The Monty Trolly problem: Three tracks, one gold 💰, two trains ☠️.

[u/Kafkaesque_meme]

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[u/Shrewta]

Did I die? Is this hell? Is there a gas leak in my house?

[u/FiikOnTheCheek]

This is a really confusing format but the meme itself is pretty clear.

For anyone confused:

You get to choose between three options. One is good, two are bad. You pick once and it is revealed that one of the other two is bad. You get to pick one more time if you want to switch.

Is it better to stay or to switch?

[u/LawyerAdventurous228 → u/FiikOnTheCheek]

Solution for anyone interested: 

Switching is better because the odds of that strategy are 2/3.  

The reason why is that switching has "flipped" odds. Suppose you guessed right initially. Then switching loses you the game. But suppose you guessed wrong initially. Then switching wins you the game. So switching wins if you initially guess wrong and that happens with a 2/3 chance.

[u/Worldly0Reflection → u/FiikOnTheCheek]

Lol, i thought there were just 2 idle trains on the tracks so my thought was "i should get on one of the tracks with an idle train" because i figured an aproaching wouldnt wanna go front to front with another train.

[u/Few_Fact4747]

I dont care what your computations say, staying is just as good as switching. I switch nonetheless, though, just in case..

[u/Kafkaesque_meme → u/Few_Fact4747]

That’s wrong actually. Switching gives you a 2/3 chance of getting the gold and staying gives you 1/3. This is mathematical fact.

[u/quityourwitchin → u/Kafkaesque_meme]

I’m having such a hard time understanding this.

If one 💀 option is eliminated, that leaves only two options; 💰 or 💀. How is that anything but a 50/50 chance?

[u/Kafkaesque_meme → u/quityourwitchin]

It’s very counterintuitive. That’s what’s fun and interesting about it. Here let’s see if this helps:

[u/InnuendoBot5001 → u/quityourwitchin]

Your original choice had a 2/3 chance of being wrong. The remaining two tracks represent that chance. When we remove one of them, the other track now represents that 2/3, because there was still a 2/3 chance of one of those two being correct, and the other of the two would always be wrong so thats the one that was revealed. Thus, the track you are on only has a 1/3 chance of having been right, but the other track has a 2/3 chance that your first guess was wrong.

[u/Hanisuir]

The second railroad switch is made in such a way that the train will derail on it.

[u/Kafkaesque_meme → u/Hanisuir]

[u/Kafkaesque_meme → u/[deleted]]

Track 3 is 100% death. You can choose it. If you want.