Monty Hall - Stick or Switch? It Depends How Often You Can Play

The Monty Hall problem is back in the news, or at least the weekend edition of the Financial Times, again, I think because Monty Hall died recently. Here’s the problem:

You’re on a quiz show with a host, Monty. There are three cabinets A, B and C. In one cabinet is a car, and in the other two a goat. You get to nominate a door, and then Monty will open one of the other doors and ask you if you want to change your choice. What you know is that Monty never opens the door with the car in it. Never. Should you change your choice?

The answer, given by Marylin vos Savant, is that you should, as in two-thirds of the cases, you will win the car. When she gave that answer, the wrath of a zillion statisticians and mathematicians descended on her. Here’s her argument: there are three options (in order A, B, C)

1. Car Goat Goat
2. Goat Car Goat
3. Goat Goat Car 

If you pick A, you lose by switching in option 1 and win in 2 and 3. Otherwise you win by switching in the other two options. Take the odds and switch. At least when you have the opportunity to play the game over and over.

What happens when you can only play once? Choose A and suppose that Monty opens door C to show a goat. Now you know there are only two options:

1. Car Goat Goat
2. Goat Car Goat

In this case, the odds are 50-50 for switching. Why? Because you don’t have third option of Goat-Goat-Car which would force Monty to open door B.

Play the game over and over, and switching will win more often. Play once, and it’s a flip of the coin, so you may as well switch, since the odds are the same. There’s a winning strategy for multiple plays, but not for a single play.

Damn that’s clever.

Statistics is not only hard, it also only applies when you can repeat the experiment.

What about all the other arguments, including one quoted on Wikipedia that says this;

By opening his door, Monty is saying to the contestant 'There are two doors you did not choose, and the probability that the prize is behind one of them is 2/3. I'll help you by using my knowledge of where the prize is to open one of those two doors to show you that it does not hide the prize. You can now take advantage of this additional information. Your choice of door A has a chance of 1 in 3 of being the winner. I have not changed that. But by eliminating door C, I have shown you that the probability that door B hides the prize is 2 in 3.’

Here’s the mistake: "the probability that the prize is behind one of them is ⅔” should read “the probability that the prize is behind one or other of them is ⅔”. No argument that tries to establish that switching always gives a 2:1 advantage can be right, because when you can only go once the odds are 50-50.

On a one-shot play, sticking is as good as switching.

And in the TV show, you only got one shot.

John Martyn's Dusty - When You Have Food Poisoning And A Tune Keeps Running In Your Head

This was the first John Martyn song I heard, on a sampler album from, I think, Island. It had Traffic's Forty Thousand Headmen on it as well. Dusty is the first hint, I think, in his folk-music period, of the sublimity that would come out of nowhere on Bless The Weather. I'm going to write about that in another post. In the meantime, enjoy the first line - "Nico, two-headed Cuban giant / Is looking with all of his eyes" - and the rest of the song.

This Post Cancelled by Food Poisoning

Retiring the Canon 1100D

Yet another ramble through a kit decision. My current camera stock consists of:

an iPhone SE
a Panasonic DMZ T-100
a Canon 1100D
an Olympus OM-10 film camera

and I have a Canon flatbed scanner and a Canon colour printer. This will matter a little further on in the discussion.

As you will have noticed, I take a lot of townscape photographs, and to look good, a townscape needs a minimum of perspective distortion. Take a snap at an angle with an iPhone or even the T-100 and it looks like you can't square up the lens. Which is one reason I went through the selection of perspective correction programs and chose DxO Perspective. I bought the 1100D a few years ago, and have not used it much. It's light but bulky, and while it does cityscapes well, it's a digital camera....

...and I wear glasses. If I take them off so Ican look through the viewer comfortably, the buttons and camera screen are a blur. If I keep them on, and look through the viewer, I'm darned if I can square up the camera properly. So if I want to adjust the f-stop I have to put the glasses on, then take them off to look through the viewer, then take them off... oh to heck with it. And no, I’m not using the screen: the whole point of a DLSR is the SLR viewer.

Plus the 1100D has a smaller chip. Which introduces perspective problems even if the lens is adjusted for that.

I had a final compare-and-contrast on the 1100D, OM-10 and T-100 the other evening, looking through viewfinders, screens, trying to adjust stuff and generally letting my short attention span hands make the decision. Which was...

...I want my full-frame back. The difference between looking through the 1100D viewer and the OM10 is, I swear the OM10 view has twice the area. The 50mm Zuiko lens has ZERO distortion, and my 28mm Zuiko lens has exactly the wide-angle distortion you need when you need it. (28mm is wide-angle, 15mm is fish-eye.) I can adjust the OM-10’s f-stop without taking the camera from my eye, or even as I'm lifting it up. I do need to wear glasses to see the view, but it feels easier to square up the lens. And yes, my thumb still has an effective wind-on-after-the-click reflex.

I could buy a full-frame digital. A reasonable consumer one only costs £1,800 with lens. Yep. Stop right there. Financial justifications needed. I could get every room in the house repainted for less. By people who know what they are doing.

A roll of 36 frames of Kodak ASA 200 colour film is around £3.50 if bought in bulk. Snappy Snaps will charge me £10 to develop and print on 4x6. (I'm not sure those prices have changed in about ten years or even more). That's around 130 reels of film to break even using a digital camera. I don't take 36 photographs a month at the moment - though I might if I loaded film. Film has a whole different psychology. That's 10 years to break even. In the meantime, I get to be old-school analogue cool and use a cameraI I like rather than one I need to re-read the manual when I want to adjust anything.

If I want to digitise stuff, I can scan the 6x4's. Or I could buy a film scanner, if I could find some reliable reviews, and just have the film developed.

Whatever I do, I’m retiring the 1100D. Not my best purchasing decision. I will go forth and buy some 35mm film and take the OM-10 for a walk and see how that works out.

The iPhone SE camera stays, as does the T-100. Each has its uses. Just not for cityscapes.

A Couple of Tunes

This is my favourite U2 song, simply because, well, pretty much everything



and I listened to the Paul Simon album on Tidal recently, and was surprised to find it was as good as I remembered, and sounded just as good the second time. This track has some of the best guitar playing Simon has done, and as for the electric guitar chording...



Oh, and you should use the Brave Browser. It's what browsing is supposed to be.

Richmond Old Deer Park / A316

Taken, so the metadata reminds me, on the 31st of August at 06:29. I like the ghostly white crane. Richmond is one of the most expensive places to live in the whole town, and it's right on the main flightpath. After a while, everyone just stops noticing.

Evaporating Arguments

More than a few times recently, I've started a piece set off by something, fired up by someone's claims and a need to explain why they are wrong, misguided or could look at it another way. I get about three hundrd words in, and the momentum dissipates. The latest was set off by the idea of "bullshit jobs" put about by a pasty-faced, soft-shellled shitlib Professor of Anthropology at the LSE, who turns out to know very little about the real world and even less about the interplay of his own ideals, government and jobs created by the need to prove conformity to government legislation which however imperfectly captures social policies the likes of soft-shell Professor Graebner would like to see implemented.

It's surprisingly hard work to discover and then explain the the false assumptions and ignorance under someone else's lousy ideas. And I'm not being paid to do this. So what happens is that I get to the point where I realise that the ideas I'm arguing against are based on assumptions that are so wrong I would actually need to explain them, and at that point, I give up.

Rollo over at The Rational Male does valuable work. But his feminine-primary society, while a useful heuristic for men starting off on their Red Pill journey, is not useful to those of us who started at the finishing point, and who are capitalists in practice and Marxists in theory. (Best combination by far.) I can't argue with his ideas anymore: he's using them to do something different to the things I want to do. There's no point in criticising a chisel because it's not a Phillips-head screwdriver.

By contrast, my long screed on Modes was as much an excuse to set out ideas that have been rattling around my head for a while. I'm not going to repeat it. And neither for that matter would I ever bother explaining to someone why contemporary music played by graduates of jazz schools has a small audience: if their ears can't tell them why, my words surely won't.

I don't discuss the finer points of the Big Book or the Ten Steps. It's not that there's no point, but that each recovering alcoholic must find an understanding that works for them. I can talk about how I did a particular Step, or how I deal with something in daily life, but the other person has to find something that works for them. What I say may or may not be useful.

The point of discussing an idea is not to convince the other person, nor to convince any bystanders. It's to test out one's own ideas on the subject by comparison and contrast. When the other ideas are just plain dumb, as Graebner's are, or are intended to instil a mindset, as many of Rollo's are, then there's nothing to test against.

As for the EU-bought-and-paid-for mainstream media, and politics divided into those on the right side of history and those without a clue, move along, there's as little to see as an Apple product announcement.

I need to find a new playground.