Hopefully what you saw in the simulation was what you expected to see:
The more samples you use (the more dice you roll) the closer, on average,
the approximate probabilities will be to the exact probability of 0.3333...

In other words, more samples should produce approximate probabilities
that vary less around 0.3333...

FOR EXAMPLE:
If you rolled 300 dice(Set Size equal to 300) then the approximate probabilities
you get should vary from about 0.2333... to about 0.4333..
BUT if you rolled 3000 dice then the approximate probabilities you get should vary
from about 0.3033... to about 0.3633.. (So very close to 0.333...)

CONVERSELY if you rolled ONLY 10 dice then the approximate probabilities you get
should vary from 0 to about 0.9 (So they can be far from 0.333...)