Looking Through Fresh Eyes 7: Knowin' what the cards were, by the way they held their eyes

(Tying up a dangling loose end left hanging at the end of Nature Studies)

Right, to it again after time spent doing other things (deviantArt, the L-Space Wiki and military modelling. Oh, and working for money.) ... This episode's soundtrack? Even cheesier... Country and Widdershins... Kenny Rogers.

The Assassins' Guild School, after the first year, streamed its pupils in maths for administrative convenience. Eleven year olds were taught within their forms. At the end of the year, they were graded on performance and ability from Stream One – the exceptionally bright – to Remedial - the duffers and dunces. This had the joint advantage of streamlining and focusing teaching, and of identifying the more cerebral students, as exceptional mathematical ability quite often went along with inability to walk in a straight line or indeed to successfully identify which shoe went on which foot in the morning. This could be a problem for the more physical aspects of Assassin training, but did not rule out exceptionally gifted students whose aptitudes leant themselves to less physical forms of inhumation – poisoning, for instance, needed a mathematical mind to accurately work out precise weights and quantities and fine calculations. It is not a discipline for a numerically dyslexic candidate. And Assassins with a gift for numbers, in the right way, could be useful. Mr Wimvoe, the Guild Bursar, had been such a boy in his time. There were never enough dual-qualified Assassin-Accountants. (1) Associate Guild Members of this inclination, – that is, pupils who attended the school for the general education, and who left without Taking Black – could and did enter the Guild's employment as lab technicians or pharmacy assistants. Mr Mericet's Poisons Lab, for instance, was ably supported by such a team of technicians.

Mr Mycroft, the Guild School's principal Mathematics teacher, was only an Associate Member. In his time at the School he had left before the Black, eventually pursuing a teaching career, and finally returning to his Alma Mortua because, well maths teachers are hard to find.

They are also hard to replace when they fall ill.

Stream Three Maths, a second year class drawn from all forms, sat at their desks and wondered who was going to cover for old Mycroft. With a bit of luck it might be some dim teaching assistant they could run rings around, or, best luck, an unwary supply teacher hired in for the day from the Teachers' Guild. They were fun....

The usual no-teacher-present antics of talking, shouting, throwing wadded balls of paper and paper darts, et c, were interrupted by two Guild porters wheeling in a large covered something on a hand-truck. Two other porters followed, manoevering a covered table in round the door.

"Errr... thank you, gentlemen". said an uncertain female voice.

"Ma'am." said the lead porter, touching his cap.

To Stream Three's delight, the person who walked in was young, and she wore the purple-and-silver sash denoting her status of Teaching Assistant. Checking out her uncertainty, the class rubbed its collective hands together with glee. Playtime.

Catherine Perry-Bowen looked up at the suddenly innocent and cheerful faces and gulped. She had only become a Teaching Assistant (Provisional) about five minutes before the class, when her mentor had handed the sash to her. Now she was looking the reality in the face, she wondered what sort of horrible indignity awaited her. A little part of her also remembered what her class had once done to an anonymous student teacher, and she quietly begged forgiveness. She also wondered if she should announce herself, or seek to impose order, or...

"Bring the large table over here, if you will, Mr Stippler, s'il tu plait.".

And then Stream Three belatedly realised exactly who was going to cover their Maths class, and suddenly sat up straight in obedient silence. This was not a teacher to disobey or be insolent to. They had all been in her Swords classes.

Madame Deux-Epées was dressed formally, in impeccable Assassin black and long dress skirt. The only sounds were those of two porters dragging the large covered table to exactly where she wanted it, just in front of the teacher's desk. And her heels clicking on the floorboards like the ticking of a sinister clock. The inevitable swords at her waist were a minor courtesy detail, a point of advertising her professional skills.

The two porters left the classroom, closing the door behind them. There was a moment's silence. Emmanuelle observed her class for a moment, reminding herself of faces and names and potential attitude problems. Then she nodded.

"You are all sitting up straight, silent, and attentive." she observed. "That is for the good. I will be covering your Mathematics class today, mes élèves. You all know me. This is Miss Perry-Bowen. While in the normal course of things she is a senior student, I have personally identified her as having potential, and therefore for this lesson she has the status of teaching assistant. You are required to give her the same courtesy and respect that you would normally give to, par example, me."

Emmanuelle smiled.

"I shall be observing closely. I would remind you that monsieur Gilette, the assistant Armourer, is always in need of volunteers to assist him in the more unskilled aspects of his job. To sweep and mop the armoury floor, peut-être, or to oil blades and points, or to clean and polish leatherwork lest it dries and cracks. To assemble chain-maille from links. And there are many blades and leather accessories requiring maintainence. Enough to occupy a detail of students for the whole of Saturday afternoon and most of Sunday."

She let the implied threat sink in, and then smiled.

"But I am certain we will have no problems. Et bien. Mathematics. Now, today's class would have covered..."

She reached for the standard text and riffled through it.

"... quadratic equations and solving for the most elusive x."

Emmanuelle closed the book with a slam, and threw it decisively over her shoulder. It landed somewhere behind her with a dull thump. The class sat up and paid attention.

"But we will not be doing that today, mes élèves. I have in mind a most valuable mathematical skill which, for those who understand and are prepared to pay attention, is most transferable to real-life situations which you will come across as adults."

She chalked the large letters "PROBABILITY THEORY" on the blackboard.

"Please distribute the teaching aids, Miss Perry-Bowen". she directed.

Catherine moved up and down the desks with the large box she had carried home from the Gamblers' Guild, passing out the contents, one per pupil. The pupils took them, puzzled but expectant, thinking, "This is maths?"

"You each hold in your hands one standard pack of playing cards, sealed and unopened, of the Guild of Gamblers' approved standard." Emmanuelle said. "In fact, the Guild, of which I am a member, was kind enough to provide me with these items to use in your education. Take a moment to open it and assess the contents. You will find it is what is known as the short deck, rather than the full expanded Caroc of eight suits and trumps. The short deck consists of fifty-two cards arranged in four suits. This is preferred for some simple card games and, in fact, the Guild recommends it for beginners and newcomers, as there is less to remember and the deck is more easily manipulated. Shuffle them, look at them, take a moment to familiarise yourselves. In a moment I will begin the lesson with a mathematical question."

She took a pack of cards herself, broke the seal, and shuffled the contents with the easy skill born of long practice. As Emmanuelle felt there was no harm in a bit of showmanship and display, she demonstrated several flamboyant and spectacular shuffles for the class, fanning, spraying and riffing the pack for her audience. The pupils looked on appreciatively. This beat old Mycroft's dry pedantic delivery hands-down.

"Eh bien." she said, fanning the deck out on the desk in front of her.

"I propose to illustrate the concept of probability theory using the standard pack of cards, and by teaching you to apply what you will shortly be learning to several simple card games. We will all enjoy ourselves, we will learn useful skills, and, who knows? You may also absorb some useful mathematics. Et maintainant. For a first question. What is the probability of my selecting any one named card from these fifty-two? If I nominate the Ace of Spades, if I then select a card at random from a thoroughly shuffled deck, how likely is it that I will select the Ace of Spades? Ideas, please?"

A pupil raised a hand. Emmanuelle nodded.

"Madame, do we include the two jokers in the deck?"

"A good question. Disregard les bateleurs, for this purpose."

There was a thoughtful silence, as the class applied itself to the question. Emmanuelle filled it. She selected a card at random, and held it up.

"The five of hearts. Not even close." She said, returning it to the deck, re-shuffling theatrically, and fanning the cards out again.

"So we see random selection, though you will get there in the end, is inefficient. In a real card game, you will very quickly run out of capital to invest. Mr Fennister, you have an answer for me?"

The nominated student lowered his hand.

"Please, madame. There are fifty-two cards in the deck. Each card is unique. Therefore the chance of drawing, randomly, the Ace of Spades, is one chance in fifty-two."

"Very well done, Mr Fennister! Formidable. You have an exact one-in-fifty two chance of drawing any nominated card at random. And this offers us a beginning point for exploring probability mathematics. Now I caution you at this point that mathematics is an exact science and offers a theoretical base for exploring probability. It does not take into account that in the real world, where there is no such thing as a perfect shuffling of the deck, and, alors, you may come up against a member of the Guild of Gamblers who will be using other techniques to augment a mathematical understanding. But that will be an advanced lesson for other times. Here, we are in a laboratoire, where we are dealing with the perfection of mathematics and making an assumption that the deal is always perfect, the cards are always shuffled perfectly randomly, and nobody is trying to finesse the deal. On this understanding, mes élèves, we proceed."

She smiled at the class. It was the smile of the professional gambler who has seen an innocent with money. She really wanted her pupils to see and remember that sort of friendly smile. It would be good education for them.

"Now we remove the Ace of Swords from the deck as a spent card. What is now the probability that the next card we randomly draw will be the Queen of Hearts?"

"Errr... one in fifty-two, madame?" a pupil asked.

She shook her head.

"Well tried. But that would only apply if all fifty-two cards were present. We have removed one as spent, if you recall? Its purpose is used. It is in the discard pile. Think more carefully. Miss Ellison? You have an observation?"

"The probability is now one in fifty-one, Madame?"

"Exactly correct! You are now getting the idea. And if we remove the Queen of Hearts and add her to the discard pile?"

Catherine stood to one side and watched her teacher demonstrate the rule of diminishing probabilities, occasionally making a permanent note on the blackboard. She suspected the point of having here wasn't just to have somebody to do the dogsbody work: she was here to be educated herself. And it was working; she found her mind moving along interesting lines.

"And so now we play a game, mes élèves!" Emmanuelle announced. "I trust you are all familiar with the game of vingt-et-un, also known as blackjack, or pontoon? No? I shall briefly explain the rules, then. And this will be a practical exercise in what we have just learnt. I will watch to see how well you have absorbed the lesson!"

The next twenty minutes were spent in one of the most interesting mathematics classes that Catherine had ever attended. She was certain this class would leave with its collective mind expanded, having certainly learnt something useful. And even mathematical.

Emmanuelle clapped her hands for attention.

"Miss Perry-Bowen, please distribute the contents of the other box, one per person." she directed.

Catherine went round the class again. This was one unique maths lesson...

"You each have a stake of play money from the Exclusive Possession game." her teacher said. "This will add something to the lesson and give you something extra to play for. I see several of you have grasped the point which I did not state explicitly, concerning counting the cards and betting accordingly. This is good. It sharpens concentration and focuses the memory, which is a very useful skill for the Assassin. I do advise you that it is frowned upon in casinos and is viewed as cheating, which is strange, as the whole purpose of gambling is to outwit the house and win. I consider that as the House will most assuredly use every edge it can to win in the long run, this little skill regains the advantage for the gambler, and should be fostered. But let us begin. I wish you to divide into groups of four, one of whom will begin as dealer. The dealership will rotate in a Turnwise direction with each new game. Let us begin!"

Another session of blackjack saw several students lose everything and others winning shrewdly, whilst the majority broke even. Emmanuelle congratulated the winners, privately marking them as people the Gamblers' Guild might later on take an interest in, commiserated with the losers, and saw the play money was redistributed so everyone was starting on an even footing again; in response to protests from the winners, she had Catherine chalk up a tally on the blackboard showing who was notionally ahead and who was behind.

"And now a more complex probability, mes élèves." she said. "I do not bet overmuch on the horses myself as there are so many variables, not the least of which is Doctor Folsom and his interesting medications. But if we assume the odds are fairly fixed and Doughnut Jimmy is not present at the racecourse, let us look at a typical horse race. Miss Perry-Bowen, please hand out the copies of the Ankh-Morpork Times, one between two students? Merci!"

The next half-hour was a discussion of how probability theory applied to racing form and how the odds were calculated. Catherine found it all made a sort of intuitive sense, and Emmanuelle explained much that was new to her.

"You will note that in a race of eight horses, the odds should be pretty much one-in-one that one of those horses will win and one will place second." Emanuelle said. "Therefore the odds offered on each horse, expressed as fractions, should sum to exactly one. Take time now to do this calculation on our selected race and tell me what you see. If vulgar fractions daunt you, convert them to decimals, so that two-to-one, for instance, becomes nought-comma-five."

She paused, seeing perplexity.

"Ah. Here in Ankh-Morpork, the decimal point and not the comma is used as separator. Nought-point-five, in this case. I apologise, I learnt my mathematics in Quirm."

She waited for an answer, as the students worked at the problem, looking increasingly perplexed. Then one raised her hand.

"Madame? However hard I try, I can't get them to add to one!" the student said. "Expressed as a decimal fraction, the best total I can get is 0.97. Sorry."

"There is no need to apologise, Miss Davies." Emmanuelle said. "You are in fact correct in your addition, and I congratulate you. Now do you as a class have any ideas as to the significance of that missing 0.03? Anyone?"

A student eventually raised his hand. She nodded.

"Madame. If I bet a dollar on a horse race, this suggests three pence of that dollar is not accounted for and has disappeared into the system somewhere?"

Emmanuelle nodded.

"Carry on." she invited him. "Where and to whom have that missing three pennies gone?"

"I paid my dollar to the bookmaker..." the student said. "Well, not me personally, obviously, as we're not allowed to gamble...ummm... but he is calculating the odds as if they only sum to ninety-seven pence. On one bet three pennies are nothing, but if the bookmaker is handling hundreds of bets, many for more than one dollar, then, umm..."

Emmanuelle clapped.

"Mon ami, you have it!" she said. "Regardless of how many bets might win, the bookmaker never loses. Ma foi, you never see a poor bookie dressed in old clothes, and this is why!"

Education is where you find it, Catherine realised. She also wondered about going into bookmaking as a career. It could be a lot less hazardous than assassination, and she would have been trained to deal with irate losers... then she wondered why she was thinking like this. She'd never before wanted to be anything but an Assassin...

The class discussed the technicalities of racing form for a while longer, learning exactly how to read the shorthand notes by each horse in the race, and incidentally absorbing some more probability theory, and Emmanuelle then moved to the large mysterious covered table. She whipped the cloth off with a theatrical flourish.

"Regardez, mes élèves!" she proclaimed.

"I now propose that for the remainder of this lesson, we explore the wonderful and precise mathematics of probability, through the medium of the roulette table. Mr Jones of the Guild of Gamblers was kind enough to loan me this fine example for educational purposes. First, take a moment to gather up and replace your cards in the box, ensuring you miss none. Miss Perry-Bowen will gather them in, if she will be so kind. Then you will all gather round at the front of the class, where I will be your croupier for the session."

The class excitedly obeyed. Maths could be fun...

Afterwards, Emmanuelle asked Catherine if she had appreciated the lesson.

"Very much so, madame!" she said.

"Tres bien. I am hoping this will stand everyone in good stead for later life. After all, the practical purpose of mathematics is to prepare a person and equip them with the skills they need to make sense of numerical issues posed by life, is it not? So often a theoretical syllabus neglects the practical applications of the subject. I shall require you again, ma petite, for other classes. Please acquire some dice and familiarise yourself with them, as we shall be looking at other practical applications of probabilities. Now if you will excuse me, I have to report to Lady T'Malia that the class was very successful indeed."

Catherine applied herself to her regular classes, finding that learning was becoming easier, even in those subject areas she had found challenging. Her class in Quirmian Language was becoming easier and easier. Monsieur LeBalouard even had to request her to stop talking so as to give other pupils an opportunity. He did add that in spoken Quirmian, he normally had the opposite problem, of getting shy and reticent pupils to start talking at all. It was pleasant to have a star in his class.

"I believe Madame Deux-Epées is taking a personal interest in you? Your spoken Quirmian has certainly improved, formidably so. Sometimes I can almost hear her in you."

"She certainly speaks to me in Quirmian, monsieur." she agreed.

"It is a fine line to walk. While we should treat all pupils equally, in practice most of us will inevitably identify and take on at least one protegée during our time teaching. Quite often it becomes an enduring friendship after graduation. You are indeed fortunate."

"I am thankful, certainly." Catherine agreed. She suddenly realised she had been listening, and replying, in perfect Quirmian; the rest of the class had listened, in varying states of incomprehension. She reddened slightly and looked over to Gareth ffitzroy-Connor. (2) Then went very red when he smiled back. She had always liked Gareth, but lately the liking was taking a more limbic form. She wasn't completely at home with this.

The class dismissed, Gareth fell in step with her on the way to their next lesson, a lecture in SehrRealPolitik from Lady T'Malia. (3). Uncomfortably, Catherine realised there were a lot of discreetly knowing sniggers and nudges going on in the background from their friends.

"Cathy, you speak really good Quirmian." he said, conversationally. "I could just about work out most of that conversation between you and Balouard. You know..." and he paused for a moment, thoughtfully, "I'd really love it if we got together some time. You could, you know, tutor me a bit. Your Quirmian is streets ahead of mine!"

She reddened as sniggering broke out behind them. She wasn't at home with this. She also blushed because... well, she quite liked Gareth. The idea of being alone with him had a certain attraction... but where to be alone in a place where other people were around all the time?

"We'll see." she said, gathering her self-control and trying not to blurt out "Oh my Gods, yes!"

"See you in Necros later?" Gareth asked, hopefully.

Necros' coffee bar was a popular meeting place for student Assassins allowed to visit the city in the all-too-brief interim after evening dinner and after all prep work was completed, before curfew and lights out. Sanctions applied to pupils returning late.

"Yes." she said. "I would rather like that." She looked directly into his face. He was unable to hold her frank gaze, and looked away quickly.

Concentrating on her next lesson was difficult. She kept thinking about him and wondering about all the sorts of things the girls in her dorm discussed in low voices without, she suspected, a shred of personal experience. Well, she was sixteen. About time to start getting some of that personal experience, she thought.

(1) Indeed, the other occupational hazard of life spent living in a world of numbers - a need for Dried Frog Pills to maintain a veneer of sanity - was another reason the Guild tried to identify such people young and steer them away from active Assassination. A Wizard with a need for dried frog pills merely hallucinates that he can fly. An Assassin's delusions might be made reality in ways that, er, impact more on people around him.

(2) Gareth was a pupil cursed with a name beginning with "ff". It happens occasionally. Nobody quite knows whether it capitalises, how to pronounce it, nor indeed whereabouts in the alphabet it fits.

(3) Extremely Real Politics. An Uberwaldean philosopher once said politics is the art of the possible. Lady T'Malia stressed how probable it was that sooner or later, the Assassin would be called upon to help turn abstract political possibilities into concrete realities.

this chapter's bonus lyrics:

On a warm summer's eve
On a train bound for nowhere
I met up with the gambler
We were both too tired to sleep
So we took turns a-starin'
Out the window at the darkness
The boredom overtook us, and he began to speak

He said, "Son, I've made my life
Out of readin' people's faces
Knowin' what the cards were
By the way they held their eyes
So if you don't mind my sayin'
I can see you're out of aces
For a taste of your whiskey
I'll give you some advice"

So I handed him my bottle
And he drank down my last swallow
Then he bummed a cigarette
And asked me for a light
And the night got deathly quiet
And his face lost all expression
He said, "If you're gonna play the game, boy
You gotta learn to play it right

You've got to know when to hold 'em
Know when to fold 'em
Know when to walk away
Know when to run
You never count your money
When you're sittin' at the table
There'll be time enough for countin'
When the dealin's done

Now every gambler knows the secret to survivin'
Is knowin' what to throw away
And knowin' what to keep
'Cause every hand's a winner
And every hand's a loser
And the best that you can hope for
Is to die in your sleep"

So when he finished speakin'
He turned back for the window
Crushed out his cigarette
And faded off to sleep then somewhere in the darkness
The gambler he broke even,
but in his final words
I found an ace that I could keep

You've got to know when to hold 'em
Know when to fold 'em
Know when to walk away
know when to run