Would you switch doors?

[Gummy_Cluster]

Mathematicians have been arguing over this probability question for hundreds of years. In the movie “21” an MIT professor taught a class in non-linear equations. (great movie) He was also an expert card counter in Vegas. But he needed a team, so he recruited his most smartly students. He had a team, but one guy moved, so he needed a new team member. So he asked this question to his students.

The game show host tells you that behind one door, there’s a car. Behind another door is a washing machine. Behind another door is a goat. You pick door number one. Without revealing what was behind door number one, he gives the students a chance to change doors. Only one guy wanted to change doors. Was he right or wrong?

[SnowedIn]

So, when I was in the Navy, I worked for an Admiral. Well, four of them over my career. They were all BRILLIANT. (Rarely do they make Flag rank without being smart.) The gentleman in question was a Naval Academy graduate. A submarine man. And one of Admiral Hyman Rickover's nuclear Sailors. SMART. This Admiral had dual major in Mathematics and Science from the Naval Academy, a Master's Degree in Mathematics from the Naval Postgraduate School, and several other Math degrees. He was, dear Gummy, Smartly, with the capital 'S'.

Two times he displayed this. Once, we were in the conference room. It was an important meeting. About The Budget. With a capital 'B'. The Comptroller was a WONDERFUL lady. And also Smartly with a capital 'S'. But prone to typos. The brief starts well. Until they got to a slide with sets of numbers. The slide was on screen for about four second when the Admiral said, "I'm sorry, but this is all now suspect. The lines don't add up." And they didn't. He had done the calculations that fast and ran through the inferences on them. We rescheduled. The Comptroller learned something: details matter. The other time was a more important meeting. The boss was briefing members of Congress. One of the representatives was struggling for a number of how a budget projection would play out over ten years. The Admiral slipped her a piece of paper. That group ended up appropriating money to the Navy.

So, yeah, my boss was good at math. Very good. But he wasn't so good at writing. One afternoon, the sun wan and low on the horizon, he called me into his office. Sat me down in the leather chair behind the mahogany desk. Pointed to his computer and said, "That's going to my boss. Fix it." It was an important report. The outcome was important. The Admiral brought me a cup of coffee while I turned the crap he had been given as a report into something his boss might read and act on. My boss' boss was so impressed with the document that he called my boss and they had a meaningful conversation about it and subsequently change was made that made a difference to a lot of Sailors' quality of life.

Gummy, I don't do math. I'll stick with my original door.

[Gummy_Cluster]

Good story. According to the professor, changing doors doubles your odds of winning. I don't get it.

[SnowedIn]

Thanks for MHO.

[Gummy_Cluster]

Sure thing.

[exitseven]

He was wrong. Usually people have good instincts and when they second guess themselves they lose.

[Gummy_Cluster]

This is how the kid explained his choice.
When you gave me a choice of three doors, I had a 1/3 chance. But when you gave me a second choice, I had a 2/3 chance. I realize that might make sense, and I don't understand it, but people way more smartly than me have been arguing about it for many years.

This is something you might find interesting. I had a brilliant idea of how to beat the casino. (there were three Indian casinos nearby)
I would sit back and watch the roulette table. If the wheel landed on red 8 times in a row, I bet on black. It made perfect sense to me. I thought it was a 50/50 thing. It’s not. I went home and researched. Every spin of the wheel or toss of a coin, is a new event. Coins don’t have memories or histories. Every toss or spin of the wheel has nothing to do with the past. There went my brilliant idea of getting rich. The only strategy I read about that could work, was “Oscar's Grind.” But you best bring a bank roll.

[exitseven]

When you roll a dice you have a 1 in 6 chance to roll a one. Every time you roll the dice you get the same 1 i 6 chance to roll a one. The same is true with the 3 doors. After you get the chance to change your mind you still have a 1 in 3 chance of getting the grand prize because you can decide to stay with your original choice.

[Gummy_Cluster]

That makes sense, but some mathematicians disagree.

[es20490446e]

Nope. That would be the same as throwing a coin 5 times, and all the 5 being even.

And saying that next throw has the same chance of getting even than odd.

It doesn't, otherwise there won't be a 50% chance for each.

[exitseven]

Thanks for the MHO😎

[Gummy_Cluster]

Sure thing.

[NamerOfStars]

Mathematically? Yes. Actually? No.

In 1993, my best friend's parents had two children: him, and his sister. What are the odds that he was a boy? In reality? One in two (rounding off a tiny edge). Mathematically, by the same process that the Monty Hall folks use? One in three- two children gives four permutations- two boys, two girls, a girl and a boy, and a boy and a girl. His sister isn't a boy, so it's not the first- that leaves three permutations, with six options- four of which are girls.

But it gets stupider. Three years later, he got another sister. NOW what are the odds that he's a boy? Well, they haven't changed; humans don't switch genders, so the addition of another girl shouldn't affect the odds, since it's already been decided. But this isn't logic, and it isn't reality, either- it's math, and says they drop to one in four.

In other words, the people who trust the evidence of their own eyes less than the system derived from the evidence of their own eyes are the same people who think that we are, in fact, clownfish.

[ShiftingMonke]

As someone who didn't graduate high school and sees this commenter went through the effort to italicize a few words, I can tell you with 100% certainty that this is correct.

[Gummy_Cluster]

@ShiftingMonke
I need to learn italics.

[Gummy_Cluster]

Why would you switch mathematically?

[ShiftingMonke]

It's like normal text, but somehow saucier.

[Gummy_Cluster]

@ShiftingMonke

They have regular, bold and italics, but they need a sarcasm text, so people could understand my Hooters joke. I can't remember if I told you or not, but three guys attacked me. They said I was a monster for forcing a guy to go to Hoooters for an hour. OMG, That's way worse than a tornado or hurricane. You should watch the movie. They had counters on the team, and players. When the count gets favorable, the girl yawned and stretched, that was the signal for a player to move in. A counter can't go from betting a dollar to one hundred dollars, or the casino would be on to them.
So the player sits at the table, and the girl said "this tea is too sweet. Sweet meant the count was 16. lol
But they fucked up and hit the casinos too hard. They should have just got a little money from each casino, and spread it out.

[ShiftingMonke]

I do remember you telling me that, you should know better than to speak ill of vintage medicre chests and flat asses in orange shirts.

That sounds like a silly move. Also, gambling is bad, it says so in the Bible. I think.

[Gummy_Cluster]

@ShiftingMonke

I think the one guy who got the probability question right, made 300 K for medical school. They had a good thing going until they got greedy.

[ShiftingMonke]

I can relate!

Not to getting 300,000 dollars, but to shooting myself in the foot because I wanted a little more. It's just part of the human condition.

[Gummy_Cluster]

@ShiftingMonke
I talked to a guy and he said him and his girlfriend do it. I don't know which of them was the counter, but it worked.

[es20490446e]

He was right, because probability depends on previous throws.

For example if you flip a coin, in the next throw there's a higher chance of getting the opposite side of it. Otherwise that would mean that there wasn't a 50% chance for each side to start with.

In the case of doors if you stay with your choice you have 1/3 the probability of getting it right, because you started with three choices.

But once you know that a door you haven't chosen has a goat on it, the probability is 1/2. Hence if you chance door you get that higher probability of success.

[es20490446e]

The idea is that by showing you that goat they are telling you this: that if you make a new choice it will be between two doors, one with a goat and one with a car.

You may argue that the car is in the same door nowadays, but then I can argue that they could have showed you that door only because they wanted you to succeed or fail.

Hence that's why only pure probability makes sense for making a choice. All you know is that before it was between 1/3, and now 1/2.

[Gummy_Cluster]

They never revealed what was behind door number one.

[es20490446e]

But when you make a choice the second time, your probability is 1/2.

I know it sounds kind of counterintuitive, but it's as simplistic as that.

Same as flipping a coin. If you get 5 times even in a row, the next throw is very unlikely to be even again. Otherwise the coin won't be 50/50.

[es20490446e]

Laws of the universe lady.

Mass doesn't exist, it's just an effect of energy.

Time doesn't exist either, it's just a simplification of thermodynamics.

[Gummy_Cluster]

I read about coin flips, and each toss is a new event. Past history doesn't matter.

[es20490446e]

Lets ask ChatGPT:

[Stevefiveo]

No, stick with your gut and go for it.