The Price Is Right made history Monday when not one, not two, but three straight Showcase Showdown contestants spun the Big Wheel twice, each ending up with the coveted $1 total — a $1,000 prize.
They cheered. They hugged. The crowd was on their feet. Twitter went bananas. Host Drew Carey couldn't remember a time three straight players have scored the top prize. (It's happened before — though possibly not with two spins each.)
So what are the odds? We did the math.
Matthew Zaremsky, visiting assistant professor of mathematics at Cornell University, walked us through it.
Let's start with the Big Wheel. It has 20 numbers in intervals of five going up to 100: 5, 10, 15, etc. You can spin it either once or twice to try to get as close to 100 (or $1) as possible without going over.
The odds of scoring 100
If you're trying to get 100 in one spin, the odds are easy: You've got a 1/20 chance. But if you're trying to land it in two, it's more complicated. Basically, you have to count all the possible outcomes in two spins. The first spin can be anything but 100, and the second spin can be anything. That's 19 times 20, or 380. Then, figure out the number of outcomes that total 100 (5 and 95, 35 and 65, etc.), which is 19.
"Nineteen times out of 380, you're going to get a sum of 100 with exactly two spins," Zaremsky said. "Nineteen over 380 is just 1/20, so surprise surprise — you have the same chances of winning in exactly two spins as you have of winning in exactly one spin!"
How about the odds of scoring 100 in two spins — three players in a row?
Because each player had an independent 1/20 chance of scoring 100, the chances of this occurring three times in a row are 1/20 to the third power. The total: 1 in 8,000, or 0.0125%.
Amazingly, according to Wikipedia, there have been about 8,000 episodes of The Price Is Right, Zaremsky pointed out — "so perhaps we shouldn't be all that surprised that this improbable event has happened!"