What are my odds of a critical hit with my level 20 Champion?

I’m trying to calculate what my odds are as a level 20 Champion to score at least one critical hit on my turn, and how many I can expect.

I make four attacks per attack action I take, and can Action Surge for another four, bringing my total to 8. I score a critical hit on a roll of 18-20, and if I get even one, my Great Weapon Master feat lets me make a fifth (or in this case ninth) attack.

I’d also be curious to know what my odds are if I’m rolling with advantage.