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Raise your hand if you’ve fantasized, for even a minute, about winning Warren Buffett’s \$1 billion sweepstakes for correctly picking all 63 NCAA Basketball Tournament games.

OK, now put down your hands.

So how likely is it for anyone to win the prize that Buffett and Quicken Loans are offering?

Here’s another way to ask the same question: Would Buffett and Quicken Loans be offering \$1 billion if the chances even approached 1 in a billion?

“I’m sure Warren Buffett’s actuaries have worked this out,” said Alan Hutson, a professor who chairs the University at Buffalo’s Biostatistics Department. “That’s why they threw \$1 billion at it, because it’s virtually a zero chance of anyone winning.”

There’s always a chance, but there’s no easy answer to what the odds are.

If each of the 63 games (following the four play-in games not listed in any brackets) was like a coin flip, with each team having a 50-50 chance of winning, then it’s easy to figure the odds.

Anyone would have half a chance of winning each game. Picking two games correctly would be ½ times ½, or ¼. So with 63 games, you’d have to multiply ½ by itself 63 times. So the chances of winning would be 1 out of 2 to the 63rd power.

That means the odds would be 1 out of 9,223,372,036,854,775,808.

Yikes.

That number also can be expressed, in scientific notation, as 9.22 times 10 to the 18th power. Or 1 in 9.22 quintillion. This is starting to sound like a bad math day in junior high school.

In other words, forget it.

But the odds aren’t quite that long.

An NCAA tournament game is not a coin flip. People filling out their brackets don’t see most games as a 50-50 proposition. There are all kinds of variables, and many of the early-round games are potential mismatches, especially when a top-rated No. 1 seed plays a bottom-rated 16 seed. Those games certainly aren’t 50-50 coin flips.

“Think of a 1 vs. a 16 as a magician flipping a coin,” Hutson says.

Since 1985, no 16 seed has beaten a 1 seed. That’s 29 years, each with four 1 vs. 16 games. That doesn’t mean it couldn’t happen, but it’s very unlikely. So a mathematician might assign a probability of 99 or 99.5 percent to the 1 seed winning that game.

Similarly, No. 15 seeds have beaten 2 seeds only seven times since 1985. And 14 seeds have beaten 3 seeds only 17 times. So a bettor can improve the odds a bit by picking the overwhelming favorite in those games.

“If you put some knowledge into the system, there are some bracket combinations that are more likely than others,” Hutson said, but it’s still just a small fractional difference.

“The odds are still infinitesimal.”

In other words, keep dreaming.

email: gwarner@buffnews.com