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Monty Hall Bet Monte Carlo — Play at home!

If you caught my last post about the back and forth I’ve had with YouTube user “adolthitler”, you know the situation.

If not, there’s a person who is wrong on the Monty Hall problem, and refuses to be corrected — so I tried to make a bet with the guy with terms that would make him money if his misunderstanding of the problem were correct, and would make me money if my understanding of the problem were correct.

adolthitler responded:

@jbwhitmore LOL you can afford to throw your money away? Give it to charity.

Sigh. I’ll press him to put up money, but in a show of my outrageous generosity, I’ve decided to release to everyone (including adolthitler) a program that I wrote that can be used to test what the outcome of the bet will be.

I wrote up some python code and posted the source code here — feel free to download and play along at home.

The Bet

Using a random number generator to determine which door holds the prize.

Step 1: We always choose the same door to start with — let’s just say we choose Door 1 every time.
Step 2: One goat is revealed (from behind Door 2 or 3).
— I am forced to always switch to the other closed door.
— adolthitler is forced to always stays with Door 1.
Step 3: Whoever ends up picking the right door gets paid by the other person. (The going rate is $1.08 that I would have to adolthitler; and $1.00 that adolthitler would pay me).

The hypothetical Results

Curious what the outcome of running this bet for 10,000,000 rounds?

SwitchBet is $1.08
StayBet is $1.00
Total Number of Doors: 3
Total Number of Rounds: 10000000
Staying Percent Wins: 33.34 %
Switching Percent Wins: 66.66 %

adolthitler nets: -$3,065,980.96
jbwhitmore nets: $3,065,980.96

adolthitler — if you want to just run this program on your home computer, and every 1000 rounds or so send me a check, I’ll be happy to take your money until you give up. I’ll also accept your pride.

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