The Full Monty HallSomething something probability mind-blown

So who is this Monty Hall guy?

The Monty Hall Problem

The Monty Hall Problem

• A brain teaser loosely based on the game show Let’s Make a Deal

The Monty Hall Problem• The contestant is presented with three closed

doors and is asked to pick one

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The Monty Hall Problem• The contestant is presented with three closed

doors and is asked to pick one

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The Monty Hall Problem• Monty Hall opens a remaining door and reveals

a goat!

1 2 3

The Monty Hall Problem• Monty Hall then asks the contestant to either

stick with their choice or switch to the other door!

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The Monty Hall Problem• Let’s say the contestant sticks with door 2…

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The Monty Hall Problem• Let’s say the contestant sticks with door 2…

1 2 3

👍

The Monty Hall Problem• And so Monty reveals what’s behind door 1

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👍

The Monty Hall Problem• And so Monty reveals what’s behind door 1

1 2 3

👍

The Monty Hall Problem• And the contestant loses

1 3

Is there a strategy to increase your chance of

winning to better than 50/50?

There are only two possible strategies: always

stick, or always switch

One of those strategies is better than the other

The Monty Hall Problem became famous as a question from a reader's letter quoted

in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990

Vos Savant revealed the winning strategy

10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos

Savant was wrong

But the smarty-pants PhD students were wrong!

Probability Theory Deep Dive

Yeah, nahTo the codes!

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Live demo time!

In conclusion…

Switching is better

If you always switch, you’ll win the car ⅔ of the

time

The only way you will lose is if you pick the door

with the car at the start.You have a ⅓ chance of doing that. So ⅔ chance

of winning.

Thank you!James Sadler @freshtonic