In grade school, we were very into the mathematics of the NCAA men’s basketball tournament. This year, Warren Buffet has raised the stakes, by participating in a Billion Dollar Prize for a perfect bracket. What is interesting, beyond the fact that Warren’s Berkshire Hathaway is writing the contingency insurance (which is totally a thing) in case someone wins, is the difference in your change of winning between guessing randomly and having some knowledge about the games – although is is still vanishingly small. Picking all 63 games correctly assuming nothing about the teams has a probablity of 2^63 = 9.22 x 10^18. However, knowing the seeding and, for example, that 1 and 2 seeds almost always win their first-round games, you can improve your odds substatinally. Estimates vary, but some think your real chances are more like one in 10^11, which is a lot better, but I’m sure Warren is not losing any sleep. This site summarizes the difference:
“If all seven billion people on Earth filled out a somewhat informed bracket with these odds, over the course of 13 years, chances would be greater than not (51 percent) that someone would nail it. If everyone filled out a coin-flip bracket, that break-even would come over the course of 911 million years.”
The reason it is still so unlikely to win, even with the collective basketball acumen of all the experts, is that there is only one way for a bracket to be perfect (ie. it has the lowest possible entropy), and a LOT of ways to be wrong.