41–50 of 331 posts
I'm familiar with the problem and my intuition is still wrong. I wonder if you couldn't design a gambling machine that has a variant of the Monty Hall problem built-in favoring the house (naturally).
I guess Monte Carlo simulations weren't well-known or easily accessible back then? It would have been the perfect way to shut up her critics.
This is partly why I think it's hard for some to comprehend "the Monty Hall problem". If you've ever seen Let's Make a Deal, you'll notice the big deal is set up very close to, but still materially different than how "the Monty Hall" problem is set up.
I wonder if people who have never seen the show can understand the math quicker...
There are 2 red and 2 blue balls in a box. One ball is removed at random, what are the odds that the ball is blue?
Now we repeat the problem, but before examining the ball, we remove a second ball. We observe that the second ball is blue. In this case, what are the odds that the first ball is blue?
Which public intellectual introduced Monty Hall to the public when awareness of the problem was at a similar low, and received the fewest incorrect responses?
For the glib answer: probably the public intellectual who received the fewest responses, period.
I'm familiar with the problem and my intuition is still wrong. I wonder if you couldn't design a gambling machine that has a variant of the Monty Hall problem built-in favoring the house (naturally).
From what I understand, that would just be overcomplicating the matter, because most modern video gambling machines just use a set number of wins per time interval.
I'm familiar with the problem and my intuition is still wrong. I wonder if you couldn't design a gambling machine that has a variant of the Monty Hall problem built-in favoring the house (naturally).
From what I understand, that would just be overcomplicating the matter, because most modern video gambling machines just use a set number of wins per time interval.
The machines are random, with no enforcement on wins per time interval.
Source: I work in the industry.
I may be missing something (not a mathematician, probabilist) but doesn’t the fact that the host would never reveal the car change the calculation? In the table shown in the article game 3 & 6 are nonsensical so with the remaining 4 games the odds are even between switch & stay.
No, it's correct. The easiest explanation, IMHO, is: 1. If you already selected the correct door, you should not switch, obviously. Equally obviously, the odds of being in this state are 1/3, because your initial choice was random. 2. If you did not select the right door, then the host clearly revealed the only one of the two remaining doors without a prize. In this state, you clearly should switch to the only door r…
Your initial chances of choosing correctly are 1 in 3. So the car is behind the door you chose 1/3 of the time. After the host reveals which of the 3 doors definitely does not have the car it's still the case that your initial choice will have the car 1/3 of the time [0]. That means the other door must contain the car 2/3 of the time. So you should switch.
[0] The haters are correct that the host hasn't changed the odds that your initial choice is correct. They just aren't tracking the implications of that fact.
There are a number of things I like about the monty hall problem. There's the history, the unintuitiveness, the subtle easy-to-screw-up nature of probability problems, the calculation, the sociology, and the overconfidence of wrong experts. Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness. In fact, it would be much harder to be so widely…
I'm familiar with the problem and my intuition is still wrong. I wonder if you couldn't design a gambling machine that has a variant of the Monty Hall problem built-in favoring the house (naturally).
Imagine you're lost somewhere in the entire universe, trying to find your way home. Friendly (but tricksy) aliens offer you a deal. First, you pick some coordinates.
(Possibility 1) If the coordinates you pick aren't on earth, they'll take you to earth.
(Possibility 2) If the coordinates you pick happen to be on earth, they'll take you god knows where.
You also have the option to be taken to the coordinates you picked.
As a lost spaceman, perhaps going by the name Arthur Dent, what's your most likely path home? Odds are, if you pick a random point in the universe, it's not on earth. The odds are literally astronomical. So you're almost certainly going to find yourself in possibility 1.
Or just imagine monty hall with infinite doors. I'm thinking of a number between 1 and infinity (secretly, it's 19083412039102388171230123). You pick a number, and then I'll narrow down your choice to two options. Do you think you just happened to pick my number, or do you switch?