Stick or Switch by Simon Flower
This story is to remember Dr Mary Morris who planted a tree on 20 February 1911
It’s later than I intended it to be. Gone 10pm. The buses don’t run too frequently at this time, especially not round here. Suburbia is all but catatonic. Silhouettes of perfectly spaced two-storey homes glare down at me. Lights in windows wink out around me as I wait – first downstairs, then up shortly after. Darkness less creeps closer so much as strides.
The section of raised curb at the stop feels like an island in the street, a focal point of sorts. The street curves gently away before it, a convex box with me at its apex. I wish there was a real shelter at this stop, one of the old brick ones where I could tuck myself away.
I huddle into my coat, arms crossed over myself. The air is cold with damp. Rain has been threatening all day. I can’t see the clouds anymore but I can still feel them, hanging thick and heavy in the air.
Mum tried to get me to take a brolly as I left tonight, but I refused. Honestly, I just wanted to be out of there. I wasn’t thinking about much else at the time.
Our fortnightly family dinner was a disaster yet again. That’s normal enough, but the burning in my cheeks when I think about it is new. I didn’t start the fighting, but my sister did not take too kindly to me trying to end it.
“Emma!” she shouted. “This is important. Are you fucking kidding?”
I haven’t seen her mad at me like that in a long time. Apparently, it’s my fault for just wanting us all to get along for once.
I still have a lesson to plan when I get home. Year 12 maths, Statistics 1. We’ve just done conditional probability, so actually, perhaps I could do the Monty Hall Problem. That’s the one fun lesson I have for stats. I’ve taught the lesson a million times, and unlike the textbooks we teach from, Monty Hall never changes. If I do it, I won’t have to plan a thing. Reasonable bed time, here I come. I will, of course, still have to read the explanation of the problem again. Even after years of teaching it, I can never properly remember why it works the way it does.
I pull my phone to google it and save some time, but I’m met with a black screen when I try the home button. Subsequent attempts to revive it are no good. The battery has died.
I tell myself that I’m not bothered by this, alone in the dark with no communication, but I’m not blind to the way all my muscles tighten up a fraction. I find myself checking over my shoulder more frequently. The shadows between streetlights seem that little bit larger.
Maybe I should leave a spare charger at my parents’, so that I’m not caught out the next time I come for dinner. Better yet, I could get one of those portable power pack things. I’d never run out again, of course, until I forget to charge that up too.
Dammit, I should have planned better than this.
My sister would tell me off for thinking that. Especially after tonight’s discussion. She’d tell me to put the blame where it really lies, and she’d be right too. I know this. But it doesn’t stop that part of me that’s always analysing what I could do better.
Ever since I can remember, Suzy has always liked picking fights. She used to torment me when we were little, wind me up until I snapped and came at her. Then our parents would always punish me worse.
I remember one time, she came up to me with my favourite stuffed rabbit and tore it in half. I hit her for that. Just once, but Mum and Dad were furious. They said I had to learn not to react to her like that. There would be plenty of people in life that would try and get under my skin and I couldn’t go around blowing up at all of them.
Fortunately, when we hit our teenage years, Suzy’s focus shifted away from me, and my parents discovered that it was not quite as easy with her. She was the picture of teenage rebellion, angsting over every world issue from sexism to animal cruelty to famine, and each one was our parents’ fault. The dinner table became a battlefield. Rows every night. 2004-2006 was a good time for the local crockery industry. Just not so good for us.
I check the timetable to make a rough guess at what time it is. 10.22pm is the final number beneath the splintered plastic. I always plan not to find myself on the last bus back, but it never quite works out that way. Even with Suzy kicking off and cutting everything short tonight, here I still am.
I see headlights approaching the end of the street, and then it swings around the corner. Even before I can see that it’s the bus, I know that it is because it’s the only vehicle that I’ve ever seen on this street when leaving Mum and Dad’s in the evening. That’s called empirical reasoning, and if one of my stats students said something like that in class, I would pick them apart for it. But I let myself continue to believe the hypothesis, because in the real world, the standards of a mathematical proof are too high a bar to always hold yourself up to.
With the Monty Hall Problem, it’s the proof that everyone finds difficult. The question and the answer are easy to remember. You start with three doors, one of them has a car behind it and the others have goats. You don't know which is which, but the host of the TV show you're on, Monty Hall, does. You are trying to guess which door has the car.
Once you make a selection, the host then opens one of the doors that has a goat. He asks whether you want to stick with your choice or switch to the other door remaining. The mathematical question posed is whether it’s better to switch or to stick.
The bus pulls up and I fish my return ticket from my handbag before handing it to the driver. Expecting my pick of seats, I’m surprised when I turn down the aisle. At just under half full, it’s busier than I’ve come to expect at this time. I do a quick scan for any potential weirdos, then pick an empty row near the middle.
I read somewhere that the tacky, awful designs on bus seats are intentional. There’s a specific reason they look the way they do. Some colour-blind exec didn’t thumb through a catalogue of choices and accidentally pick the one the artist did as a joke. Someone knew exactly what they were doing when they picked those colours.
I try and remember the reason, but it’s not coming. I’ve googled the answer before, but I always forget it. Much as with the Monty Hall Problem, the answer is just so nebulous and counter-intuitive that it’s hard to hold onto in my mind.
After the host has revealed a goat, you have two doors remaining - the one that you chose and the one that the host didn’t open. The car is behind one of them. Should you stick or switch?
The intuitive answer is that it doesn’t matter. You have two blind choices, one of them wins and the other loses. The problem basically becomes heads or tails. Both choices are as good as each other, right?
Wrong. You’re actually twice as likely to win the car if you switch away from your initial choice. Why is this? Why is it better to reconsider?
Over time, the plate-breaking stopped. But the rest of it never really did. Suzy became a full-time activist right out of school, devoting her life to every issue that ever caused an argument at the table, and things have been a little awkward ever since. To their credit, Mum and Dad are accepting of Suzy’s life, but only to a point. They’re always asking when she’ll settle down and do something more stable, like teaching for example.
“The classroom is a great place to influence young minds. Isn’t it, Emma? Why don’t you speak to your school and see if you can get her something?”
Suzy is the black sheep and, unfortunately, that makes me the white. Somehow, I became the good daughter – constantly touted as the shining example. She who always used to get into the most trouble.
I’m now the mediator at the dinner table. They row while I stay calm and poised. All those childhood lessons paying off.
The skies have finally opened. A drizzle for now, rather than the torrent threatened. Rain droplets patter against a reflection of my face in the glass. In the dark of night, the window has become a mirror. Unfortunately, I’m not the only one who has noticed.
Despite my best efforts, I’ve ended up sitting too close to the wrong person. The guy two rows behind is staring at me via my reflection. He thinks he’s being subtle, but I fail to see how. If he can look at me that way, I can obviously do the same to him.
He catches me looking back, and rather than turning away ashamed, he ups it, now openly leering, a breathy smirk twitching on his lips.
I debate saying something. Images of me standing up and shouting at him flash through my mind, but I don’t act on them. I’m not the girl that blows up like that anymore. It wouldn’t help anyway. I would yell and then he’d just pretend like he didn’t do anything. He’d make out like I’m crazy and half of me would probably feel like he’s right. I’d be the stranger yelling on the bus after all. Everyone would look round at me and they’ll be like “Oh, there’s the crazy person. Found her.” Then I would have to justify myself to a bunch of strangers.
It’s just easier to keep quiet.
The reason the Monty Hall Problem became famous is a magazine column called Ask Marilyn. In 1990, the writer of the column, Marilyn Vos Savant, was posed the question in a fan letter. She published that it was better to switch and, despite providing a sound explanation, promptly received thousands of letters telling her she was wrong, including hundreds from actual PhDs. It took years and, eventually, computer simulations to convince some of the most prolific mathematical minds that she was right.
There are many cognitive biases that make switching hard to accept as the right answer, but it seems to me that the biggest one, at least for most of those PhDs, involved the person providing the solution. Because when the problem and answer were initially published in American Statistician by Steve Selvin in 1975, it drew no infamy and no snide letter-writing campaign.
I put my head down and ignore the creep. No scrutiny for me, just one overzealous fan. I focus very intently on the patterns of the fabric I’m sitting on. I study every line, and there’s plenty enough that I don’t have to look up for a long time. I decide that, even if reality says different, I know why the seats are designed the way they are.
My stop is in the centre of town and then it’s a 10-minute walk from there. I’m first up when the bus pulls in, at the front before anyone else has thought to stand. I remind myself of those kids that turn up way before the lesson starts, burning a hole in the door with their infuriating, overeager smiles.
The streets are pretty empty when I step out. It may be the centre of town, but the Clintons and Sue Ryders I find myself amongst surprisingly aren’t where people congregate at this hour. Passengers file out behind me and I hear their footsteps disperse as varying paces and destinations pull us apart.
Except, I realise once I get a couple of streets over, for one person. There’s still one set of footsteps behind me, a mirror accompaniment to my own. Clack, clack, clack on the stone flags.
I don’t look round. There’s no need. Someone just has a similar route. It’s nothing. At some point our paths will diverge, and the sound will fade into nothing.
Except it doesn’t.
The minutes wear on, and my footsteps echo resolutely behind me, just a fraction out of sync. My hand finds itself inside my bag, closed tight around my keys. Metal between fingers. I’ve heard this is a terrible defence. It’s expected these days. Planned for. If you find yourself within key-using range, they’ve probably already won. Still, I don’t know what else to do.
I want to run, but even now I can’t bring myself to react too strongly. Old lessons far too ingrained. If I run, it means abandoning the possibility that this could be in my head. Somehow, being crazy and paranoid seems preferable. At least that would be a problem of my own making.
“I wish you would move, Emma,” Dad talks through a mouthful of beef. “That city centre just gets worse and worse.”
“It’s close to school,” I say.
“I live in the city too,” Suzy says. “Shouldn’t I move?”
“Leave her alone, dear,” Mum nudges Dad’s arm. “She’s fine where she is.”
“What about that girl in the paper that got assaulted the other week?” he says. “That was right by her.”
“I heard she was cutting through that dark little road by the hotel though,” Mum slices a brussels sprout into quarters. “I mean, fancy being down there at that time of night.”
“What does that mean?” Suzy’s fork hits the table prongs first, denting the finish. “You’re saying it was her fault?”
“No,” Mum makes a show of acting patient. “No, of course I’m not, dear. I’m just saying Emma would be smart enough not to be in the wrong place like that. That’s all.”
“The wrong place? Mum, every place is the wrong fucking place! Seriously, you’re gonna blame her when–”
“Honey, don’t swear please.”
“Fuck off, Dad!”
“Susan! Apologise to–”
“If there was a foolproof checklist, don’t you think everyone would–”
“Guys!” I cut everyone off. “I thought we weren’t going to fight today.”
“Emma!” Suzy stares at me. “This is important. Are you fucking kidding? Ignorance only emboldens–”
“Just like last time was important,” Mum rolls her eyes. “Emma’s right. Let’s finish dinner. You can educate us later if you want.”
We finish our meal in silence. I catch Suzy glowering at me several times. She races through the rest of her food, then leaves without saying a word.
I keep walking as calmly as I can manage. Desperate to do something, I pull out my phone to call someone. Suzy. I want to talk to Suzy, just to hear her voice if nothing else. It’s only when the phone is in my hand I remember it’s dead.
I place it to my ear anyway.
“Hey Suzy,” I say to no one, then pause for an imagined response, feeling ridiculous. “Yeah, I made the bus, don’t worry.”
“Yeah, I’m almost home now.” I make my voice carry, becoming that one friend that can’t help but project their conversation to the room. “I’m on Prince Street. Just passing All Saints at the minute.”
I don’t really know what else to say. I’ve never been good at small talk, I usually rely on my conversation partner to help me through it. But that strategy obviously won’t work currently, and I still have a couple of minutes to my door.
“I…I’m sorry about earlier,” I find myself saying. “I guess my first instinct is just to try and keep everyone happy. I don’t like it when we argue. I just wanted everything to be fine.
“But…I know things aren’t fine. And I know ignoring it all won’t change anything. You’re right, we need to talk about this stuff more or it won’t get better. It’s just hard to fight that conditioning, you know?”
I turn onto the street that, in a minute or so, will bring me to the door of my flat. “Anyway, uh…I’ll see you soon, okay? Love you.”
I put down the phone, and for a moment it’s hard to imagine that I hadn’t actually talked to anyone. Behind me, the footsteps fade into the distance, staying straight where I took the corner. Sticking where I switched.
The reason the Monty Hall Problem is now taught at one point or another by every stats teacher worth a damn is because of the way it shows students how little their intuition means in the face of cold, hard numbers. When I teach it, the point is to get the kids to think about problems in depth rather than just going with the answer that comes to mind first. I always call it a fun lesson, but the reality is that it tends to upset a few of the kids each year. I can empathise with that. Watching your first instinct fail you is never a pleasant experience.
When I get in, I put my phone on charge straight away and collapse onto my bed. There aren’t enough hours before I need to get up again. As I lie there, I’m determined to call Suzy and apologise for real as soon as my phone will let me. But I never do. Instead, I fall asleep right where I am, with my clothes still on, and an explanation of the Monty Hall Problem open in front of me, unread.
Simon is an aspiring writer based in Norwich