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There's two things that I'm sick of reading about because they pop up cyclically.
I mentioned the airplane on a treadmill problem.
The other is the Monty Hall Equation.
It's provable in several variations pick one of three boxes, reveal one as empty, change your answer.
Here's the thing.
It doesn't fucking matter.
The only person playing this game more than the one time is Monty himself.
The chance of picking the correct door on your initial selection is 1 in 3.
Changing your answer ups that to 2 in 3.
Decent odds.
The Price is Right ran the "honest" version of the game.
The prize location was decided before the initial guess. One door without a prize is shown after the guess.
2 in 3 odds if you change your answer.
Grab your d6 or d12.
Assign 1/3 of the faces to represent a loss. 2/3 for a win. (1 and 2 for the d6 loss and 1-4 for the d12 loss).
Roll.
Did you win?
You should have.
I just tried it out with a d12. I rolled a 1, 3, 2 and 11. I only won one game in four chances.
That's three more times than I would have been given on the show.
People use this equation as if changing your answer, which DOES double your odds of winning, guarantees a win.
It does not.
If the prize was behind door #1 and you change your answer to #3 after being shown nothing behind #2 means you still lose.
By all means, play the odds, but don't get mad if you lose; because the sure thing sometimes loses and the longshot sometimes wins.
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