Hi All!

I'm stumped and need some help.

The problem:

How many 2 mana (aka 'drop') cards would I need to guarantee one at the start of the game?

IIt seems to me this is kinda like a Bernoulli Trial.


Except, the odds here aren't really independent between each trial. 

If you go first, you have 3 cards in hand. You have a x / 30, x / 29, and x / 28 chance of getting your 2 drop in that hand.

Say none of those work out, and you return them all to deck. Then you've got a x / 27, x / 26, x / 25 chance on the refill.

Finally, at the beginning of turn one and two, you have an x / 27 and an x / 26 chance to draw your 2 drop.

SO! This math doesn't exactly lend itself to a Bernoulli trial... but I could oversimplify and just say "I have an X in 30 chance at every draw".

Anyways! The question really is, what's the better way to do this Math?

When I build a deck, I'd love to know what the "ideal" number of cards is for 2 drops, 3 drops, etc.