Puzzle Description:

Multiple Choices

#1: Joe (infrapinklizzard) on Mar 30, 2019 [SPOILER]

Say I were to give you the choice of one of three doors A, B, and C (go ahead and pick one). Behind one of them is a new car. Behind each of the other two is a goat.

Now that you've chosen a door, I open one of the other two to show you a goat behind it. (Very cute, but it's not a commuter vehicle.)

And then I give you the choice to stay with your original door or switch to the third (unopened) one. Should you? What are your chances if you stay or switch?

This is a famous puzzle with such a non-intuitive answer that even prodigy mathematicians have argued against it. It has been proven beyond a doubt, however.

After LL/CL finishes the green
EL 3 c1 places it.
LL
IEL 9 r8 - it can't go right past c21 without causing a conflict,. So r8c13-15 must be black
LL
two-way logic 2 c21: the 1 in c22 must be in either r7 or r9. So the rest of the column must be white.
LL to finish

Found to be solvable with moderate lookahead by infrapinklizzard.

fun solve! couldn't tell what it was til the end and then the goat popped out immediately. Good stuff!

I used el on the 3 in c12 to put a dot in r1 instead of your 2-way step..

I've heard this before, but it was presented differently. I wanna say that Mythbusters tested it. Trying to remember....but I haven't had my daily dose of coffee yet and my brain doesn't want to think. Intuitively, you'd think you've got a 50/50 shot. But that's not the case. You've got a 1 in 3 chance of having it originally, or 67% chance of being wrong. Your odds are better if you switch choices. I know it's proven, but my noodle's sorting out why still. Where-ever I originally seen it explained it well...

https://mythresults.com/wheel-of-mythfortune

The best explanation I have (and that I never see anyone make) is that the information you have influences the chances.
For example, lets take the chances of the sun rising tomorrow. There are only two cases:
X: it will
Y: it won't
And yet you won't find many people arguing that there is a 50% chance that it will rise. It's because we have more information that shows that there is an incalculably small chance that it won't thanks to the way the universe works.

The reason that our choice is not 50% is because the host gives us information when he opens the door with a goat behind it.

The procedure is this:
> contestant chooses a door (effectively random)
> the host then opens one of the two remaining doors and reveals the goat behind it.
> you get a choice to stick or choose the remaining door

With this procedure you have a 2/3 chance of winning if you change doors, and only 1/3 if you stay.

Here's why.
> Let's say you choose door A. You have a 1/3 chance of winning. In other words there is a 2/3 chance that the car is in the group of [doors B & C].
> Now I open door B and show you a goat. I have given away information on my 2/3 chance. Now all of my 2/3 chance is concentrated on the remaining door.

Let me clarify my first sentence. "...the information you have influences the chances."

"Probability" can mean two things: the actual chance that something will happen, and the chance that our prediction of something will be correct.

Most people think of it as the former, when generally it is the latter.

Figuring the probability of a random event is generally quite easy. Flipping coins, for instance.

Figuring the probability of a non-random event is trickier, and the more information you have the better your chances are of making the correct prediction. In some cases you can make astonishingly massive improvements, like my sun rising example above where the chances of a correct prediction go from 50% to as close to 100% as you can get.

Others are not so great, like weather prediction. However, notice how much better weather prediction is now than it used to be. That is because we keep getting more information about how the weather works.

So when I said that information influences the chances, I am not implying that the information changes the universe, but that it changes our predictions, and thus the chance that our prediction is correct.

The Monty Hall problem (from the game show "Let's Make a Deal).

Cool.

Love the goat!

I like the goat. Is he/she mowing the lawn?

My brain hurts after that solve and statistics lesson, but I feel so much smarter now. (✬‿✬)

I think this conversation is starting to get my goat.

Awesome goat. Fun puzzle.

Goto next topic

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