Our waiter brought the bill on a silver plate. Tom reached for his wallet, then changed his mind. For all the wine and champagne he sounded clear-headed. We both did. We wanted to show each other we could hold our drink.
‘It’s obvious. With box one I had a one in three chance to start with. When box three is opened my chances narrow to one in two. And the same has to be true for box two. Equal chances that my fat pension is in either box. It makes no difference whether I move or not. Serena, you’re looking unbearably beautiful.’
‘Thank you. You’d be in good company with that choice. But you’d be wrong. If you go for the other box you double your chances of never needing to take a job again.’
‘Nonsense.’
I watched him take out his wallet to settle the bill. It was almost thirty pounds. He slapped down a twenty-pound tip, and the looseness of the gesture revealed how drunk he was. This was more than my weekly wage. He was trapped by precedent.
I said, ‘Your chance of choosing the box with your pension remains one in three. The sum of probabilities has to add up to one. So the chances of it being in one of the other two boxes has to be two in three. Box three is open and empty, so it’s two in three that it’s in box two.’
He was looking at me pityingly, as though I were an evangelical member of some extreme religious sect. ‘Monty has given me more information by opening the box. My chances were one in three. Now they’re one in two.’
‘That would only be true if you had just come in the room after he opened the box and
then
you were asked to choose between the other two boxes. Then you’d be looking at odds of one in two.’
‘Serena. I’m surprised you can’t see what’s there.’
I was beginning to feel a distinctive and unusual kind of pleasure, a sense of being set free. In a portion of mental space, perhaps quite a large portion, I was actually cleverer than Tom. How strange that seemed. What was so very simple for me, for him was apparently beyond comprehension.
‘Look at it this way,’ I said. ‘Moving from box one to box two is only a bad idea if you’d made the right choice at the start and your pension is in box one. And the chances of that are one in three. So, one-third of the time it’s a bad idea to move, which means that two-thirds of the time it’s a good idea.’
He was frowning, struggling. He had glimpsed for a moment the truth, and then he blinked and it was gone.
‘I know I’m right,’ he said. ‘I’m just not explaining it well. This Monty has chosen at random the box to put my pension in. There are only two boxes it can be in, so there has to be an equal chance it’s one or the other.’ He was about to get up and slumped back in his chair. ‘Thinking about it is making me dizzy.’
‘There’s another way of approaching it,’ I said. ‘Suppose we have a million boxes. Same rules. Let’s say you choose box seven hundred thousand. Monty comes along the line opening box after box, all empty. All the time he’s avoiding opening the box that has your prize. He stops when the only closed boxes left are yours and, say, number ninety-five. What are the chances now?’
‘Equal,’ he said in a muffled voice. ‘Fifty–fifty each box.’
I tried not to sound like I was speaking to a child. ‘Tom, it’s a million to one against it being in your box, and almost certain that it’s in the other.’
He had that same look of fleeting insight, then it was gone. ‘Well, no, I don’t think that’s right, I mean I … Actually, I think I’m going to be sick.’
He lurched to his feet and hurried past the waiters without saying goodbye. When I caught up with him outside he was leaning by a car, staring at his shoes. The cold air had revived him and he hadn’t been sick after all. Arm in arm we headed for home.
When I thought he had recovered sufficiently I said, ‘If it helps, we could test this empirically using playing cards. We could get …’
‘Serena, darling, no more. If I think about this again I really will throw up.’
‘You wanted something counter-intuitive.’
‘Yes. Sorry. I won’t ask you again. Let’s stick with prointuitive.’
So we talked of other things and as soon as we got back to the flat we went to bed and slept deeply. But early on Sunday morning Tom, in a state of excitement, shook me awake from confused dreams.
‘I get it! Serena, I understand how it works. Everything you were saying, it’s so simple. It just popped into place, like, you know, that drawing of a what’s-it cube.’
‘Necker.’
‘And I can
do
something with it.’
‘Yes, why not …’
I fell asleep to the rattle of his typewriter keys next door and didn’t wake for another three hours. We barely referred to Monty Hall during the rest of that Sunday. I made a roast lunch while he worked. It may have been the lowering effect of a hangover, but I was more than usually sad at the prospect of returning to St Augustine’s Road and my lonely room, of
turning on my single-bar electric fire, of washing my hair in the sink and ironing a blouse for work.
In sombre afternoon light Tom walked me to the station. I was almost tearful as we embraced on the platform, but I didn’t make a big scene, and I don’t think he noticed.
16
T
hree days later his story arrived in the post. Attached to the first page was a postcard of the West Pier and on the reverse was, ‘Have I got this right?’
I read ‘Probable Adultery’ in the icy kitchen over a mug of tea before I left for work. Terry Mole is a London architect whose childless marriage is being steadily destroyed by the serial affairs of his wife Sally. She has no job and, with no children to attend to and a housekeeper to do the chores, she’s able
to dedicate herself to constant and reckless infidelity
. She also applies herself each day to smoking pot and prefers a large whisky or two before lunch. Meanwhile, Terry puts in a seventy-hour week designing cheap high-rise council flats which will probably be pulled down within fifteen years. Sally has assignations with men she barely knows.
Her lies and excuses were insultingly transparent but he could never disprove them. He didn’t have the time
. But one day a number of on-site meetings are cancelled and the architect decides to spend his free hours following his wife.
He was eaten away by sadness and jealousy and needed to see her with a man in order to feed his desolation and strengthen his resolve to leave her
. She’s told him she’s going to spend the day with her aunt in St Albans. Instead, she heads for Victoria station and Terry follows.
She boards a train for Brighton, and so does he, two carriages back. He tracks her through the town, across the Steine and into the back streets of Kemp Town until she comes to a small hotel in Upper Rock Gardens. From the pavement he sees her in the lobby with a man, fortunately a rather puny fellow, Terry thinks. He sees the couple take a key from the receptionist and begin to climb the narrow stairs. Terry enters the hotel and, unnoticed or ignored by the receptionist, also goes up the stairs. He can hear their footsteps above him. He hangs back as they reach the fourth floor. He hears a door being opened, then closed. He arrives on the landing. Facing him there are only three rooms, 401, 402 and 403. His plan is to wait until the couple are in bed, then he’ll kick their door down, shame his wife and give that little fellow a hard smack to the head.
But he doesn’t know which room they’re in.
He stands quietly on the landing, hoping to hear a sound.
He craved to hear it, a moan, a yelp, a bedspring, anything would do. But there was nothing
. The minutes pass and he has to make a choice. He decides on 401 because it’s the nearest. All the doors look flimsy enough and he knows a good flying kick will do the job. He’s stepping back to make his run when the door of 403 opens and out step an Indian couple with their baby, who has a harelip. They smile shyly as they go past him and then they descend the stairs.
When they’ve gone Terry hesitates. Here the story becomes tense as it rises towards its climax. As an architect and an amateur mathematician he has a good grasp of numbers. He makes a hurried reckoning. There was always a one-in-three chance his wife is in 401. Which means that until just now there was a two in three chance she’s either in 402 or 403. And now that 403 is shown to be empty, there must be a two in three chance she’s in 402.
Only a fool would stay with his first choice, for the steely laws of probability are inflexibly true
. He makes his run, he leaps, the door of 402 smashes open and there are the couple, naked in bed, just getting going. He
gives the man
a beefy slap round the chops, threw his wife a look of cold contempt
, then leaves for London, where he’ll institute divorce proceedings and start a new life.
All that Wednesday I sorted and filed documents relating to one Joe Cahill of the Provisionals, his connection with Colonel Qaddafi and an arms shipment from Libya, tracked by Six and intercepted by the Irish navy off the coast of Waterford at the end of March. Cahill was on board and didn’t know a thing until he felt the barrel of a gun in the back of his neck. As far as I could tell from paper-clipped addenda, our lot had been out of the loop and were irritated. ‘This mistake’, read one furious minute, ‘must not be made again.’ Interesting enough, up to a point. But I knew which location – the good ship
Claudia
or the inside of my lover’s mind – interested me more. More than that, I was worried, fretful. Whenever I had a break, my thoughts returned to the doors on the fourth floor of a Brighton hotel.
It was a good story. Even if it wasn’t one of his best, he was back on form, the right kind of form. But when I read it that morning, I knew at a stroke that it was flawed, built on specious assumptions, unworkable parallels, hopeless mathematics. He hadn’t understood me or the problem at all. His excitement, his Necker-cube moment, had carried him away. Thinking about his boyish exultation and how I had drifted back to sleep and failed to discuss his idea when I woke made me feel ashamed. He had been thrilled by the prospect of carrying over into his fiction the paradox of weighted choice. His ambition was magnificent – to dramatise and give ethical dimension to a line of mathematics. His message on the postcard was clear. He depended on me in his heroic attempt to bridge the chasm between art and logic, and I had let him charge off in the wrong direction. His story couldn’t stand, it made no sense, and it touched me that he thought it could. But how could I tell him that his story was worthless when I was, in part, responsible for it?
For the simple truth, self-evident to me, to him quite opaque, was that the Indian couple emerging from 403 could not possibly tip the odds in favour of 402. They could never replace the part that Monty Hall has in the TV game. Their emergence is random, while Monty’s choices are constrained, determined by the contestant. Monty cannot be replaced by a random selector. If Terry had chosen 403, the couple and their baby couldn’t magically transfer themselves to another room so they could emerge through a different door. After their appearance Terry’s wife is just as likely to be in Room 402 as 401. He might as well kick down the door of his first choice.
Then, as I went along the corridor to get a mid-morning tea from the trolley, I suddenly understood the source of Tom’s mistake. It was me! I stopped and would have put a hand over my mouth, but there was a man coming towards me carrying a cup and saucer. I saw him clearly, but I was too preoccupied, too shocked by my insight to take him in properly. A handsome man with protruding ears, now slowing down, blocking my way. Max, of course, my boss, my one-time confidant. Did I owe him another de-briefing?
‘Serena. Are you all right?’
‘Yes. Sorry. Head in the clouds, you know …’
He was staring at me in an intense way and his bony shoulders looked awkwardly hunched inside his over-sized tweed jacket. His cup clinked in its saucer until he steadied it with his free hand.
He said, ‘I think we really ought to talk.’
‘Tell me when and I’ll come to your office.’
‘I mean, not here. A drink after work, or a meal, or something.’
I was edging around him. ‘That would be nice.’
‘Friday?’
‘I can’t do Friday.’
‘Monday then.’
‘Yes, OK.’
When I was well clear of him, I half turned and gave him a little wave with my fingers, walked on and instantly forgot him. For I’d remembered clearly what I’d said in the restaurant last weekend. I’d told Tom that Monty chooses an empty box
at random
. And of course, two-thirds of the time that couldn’t be true. In the game, Monty can only open an unchosen empty box. In two out of three occasions the contestant is bound to choose just that – an empty box. In which case there’s only one box that Monty can go for. Only when the contestant guesses right and chooses the box with the prize, the pension, does Monty have two empty boxes to choose from randomly. Of course, I knew all this, but I hadn’t explained it well. This was a shipwreck of a short story and it was my fault. It was from me that Tom had got the idea that fate could play the part of a gameshow host.
With my burden of guilt doubled, I realised that I could not simply tell Tom that his story didn’t work. The obligation was on me to come up with a solution. Instead of going out of the building, as I usually did at lunchtime, I stayed by my typewriter and took Tom’s story from my handbag. As I threaded in a fresh sheet of paper I felt a stirring of pleasure, and then, as I started to type, even excitement. I had an idea, I knew how Tom could rewrite the end of the story, and let Terry kick down the door that doubles his chances of finding his wife in bed with another man. First of all, I got rid of the Indian couple and their harelipped baby. Charming as they were, they could play no part in this drama. Then, as Terry takes a few paces back, the better to run at the door of Room 401, he overhears two chambermaids talking on the landing below. Their voices drift up to him clearly. One of them says, ‘I’ll just pop upstairs and do one of them two empty rooms.’ And the other says, ‘Watch out, that couple are in their usual.’ They laugh knowingly.