Do you become more complicated when you have a complex thought on your mind?
Yes. Please see neuroplasticity. More importantly, people are more complex than any single idea they have.
To account for the number of throws of the dice to have US and OUR universe to happen
This is pure conjecture and is not supported by science. Without knowing how many sides are on a dice - and not knowing how often numbers repeat on that dice - there is no way to know what the odds are for rolling any particular number. Likewise, our universe is the only one we can look at so we have no way of knowing if other kinds of universes are possible. Our universe could be unlikely. Or, our universe could be the only possible kind of universe there is. We just don't know.
Some scientest think there might be a multiverse because certain branches of String Theory make that prediction. But the multiverse is NOT made up to solve or explain the likelyhood of the physics we see inside our universe.