three door monty

Monty Hall has died. He was 96 years old, so he had a good deal. Here's the pilot from his show.

I wasn't a big fan of Let's Make a Deal, so I don't really know what to say about him. But I’ve always wanted to write an essay about the Let’s Make A Deal Problem (LMaDP),  and I’ve never had an opportunity to do so. Well, it's now or never.

I’m not sure how well known LMaDP is outside of actuarial and mathy types of crowds. It was made famous in 1990 in a letter to Marilyn Vos Savant, who answered questions for her “Ask Marilyn” column in Parade Magazine.

The gist of the problem is as follows:

You are on a TV gameshow, and given a choice of three doors. One door hides a prize. The other two doors each hide garbage. You pick a door, and win what’s behind it. But before the host opens the door to reveal what you’ve won, he picks one of the other two doors and reveals that it hides garbage. He then gives you a choice between staying with the door you originally chose and switching to the other as-yet-unrevealed door. Should you switch? Before you answer, let me add some information which is essential, but often elided in the retelling: Going in, the host knows which door hides the prize, and is required by the rules of the game to open a door that you didn’t pick, and which hides garbage behind it. This, presumably, is to build excitement. Now, with that extra bit of information, should you switch or stick.

When Vos Savant was presented with the problem, she (correctly answered that you should switch. Specifically, you have a 2/3 chance of winning if you switch and a 1/3 chance of winning if you stick. The response was angry and vocal. She was roundly condemned as a know-nothing, setting back the cause of education, blah blah blah. I remember some of the senior actuaries at work were similarly incensed. Her response does initially seem counterintuitive; since you have two doors to choose from, and they seem the same. But she stuck to her guns. And she was right to do so.

What I'd like to do now is argue in several different ways. Then, finally, I want to end by answering the question of what makes the doors different.

Arguments

Argument 1: 100 doors

One of the most commonly used arguments presents a situation that is similar, but different in one crucial way. Specifically, it supposes that there are 100 doors, with one hiding a prize. After you pick a door, the host opens 98 others, revealing them all to be losers. he then gives you the chance to switch. Are you better off switching? Presumably the fact that there are so many more doors makes it easier to visualize that it's unlikely that you won with your initial pick.

Argument 2: Under what circumstances do you win by switching/sticking

Consider what circumstances lead you to win by switching and what circumstances lead you to win by sticking. If you initially choose the winning door (something which happens one time in three), you will win by sticking. If you initially chose a losing door (something which happens two times in three), you will win by switching. QED.

Argument 3: Enter the Bayesians

This is actually closely related to argument 2. Assume it doesn't matter whether you stick or switch. That means that you have a 50% chance of winning with your door. But you know that, once you choose your door, the host will open another and give you the choice. In other words, no matter what he does (i.e., whichever other door he reveals), your door will then have a 50% chance of being the winner. That means that, before he does anything your door has a 50% chance of being the winner, since the chance of your door being a winner (before he does anything) is equal to the weighted average of it being the winner after he does something (weighted by the probabilities of his taking each possible action).

So let's get this straight. If the game were different -- you pick a door and then, without anything being revealed, you can keep it or switch to one of the others -- the chances of your door being the winner are one in three. But adding the extra rules of the game as stated above, your initial door goes up from 1/3 to 1/2! That's a pretty good Schroedinger's door, there.

Argument 4: Simulation by spreadsheet
I created a little spreadsheet to simulate the situation. It's here. You can play along at home. Sheet1 has 10,000 simulations. In each, there are three doors -- A, B and C. The following happens:

• In column C, the winning door is determined randomly
• In column E, the door you (as the contestant) is determined randomly
• In column H, the door the host opens is determined randomly, subject to the rule that it not be either the door chosen in column C or the door chosen in column E
• Columns I and K display the doors you have by sticking and by switching
• Columns L and M indicate whether you win by sticking or by switching (with a "1" in the appropriate column).
• Column N is simply a check column. It should always be 1. Cell N1 serves as a check that every entry in column N is a 1. N1 should be zero, indicating that everything else is the same.
• Cells L1 and M1 add up the number of simulations in which you win by sticking and in which you win by switching.

You can rerun the 10,000 simulations by selecting an empty cell (e.g., R2) and hitting the delete key. The relevant cells will be recalculated, and you can see that cells L1 and M1 will be somewhat close to 3,333 and 6,667 (respectively). I have rerun this simulation several times, and each time I get close to that split. Note that the odds of getting that exact split are low. If you flip a fair coin 1000 times, you will likely get close to 500 heads and 500 tails. But you are unlikely to get exactly that.

What Makes the doors different?

As I wrote above, it initially seems counterintuitive to say that one door is more likely to win than the other. There are two possibilities, and on the surface it can seem like they are the same, and therefore each has a 50% chance of winning. If the chances are not the same, there must be some asymmetry between them. So what is that asymmetry?

The asymmetry is in the way the two doors came to be candidates (i.e., why each is not the one that was revealed as not the winner).

• The door you did not choose was not revealed to be a loser for one of two possible reasons:
• Possibly, you chose the winner to start, in which case the host could have opened either remaining door, and he just chose the one he did; or
• Possibly, you chose a loser, in which case one of the remaining doors is a winner, and the host had no choice but to reveal the one he revealed.
• The door you initially chose was not revealed because the host is not allowed to reveal it.

Since the two remaining doors are not the same. the argument that they are equally likely to win because they are the same is false.

the records that parted the clouds

I was in high school when I first started getting seriously interested in music. In the time since then I have gotten many records and CDs in a variety of styles. There are some that I love, and some that I consider unlistenable.

But there are three records that will always have a place in my heart for (for lack of a better way of putting it) opening my eyes. I vividly remember my first time listening to each of these records. With each, it was like the clouds parted and I was in a new state of being. Yeah, that sounds melodramatic, but that's how it felt. I loved each of these records, and still do. I doubt that will ever change. But they are not necesarily my favorites.

There are other records that I like as much or more, but which weren't eye-opening the same way. There are some records that didn't make the same strong first impression on me, but that grew on me over time. Brinsley Schwarz' third album, Silver Pistol, comes to mind. There are others that I loved at first listen, but that didn't open my ears to something new. Sundown by Rank and File is a good example of that. It's probably my favorite cowpunk album, but by the time I heard it, I was already somewhat familiar with the genre so it didn't open a new frontier the same way Tales of the New West (listed below) by the Beat Farmers did.

One thing that these discs have in common is that they don't have a single weak track; they are strong from start to finish.

DE 7th (Dave Edmunds)

I bought Dave Edmunds' seventh solo album -- when it was a new release -- in the mistaken belief that he had been a member of the band, Ducks Deluxe. The straight-ahead no-nonsense rock and roll took my breath away. To this day Edmunds remains one of my favorites. I am not sure if this is his best album, as Repeat When Necessary and Tracks on Wax 4 each can make a string case. But this was my intro to Edmunds.

Tales of the New West (The Beat Farmers)

I got this record to review, as the music editor of a campus newspaper. It looked a little odd -- kind of country-ish based on the cover But it was put out by Rhino, which was a company I liked, so I took it for myself (instead of passing it on to one of my writers to review). And that was my introduction to cowpunk, which is still one of my favorite subgenres. I followed the Beat Farmers, buying every record, until the untimely death of Country Dick (onstage, during a concert) in 1995. They put out more good records, but none that came close to equaling their debut.

Heroes, Angels & Friends (Janey Street)

This was another review copy I got in college. My contact at Arista records included something in her cover letter about how Janey is from Queens (which, I guess, mattered to me because it was Queens College). I rolled my eyes at that, but when I put the record on the turntable, it convinced me. From the opening riff of "Me and My Friends," this was a tour de force of lust and machismo. In some ways she was like a female Bruce Springsteen, belting out songs of working class heroes trying to get by, or reaching for stardom. It's more melodic than Springsteen, though, with more piano and strings. And you could sing along to it. This is still one of my favorites, and I still listen to it and sing along (when no one is around to hear me).

watching twilight zone with sharon

Great news! Sharon has discovered The Twilight Zone. I'm not quite sure what the catalyst was, but she was asking about it a week or so ago. I explained the basic idea behind the show, and suggested she watch a couple of episodes on Netflix.

Ethan, of course, thinks she should watch Tales of Tomorrow. He says it was a better show with better-written stories and better stars. He's probably right -- my experience with this kind of thing is that he has good judgement. Except for Carnival of Souls. That's a great movie that seems like a long episode of TZ, yet he doesn't care for it. Anyway, it's not as easy to see ToT. TZ  is on  Netflix -- at least seasons 1,2,3 and  are. What's with that?

So last night, when I was just sitting down to write a blogpost -- yes, I have a bajillion ideas for posts that I need to write -- she asked me to watch TZ with her. Guess what won.

She asked me to suggest the best episodes to watch. Nothing wrong with that, except that I feel the pressure. What if I pick episodes that she doesn't like? Then she'll decide she doesn't like the show, and it'll be all my fault. So, to a degree, I punted and asked Blair to suggest episodes.

One thing I found interesting is that Sharon asked me if the "twilight zone" is a real thing. I explained that it isn't, but Rod Serling chose the name because it 's ill-defined but sounds serious and spooky. The main reason I find this interesting is that I remember having the same conversation with my mother decades ago when I first watched the show. With any luck we'll be watching some more on Friday.

It's been a long time since I'd watched the show. I remember most episodes well enough, but even so there are generally a lot of details that I'd forgotten. These are the ones we watched (not in order):

The Monsters Are Due on Maple Street

A neighborhood runs amok, and friends are at each others' throats as weird things are going on and they're convinced that it has to be space aliens and that one among them is a space alien.

Blair suggested this, because it reminds her of today's political scene, with the aliens in the role of the Russians, who are busy trying to create havoc and distrust in each other. I waspleasantly surprised to see Claude Akins in the lead. I remember him as Sherrif Lobo from BJ and the Bear (and its spinoff, The Misadventures of Sheriff Lobo). 

I have always felt that everyone is too quick to accept the teenager's suggestion that his comic books are a blueprint for what's ocurring, but I suppose that is necessary in order to fit the story in a half-hour show. And the explanatory coda is kind of goofy, but not bad.

The Eye of the Beholder

A woman is in a hospital, her face all bandaged up, because she's ugly. This is the eleventh attempt to make her less ugly, and she is anxiously waiting for the bandages to come off. Will she get to join society as a pretty woman? Or will she be banished to a community of ugly people?

This was my idea. It's not one of my favorite episodes, but my impression is that it's one of the better-known episodes, and gets referenced a lot in pop culture, so it's good for it to be part of her TZ education. As we were watching, I was noting how all the hospital personnel are shown in shadow so you never get to see their faces. That's necessary, of course, to make the whole episode work. But I was wondering if Sharon would pick up on it. She says she didn't think much about it, though in one scene she wondered, if it wouldnt be easier to just show the faces.

At the end, when you see close-ups of the staff's faces, she noted that they looked so fake. I pointed out that budgeting was probably very tight. Also, this was made for black and white TV, which had lower resolution than what she's watching now -- a remastered version on a high-definition TV. Given the technology of the time, the effect was probably adequate. That's something I wouldn't have thought of if not for the cinema history class I take with Keith Crocker.

And, as I was writing this post, Sharon came into the room with a rubber band around her head holding her nose up. 'I look like one of the pig people from "Eye of the Beholder.'"

The Silence

A loudmouth will not shut his yap, much to the annoyance of a fellow member of his aristocratic social club. So they bet -- $500,000 for a year of silence.

I suggested this episode. I believe it's one of the lesser known ones, but I have always found it haunting. It's also interesting because there's nothing supernatural or otherworldly about it. The twist ending is purely natural. 

One detail I'd forgotten (assuming I'd ever noticed it) is that Jonathan Harris (Doctor Smith in Lost in Space) played the lawyer. The final scene is still as powerful, all these years later. And it elicited a "whoa" from Sharon.

The episode also gave me a chance to talk to her about inflation -- the $500,000 bet was worth a lot more then than it would be now.

It's a Good Life

Life is good in Peaksville. And you'd better believe it, or little Anthony will kill you with his mind.

This one was Blair's idea, because it seems almost as if it was written as an allegory for life in North Korea. But even aside from that this is one of the best, one of the creepiest, episodes of the show. Also, like a couple other episodes on this list, it's one of the iconic installments, and gets frequently referenced in pop culture. Billy Mumy, in his second of three appearances on the show, is great. I sat there with Sharon, pointing out to her how Dan was sitting in the back of the room, getting drunk and angry.

Living Doll
Annabelle has bought her daughter a doll named Talky Tina. But her husband doesn't approve of the purchase. Tina, in turn, doesn't approve of the husband.

This is another one of the iconic episodes that should be a part of anyone's basic Twilight Zone education. What's amazing about this episode is that it's so good. Seriously, a man is having a feud with his stepdaughter's doll. WTF? But it works; the suspense is palpable. And Sharon really liked this one.

I was curious about who voiced Tina. Since she sounded a lot like the girl, I was wondering if it was the same actress. That would have lent an extra creep factor to the show -- the notion that maybe Tina is really just some kind of manifestation of the daughter's latent ESP, and acting out her anger. Alas, she was voiced by June Foray. That's kind of interesting to me; three months ago, I wouldn't have recognized the name. But Foray died in July, and we talked about her in the cinema history class -- she was one of the great voice actors in cartoondom, and that's an area that Joe (from class) is really interested in. The only question left is whether Foray was purposely trying to sound like the daughter.

deranged (cinema history class)

Session: Cinematic Serial Killers, week 3
Movie: Deranged (197)
Directed by Jeff Gillen and Alan Ormsby
As always, there may be spoilers here. And the trailer may be NSFW and/or NSFL

Plot:
Ezra, devoted to his mother, can't cope with her death. His mind snaps and he turns rather ghoulish. Hilarity ensues.

Background and Reaction:
Long story short? Roberts Blossom should have gotten an Oscar for this portrayal of Ezra Cobb, a fictionalized version of real-life serial killer Ed Gein. Of course, the Academy doesn't give Oscars for low budget horror movies. Pity.

Knowing that this film, like The Texas Chainsaw Massacre, was based on Gein, I was somewhat apprehensively expecting something like that well-known classic. I was pleasantly surprised to find that it was very different. It appears to me that the best way to put it is that TCM was inspired by Gein while this is more of a retelling of his story, modified as appropriate.

This is one of those movies that really just gets under your skin -- Cannibal Holocaust is another example. It's creepy and disturbing, but also compelling. It's the kind of thing that anyone interested in the horror film genre should see. Blossom, as Cobb, is brilliant. His facial ticks and mannerisms were a work of art. The story-telling is paced really nicely, and the use of subtle irony for humor is good as a kind of pressure valve to relieve just enough tension.

What made this so great as a "ten" is that it was such a surprise. When Joe quipped that it was "an unexpected ten" I noted that "The unexpected tens are the tenniest tens of all."

Ratings:
Joe: 10
Dave: 9.8-9.9
Sean: 3 out of 4
Scott: 9
Me: 10
Ethan: 9.5

Bechdel:
Deranged fails the Bechdel test.

the honeymoon killers (cinema history class)

Session: Cinematic Serial Killers, week 2
Movie: The Honeymoon Killers (1970)
Directed by Leonard Kastle
As always, there may be spoilers here. And the trailer may be NSFW and/or NSFL

Plot:
A con man marries women to cheat them out of their money. But his true love is jealous. Hilarity ensues.

Background and Reaction:
I went into this with somewhat low expectations, though I'm not exactly sure why. But it was really quite good. Since it was low budget, and shot in documentary style, it reminded me of Pink Flamingos, though it wasn't obscenity-driven the way that was. In addition to similar production values as PF, though this had better values, Shirley Stoler seemed in many ways like a female Divine. Of course, when she's in the lake screaming "you promised!" she reminded me more of Edith Massey as the Edie (the egg lady).

I kept finding myself trying to figure out what was going to happen -- is this woman playing them? will they get caught now? And that's often a good sign, since it means I've engaged with the movie. The acting was generally subpar, but that didn't really deter my appreciation.

This is really a hidden gem.

Ratings:
Christina: 9
Dave: 9.2-9.3
Scott: 8
Ethan: 7
Sean: 2 (out of 4)
Me: 9.25

Bechdel:
The Honeymoon Killers passes the Bechdel test.

Pittsburgh Reference:
At some point one of the characters asked "where will we go?" I suggested Pittsburgh.

jamaica estates gardening club meeting 2: i am now the club secretary

Club business

A day after the annual LIDS barbecue, we had the second meeting of the embryonic Jamaica Estates Gardening Club.

The first meeting (which I wrote about here) was a month ago, at the home of Mohsin Patwary (who originally suggested having the club. The second meeting was at our house, simply because no one else volunteered theirs.

We proceeded through this meeting still a bit unsure of the direction we want to take the club. Ed Morrill was there, since he's on the Jamaica Estates Association board. He's in charge of Parks and Landscaping, so when the board got Mohsin's suggestion that a gardening club be formed, it went to Ed and the club is now under him (in some form I don't quite understand). But Ed made it clear that he's not there to run the club. He can provide some support and guidance, but we have to set our own agenda.

So we faced the really important business of setting a leadership structure. By acclimation we chose Mohsin as our Chairman and me as our Secretary. Three other members agreed to make up an executive committee. At this point, I don't fully know what my job is, but I did email minutes to the group (including those who were there and those who have expressed interest in the club). I'm also keeping the list of interested parties, and will be sending out meeting announcements. Mohsin and I need to get together and agree on a calendar of future meetings.

Marilyn shows off her garden

I forget how we got onto the topic, but Ed explained what exactly constitute "city trees" that the homeowner can't cut down. For those not familiar, in New York City some trees in yards are designated as "city trees" (that is, trees owned by the city). If you cut down a city tree you may be subject to huge fines as well as the cost of replacement. I'd always been under the impression that trees in the grass between the sidewalk and the curb are city trees, and those behind the sidewalk aren't. Of course, I am aware that some blocks don't have sidewalks, but I never worried about that wrinkle since it doesn't affect me. Ed explained the rule: trees that are within thirty feet of the center of the street are city trees. So, in practice, the city's domain extends a few feet past the sidewalk. I'll have to be careful.

Afterwards, Marilyn and Michael invited us all to tour their garden, which was quite the treat. I had been nervous about volunteering our place for the meeting, since our garden isn't really up to par. So their invitation saved the day.

lids barbecue 2017

I think my favorite events in the LIDS calendar is the annual barbecue. It's the only time we get together without any real agenda other than relaxing and schmoozing. OK, and eating. Mustn't forget eating. For the second year in a row, the barbecue was hosted by club President, Chris Petersen, at her place by the waters of Long Island Sound. As always, it was a really good relaxing day.

Gene and Paul auction daylilies

One twist this year was that we had a mini-auction of daylilies donated by Rich Howard. Howard, who runs CT Daylily, had spoken at LIDS' annual luncheon this summer. It was there that I bid (successfully) for Bedhead, which is one of Howard's 2017 introductions. At this auction, I was planning not to bid. But, of course, I couldn't help myself and ended up with Snaggle Tooth and Ducks on Stilts. The money is going to help fund the regional meeting that LIDS will be hosting in 2019. As I wrote here, I have expressed interest in helping to put the meeting together. So, if buying daylilies at auction gets us closer, well, all the better.

The food was wonderful. I'm a sucker for hamburgers and hot dogs off the grill. And the desserts in what seemed like a never-ending succession were great too.

As always, I managed to get a few gardening tips. Bob Stanton and Frank Chaloupecky both advised me on my incipient hybridizing program. For the record, I have some seeds (I hope they're viable) in wet paper towel in the refrigerator in the basement, and Bob and Frank helped advise as to when I should try planting them. Chris, for her part, explained (and demonstrated) the concept of pinching back coleus to make it grow more full. I'll need to try that.

Everyone seemed to be having a good time, and hated to leave.

spreadsheet blues ii: graphing a series that may or may not end

UPDATE BELOW

My latest frustration with Excel? Graphing a data series that may or may not come to an end. As a baseline, consider Figure 1, which shows a simple table and an accompanying chart.

Figure 1: A table of data and accompanying chart

There's not a whole lot to say about this. There are three data series, and three accompanying lines on the chart.

Now, suppose one of the data series ends in 1987. Maybe these are some government statistics and one of them was no longer-calculated as of 1988. Our table and chart might look like this:

Figure 2: One series ends abruptly.

It makes perfect sense. The series ends in 1987, and so does the line that tracks it. Easy peasy, George loves Weezie.

But suppose I build a table without knowing when a series will end. So instead of leaving blanks in the third series starting with 1988, I have a formula that evaluates to a blank. That's what we have in Figure 3.

Figure 3: One series ends, but with a formula to have it end.

The cells in the third data series look blank, but there's a formula there: =""

They formula sets them to be blank, so they appear blank. But because the cell is not truly blank (i.e., it has a formula), Excel charts it as if it's zero.

I would love it if Excel would, for graphing purposes, treat non-numbers as blanks rather than as zeroes.

UPDATE: My actuarial student gave me a solution. I wrote about it here.

the boston strangler (cinema history class)

Session: Cinematic Serial Killers, week 1
Movie: The Boston Strangler (1968)
Directed by Richard Fleischer
As always, there may be spoilers here. And the trailer may be NSFW and/or NSFL

Plot:
The women of Boston are being murdered and the authorities (as is their wont) are trying to put a stop to it. Hilarity ensues.

Background and Reaction:
Class is on Thursdays. I don't generally write up my thoughts until the weekend because I like to mull it over a bit. And in the couple of days between class and my post, I spend a good deal of energy thinking about what I want to say. But this week, no. Here, it's Tuesday night and I've hardly though about the movie. For those keeping score at home, that's a bad thing.

When it comes right down to it, this movie didn't really make a big impression on me. It was decent, don't get me wrong. Tony Curtis' performance was really inspired. But...well...I dunno. It just didn't stick with me.

Part of it may be that it was too ambitious. In some ways it seemed like multiple movies, one after the other. But it just didn't hold my interest,

The post-viewing discussion was more interesting than the movie itself, as we debated the question of how true-to-fact a movie needs to be if it's billed as being based on true events. Not that we came to an agreement. From my perspective, I'm happy to give wide lattitude to fictionalize events. As long as they're not calling it a documentary or otherwise claiming accuracy, they can say that a movie was based on American history and show Abraham Lincoln fighting with Captain Kirk. It makes me no nevermind.

Ratings:
Sean: 2 out of 4
Me: 5.5
Dave: 9.2-9.3
Scott: 6
Joe: 8
Ethan: 5

Bechdel:
The Boston Strangler passess the Bechdel test, which just shows what a low standard the test is.

Star Trek reference:
William Marshall, who made a guest appearance as Dr. Richard Daystrom, had a small role in this movie. So I (or was it Joe?) made some snide remark when he appeared.

Pittsburgh Reference:
Talking about catatonic patients in a psychiatric hospital, a doctor said "Nobody knows where the withdraw to. I suggested "Pittsburgh."

stack-up cream

Sharon's cat, Cream, has become a sort-of unofficial mascot for our chapter of Stack-Up.

It happened because, through the summer, the Friends of Cunningham Park (a local civic group that focuses on the local park had a series of evening events in the park -- movies, plays, concerts and the like. We go to a lot of them and set up an informational table. We got permission to do so from the leadership of FoCP, One local politician told us we don't technically need permission. First amendment and all. Fact is, we don't need permission. We know that. But if we're setting up our table right by someone else's event, it seems only right to ask permission -- especially since we want to have a good working relationship with FoCP.

Anway, We've been bringing Cream. He clearly like to get time outdoors -- we've been taking him out onto the lawn ever since we first realized that he's blind, and he likes the fresh air. Because he's blind, he doesn;t try to run away, so sticks with us. He'll pad around slowly, but as long as we keep with him there's no problem.

And, with his Stack-Up shirt, he's the belle of the ball. Kids come up to pet him, which lets us talk to the parents . And he seems to love being pet.

The most recent such event is described on Stack-Up's website, here.

out-smart-alecked

Ethan was sharing random facts about Presidents, and mentioned that James Buchanan was the only President who never married. He then noted that Grover Cleveland was the only other one who was a bachelor when he entered the White House*

Trying to be clever, I noted that that means we had three presidents who were bachelors when they became president. I was, of course, hanging my hat on the fact that Grover Cleveland was two presidents (numbers number 22 and 24).

Ethan got a puzzled look. Then he realized what I was on about -- he's seen me make similar points -- and got an annoyed look on his face. I was feeling pretty smug.

Then Ethan pointed out that Cleveland was married by the time of his second election.

He beat me at my own game...

*There were others who were widowers, but that's another matter.

a turn too far

What is a driver to do when faced with contradictory direction? Can you get a ticket if you were following the clear instructions on a sign, but disobeying the (less visually obvious) instruction painted on the pavement?

This photo was taken facing South on Homelawn Street / Utopia Parkway, under the Grand Central Parkway overpass. There are two southbound lanes.

Notice that the physical metal sign indicates that you can make a left turn from the right lane. But the directions painted on the street indicate that the right lane is only for going straight.

So, with contradictory directions, which signs govern?

Certainly, the prudent course for a driver who wants to avoid tickets is to obey the street-painted instructions (i.e., to treat the right lane as a straight-only one), since that way you're obeying both traffic control devices (as I believe they are called).

But what if someone sees the sign and not the street painting, and makes the left turn from the right lane? Can he get a ticket? Can he successfully fight the ticket on the grounds that there's a sign that explicitly says he can do what he did?

But, more fundamental than a ticket is the question of safety. I can see a situation where someone in a  hurry uses the left lane to go straight to save time. Noting the street-painted sign (and missing the metal one), he thinks that no one will turn left from the right lane. It would be an illegal straight, but let's not pretend people don't do that kind of thing. At the same time, someone makes the left turn from the right lane. Accidents will happen. The combination of signs makes it more likely.

I'm not sure whether I'd prefer that they allow or disallow the left turn from right lane. But I do know that I'd like them to make a decision and have their signage agree.

eine kleine mind game

Here's a little mind game.

Suppose you are presented with two doors. Behind each door is a cash prize. You are told that one of the prizes is exactly twice as much as the other. You can choose either door and get what's behind it. You choose a door. Now, before finding out what's behind it, you are given the option to switch doors and take the other prize instead. Should you switch? Common sense dictates that it doesn't matter; you've been given no additional information.

But look at it mathematically. Let N represent the prize (in dollars) behind your door. The prize behind the other door is either ½N or 2N (with equal probability). That means that the expected value of the amount behind the other door is 1.25×N (calculated as ½×(½N) + ½×(2N)). So, by switching you increase your expected prize from N to 1.25×N.

But that can't be right. And to emphasize, you can do the switch and then be faced with the same conundrum. Your new prize is X, but by switching back you have an expected prize of 1.25×X. And you can keep going back and forth, forever increasing your expected prize.

So where's the flaw? I note, by the way, that showing that there is a flaw (as done in the last paragraph) is not the same as finding the flaw. What assertion is it that's wrong?

While you're thinking, I'll separate the question from the answer with this charming video.

The mistake is in the statement, "That means that the expected value of the amount behind the other door is 1.25×N (calculated as ½×(½N) + ½×(2N))." That statement implicitly assumes that, regardless of whatever value is behind the door you chose, the other door is equally likely to have twice that amount and and to have half that amount. But that assumption is faulty; there is no probability function (or probability distribution function if you want to work in the continuous world) that will give you that property.*

In the remaining paragraphs, I will use the convention that you initially choose door A. I will use VA to indicate the value behind door A. B represents the other door and VB represents the value behind door B

To calculate the expected value if you don't switch, you have to multiply all the possible values of VA by their respective likelihoods and then add up the products. Of course, to calculate your expected winnings if you switch, you do the same thing for B and get the same result. But if you want to avoid explicitly assuming that they're the same (which kind of renders the proof that they're the same moot), you have to look at all the values of VA, then get the expected values of VB conditional on VA, and multiply them by the likelihoods of the respective possible VAs.

To take a simple example, assume that there are two possible pairs of values for the two doors: (50, 100) and (100, 200). The possible values of VA are 50, 100 and 200. These have likelihoods ¼, ½ and ¼. So the expected value of VA is 112.5, calculated as follows:

Calculating the expected value of VB involves more calculations, but none of them is particularly difficult. You need each value of VA and its likelihood. Then you need to calculate the expected value of VB given the value of VA. To do that, you have to look at the values of VB if VA is the greater of the two and if VA is the lesser of the two, and the likelihoods of all those. Calculating the expected value of VB yields 112.5, which is the same as the expected value of VA.

QED.

*Put more exactly, for all values X, the probability that the two prizes are ½X and X is equal to the probability that the two prizes are X and 2X. That's mathematically impossible unless you're taking the trivial case where X is equal to zero with probability 1.

why a work talent show is so intimidating

I've written a couple posts now about the talent show at work. And I last year I wrote about that one. Both times I had fun. I enjoyed singing my songs even though I made some mistakes in the lyrics and chord changes. But none of the performances* were of professional quality. And why should they be? We're not professional entertainers**. We're actuaries and auditors and lawyers and accountants and I don't know what else.

And yet I still get nervous. Because when I think of talent shows, I think of the stuff from TV sitcoms. It seems that almost every sitcom from the 1970s found some excuse to have a talent show episode. Where all the stars somehow found their way to performing in the same show. I'll bet it was fun for the stars, since they got to show off talents that normally didn't make it into their roles. And it shouldn't be forgotten that they had the advantages of budget and full wardrobe and makeup departments.

So I think forward to the show, anticipating what I will do, and comparing it to what the TV stars did. Following are a few memorable examples of what my brain thinks of as talent show performances. You can see why I get intimidated.

From "One Day at a Time"

From "Laverne and Shirley"

From "The Brady Bunch"

From "Maude"

*There were singing performances, poetry readings and recitals, monologues about language, comedy routines. I'm sure there was other stuff, but I don;t recall what.

**With the exception of Brandon  Bujnowski, who performed last year. He's a guitarist with the neo-punk band, Bedpan Fight. Of course, he wasn't on the original schedule. But that's another matter.

i wasn't the only performing actuary

A little bit ago, I posted this, about my performance of a couple original songs at my company's Diversity and Inclusion talent show. One of my colleagues -- another Fellow in the valuation unit, performed a comedy routine. There were some jokes I'd heard before, some variations that I hadn't, and a few new ones.

And without further ado, here's Phil...

The CEO was in the audience, and Phil is still working for the comapny, so it couldn;t have been too bad.

coming soon to cinema history class: cinematic serial killers

With the summer going on and all, we had a break from Keith's basement-taught cinema history class.

But the class kicks up again next week with "Cinematic Serial Killer" month. That is, movies based on actual serial killers.

For this series, we will be screening the following four films:

The Boston Strangler (1968), starring Tony Curtis and Henry Fonda. I assume it's based on the Boston Strangler.

The Honeymoon Killers (1970) starring Tony LoBianco and Shirley Stoller. It was based on the Lonely Hearts Murders of the 1940s, which had a Long Island connection. I'm totally unfamiliar with that case.

Deranged (1974) starring Robert Blossoms. It was based on the life of Ed Gein. If memory serves, Gein was also the basis for The Texas Chainsaw Massacre. But we already saw that in Keith's class. There was also a band called Ed Gein's Car. But I don't think they were linked to any murders.

The Town the Dreaded Sundown (1976) starring Ben Johnson, Andrew Prine and Dawn Wells. This was based on a series of murders by a hooded killer in Arkansas in the 1940s. The trailer says it occured in Texarkana, Arkansas. I well remember pulling into a gas station in Texarkana Texas and asking what state I was in. "Well, sweetie, right now you're in Texas," came the response. "But if you cross the street you're in Arkansas." I don't know why I just brought that up.