[MickeyHoldem]

I think this term is a wee bit high... it over counts the times there are 4 hands of A6 by a factor of 4.

Four A6:
Q4 = ((16*9*4*1)/24) * 44c12 * 11!! = 5261703498291240

Three A6:
Q3 = ((16*9*4)/6) * 46c14 * 13!! - 4 * Q4 = 3111921783275104800

# deals:
D = 52c20 * 19!! = 82492346176096206475125

so exactly 3 A6 = 3111921783275104800 / 82492346176096206475125 = 0.000037468627243
= ~1 in 26689

atleast 3 A6 = (5261703498291240 + 3111921783275104800) / 82492346176096206475125 = 0.000037532411385 = ~1 in 26644

you answer is the first part of Q3 / D

((16*9*4)/6) * 46c14 * 13!! / (52c20 * 19!!) = ~1 in 26508