How many dice can you roll without rolling the most probable number
Python 2, 70 bytes



from random import*
n=2
while eval("+randrange(6)-2.5"*n):print n;n+=2


Try it online!

The trick is to compute the sum by evaling a string the looks like

'+randrange(6)-2.5+randrange(6)-2.5'


with n copies of the expression concatenated. The randrange(6) outputs a random number from [0,1,2,3,4,5], which is shifted down by 2.5 to have average of 0. When the sum if 0, the while condition fails and the loop terminates.

An alternative using map was 4 bytes longer:

from random import*
n=2
while sum(map(randrange,[6]*n))-2.5*n:print n;n+=2


I've found a bunch of equal-length expressions for a die shifted to mean zero, but none shorter

randrange(6)-2.5
randint(0,5)-2.5
randrange(6)*2-5
uniform(-3,3)//1