re: Let's Find Out How Smart You Baws Are

If you, as the shell dealer, know where the treefiddy is, you would not offer me the option to switch if I had chosen the empty shell.

quote:

---

You just watch the movie 21 or something?

---

Never seen it. I learned about this problem many years ago after reading about Marilyn vos Savant. She is the first one who solved it back in the 80's. (Or at least the first one who made the solution famous).

There is an advantage, because your odds went from 33% to 50%. But realistically, if you step away from the situation and re-select the same one that you initially selected your odds are still 50%.

Your shoes are on your feet

It’s a trick question. The correct answer is I punch you in the face and grab all of the shells and cash and run.

quote:

---

Question: Is there any probability advantage to switching or is it 50/50 between your shell and the other remaining one? Explain your answer.

---

If you ever took a statistics class you know that you should switch. But I used to get into this argument with my teacher all the time, where the actual probability is still 50/50 since you know going into it that you're going to remove one in the first place.

But the best way he explained it was instead of 3 let's say there are 100 shells. You choose one and then I'll remove 98 empty ones leaving only yours and one shell left. Would you switch then?

So as much of a problem as I had with the three shell scenario as presented, my stats teacher was one of the smartest people I knew, so I would switch every time.

How is it any different than simply starting with two shells?
The odds reset once you remove the shell.

Start with 100 shells - 100:1 odds
Remove 50 of the losing shells - 50:1
Remove 48 more of the losing shells - 2:1

quote:

---

The probability change is because going in you had a 66.6% chance of being wrong. By showing you one of the wrong choices, you now only have a 33.3% chance of being wrong.

---

Oh I know how it works.

The idea is that you choose one and it has its own probability, but however many other shells are removed, their probabilities shift onto the other remaining one.

I’m not doing your homework.

Don't feel bad, baws. Paul Erdos got it wrong. Erdos was at Princeton and had more than 1,500 published papers in topics like graph theory, analysis, number theory, set theory, and probability theory. Erdos never won a Field's medal, but did win the Wolf prize and some other awards.

One day one of his colleagues posed the Monty Hall problem to him just for fun and told Erdos that switching is best. Erdos responded "That's impossible. Switching gives no advantage."

After going back and forth for a while, the professor did a Monte Carlo simulation on a computer that proved over 100,000 trials that switching gives a 2/3rds chance of winning. Erdos accepted the results but still did not understand why it was true.

A week later he got a call from Erdos who said another one of his colleagues explained it to him and that he now understood it. Erdos explained the reasoning, but the guy did not understand Erdos' line of reasoning. He said he was just glad that Erdos was now convinced.