Month: October 2021

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The Monty Hall Problem

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

The official answer is…switch. You double your odds of being right by switching.

This has led to some vigorous debate.

I read it in Jo Craven McGinty’s final column, instantly decided all of these idiots were wrong, and did some Matlabbery.

The idiots were right. You double your chances of being right by switching.

BUT WHY?

Let’s go chronologically.

Step 1:

The car is somewhere, the goats are somewhere. These positions are fixed. No car-goat switching shenanigans take place.

Step 2:

You pick a door.

You have 1/3 chance, 33.33….% chance of getting it right.

THAT IS IT. THIS GUESS IS DONE. THE CHANCE OF YOUR INITIAL GUESS BEING CORRECT IS FINISHED, COMPLETED, SET, and NOT CHANGING.

Step 3:

The host looks behind the doors and picks one with a goat. This door is opened. You, the contestant, can see the hosts door opened to reveal a goat.

Step 4:

You may change your guess to the other door.

This is where the magic happens.

That initial guess is locked at 1/3 chance, 33% (and hereafter I’m neglecting the .333… repeating). It cannot change. But there’s still an outstanding 2/3 chance of finding the car. The car has to be somewhere. Since you already know, for a fact, that there’s only 1/3 chance of your first guess being correct, and you know there’s 0% chance of it being behind the host’s door (remember, the host opened that door. You can see the goat), the remaining chance has to be behind the other door.

So switching has to improve your odds.

But it just doesn’t feel right, does it? Why not?

Because you think about things after they’re done.

If you picked your first guess after the host opened a door, then the two options would be 50/50, what feels right. But that’s not what happens. The first guess is made and locked BEFORE the host opens the door, so it has to be fixed at 1/3. The host doesn’t move the cars and goats around after opening a door, so the odds don’t reset.

Matlab: MontyHall
(Change ending from .txt to .m or copy and paste)

I suppose you also might want a goat. I’m neglecting that.

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Fat Bear Week Conclusion 2021

As we wait for the final votes to be posted, I have some important points.

First of all, 132 was a fantastic cub, and I can’t believe he lost to Walker. What is this nonsense?

Second, my candidate, Chunk, fought the fat fight, and fought fat with honor. He’s the champion to me.

Third, both Walker and Otis are excellent competitors. I wish them the best. Otis has the better headshot.

Fourth, I wish they’d keep the voting open past 7pm MDT.

Five, in the semi-finals, both bears that won had names. Not counting this year, of the last 7 years, all but one winner had names. 747 won once, while Otis won 3 times, Beadnose twice, and Holly once. Having a name is a significant performance-enhancing advantage.

Next year, all bears should be named.

Also, Chunk should win.

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Arguments

The big difference between logical and emotional arguments is whether or not internal inconsistency implies invalidity.

In logic, an inconsistent argument is fallacious or invalid. In emotion, an inconsistent argument is perfectly normal. There’s no causal relationship between (in)consistency and (in)validity.

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OTOH

I left the best engineering job I’ve ever had, or am liable to get, because I don’t like engineering that much. Maybe I need to go hard in the writing and creative stuff, and keep everything else in perspective.

Realistically, the answer is probably moderation.

But that’s no fun. Engineering pays the bills. Writing fuels the soul. I do quite enjoy sleeping indoors.

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Worth

Someone said to me, ‘My friend is a good person, so she deserves to win the lottery.’

Okay?

I don’t see what the argument is here. That’s not how lotteries work. Winning or not winning the lottery isn’t related in any causal relationship to moral worth, other than perhaps inversely through fraud. Those two points just don’t reflect each other.

The Christian Bible has a good bit on this. ‘Give to Ceasar what is Ceasar’s; give to the Lord what is the Lord’s.’ Generalized, things can be different. One thing might not affect another. Moral goodness, the Lord’s affair, has little to do with money, Ceasar’s.

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Mara

I think I’ll make the Mara ebook free again the first week of November and once again in December.

That will probably be the last of it. I need to focus on work.