Let's say for example, there was a dye in which any number with any amount of digits could be scored. You also had an equal chance of scoring every number. Which means that you have the same chance of rolling a 1 as you do 5 billion. If you rolled that dye, how many digits would that number likely be. Considering this, the percentage of numbers that have less than gogol digits compared to an infinite amount of numbers would be infinitesimal . For example, there are a certain amount of numbers that have gogol digits or less. But out of an infinity of numbers, less than 1 in, let's say a quintillion have gogol digits or less. So you have much less than 1 in a quintillion chance of scoring a number that has less than a gogol digits. And that number can be expanded infinitely into something much larger than 1 in a quintillion or gogol digits. Bit a number has to be rolled, and it must represent a finite amount, so how large would that number likely be?