Heh. I'm getting a different number than either of you.
30 cards, 12 towers = 18 nontowers
Starting hand = 7 cards, probability of all those being nontowers = (18/30)*(17/29)*etcetc*(12/24) = 0.015632184
To account for automulligan, we square that number, since there's also a .015 chance of that happening the second time. SO we have 0.000244365
Account for the remaining cards:
0.000244365*(11/23)*(10/22)*(9/21)*etcetc*(3/15) = 0.00000001644671 for not getting any towers until the deck has 14 cards left.
There's (12/14) chance of getting the tower on the next draw, so we multiply that for our final answer of 0.0000000140972 = 1.40972*10-8 = 0.00000140972%
