The Math Missus: Gaming the game shows

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The Math Missus: Gaming the game shows

Come on down and make a deal! This week we're looking at two popular game show games to see if it really is all about luck.

Mathieu Boudreau, a PhD student at McGill and the Montreal Neurological Institute, is our lovely assistant for this episode.

He shows us how Plinko, the most popular game on The Price is Right, is all about probabilities and pathways, and introduces us to a classic probability puzzle called the Monty Hall problem.

Plinko 101

A Plinko board is a tall, flat board covered in pegs. The contestant goes to the top of the board and releases flat disks, or Plinko chips, down into the field of pegs.

The chips bounce down through the pegs and land in a slot marked with a price at the bottom of the board.

Contestants aim for the slot worth $10,000, but their chips often wind up in a slot worth $0.

Boudreau shows us there's a sweet spot on the Plinko board. If you drop your chips from this spot, they have the best chance of landing in that $10,000 slot.

From this spot, you've also got the highest chance of landing in one of the $0 slots on either side of the big money.

But like most gambles, the biggest payoffs come from the biggest risks.

The Monty Hall problem

Speaking of risk, remember Let's Make A Deal, the classic '70s game show hosted by Monty Hall?

Turns out there's a famous math problem based on that show. Fittingly, it's called the Monty Hall Problem.

Here's the deal: a contestant is shown three doors. Behind those doors are two lousy prizes and one fantastic prize. The contestant picks a door.

The host then reveals what's behind one of the other two doors, and shows that it does not contain the fantastic prize. The host then gives the contestant a choice: she can either stay with her original choice of door, or she can switch her choice to the remaining unopened door.

Is she better off staying with her original choice or should she switch? You may think that it doesn't matter: the contestant should have a 50/50 chance of the winning the big prize either way. 

But the real answer is counterintuitive, and even a little bizarre. If you're baffled, you're in good company.

Paul Erdos, one of the most talented and prolific mathematicians of our time, needed days of thinking and multiple demonstrations before it sunk in for him.

Can you do the math? Watch the video above as Mathieu and Sarah show you one way to game the game shows. 

If you enjoyed today's lesson, tune in next week for third episode of the Math Missus! And check out the other great videos on the CBCNL YouTube channel.