Probability theory looks to be one of the harder areas in math to get anywhere with by just being smart, as opposed to studying it. Plenty of professional mathematicians, including Paul Erdös who was pretty smart about math stuff, got the Monty Hall problem wrong when they first encountered it, for example.
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Everyone here seems to be so much smarter than me at this math stuff.
I think I'll stick to writing accounting software.
Probability theory looks to be one of the harder areas in math to get anywhere with by just being smart, as opposed to studying it. Plenty of professional mathematicians, including Paul Erdös who was pretty smart about math stuff, got the Monty Hall problem wrong when they first encountered it, for example.