Nine-year-old poker players are pretty easy to beat because they tend to be very aggressive, betting on all kinds of crazy hands. After The Little Clown went all in with three cards to a straight for the umpteenth time I decided it was time for a lesson in probability. As synchronicity would have it, The Little Clown’s annual science fair was coming up and we agreed that he would choose as his question:

What should I bet if I draw three cards to a straight in Texas Hold’em?

We filled in the forms and it didn’t take long before his teacher contacted me, appalled that a nine-year-old would be playing poker, let alone that he would have the audacity to want to study the topic in a science project. After some negotiation, we compromised on a less provocative hypothesis:

What is the probability of a pair if you draw two random cards from a deck?

Little Clown did a science project every year from kindergarten to fifth grade but this one was my favourite as it fulfilled all of my criteria for a good science project.

1. There should be an obvious hypothesis that is wrong.
2. The hypothesis can easily be proved wrong by an experiment.
3. The experimental result can easily be confirmed with maths.

Excuse me for a second while I rant a little about elementary school science projects.

Who exactly was it that decided that filling a cardboard volcano with baking soda and vinegar was a good science project? What is the child learning from the experiment?  What is the hypothesis? How come the vast majority of children’s science projects are either variants on the volcano “experiment” or an exercise in building a model out of lollipop sticks and elastic bands?

I predict that if I leave bread out for three months it will go moldy.

I predict that if I make a little car that is jet-propelled by a balloon, the car will be jet-propelled by the balloon.

How is that science? Where is the experiment?

Anyhoo…

The poker experiment is perfect because 9-year-olds (like most people) don’t really get probability and will always get the answer wrong (that’s why they are easy to beat at poker). It’s also easy to demonstrate by choosing random pairs of cards from a deck and recording the results. The maths is a bit harder, but this was actually my favourite bit of maths instruction ever with my budding scientist. We started with a coin.

What is the chance of getting heads if you flip a coin?

We tried it a hundred times and confirmed our intuitions before moving on to something more complex.

What are the chances of getting two heads if you flip two coins?

This was a little bit harder but we figured it out and experiments again confirmed our intuition. We tried more coins.

What are the chances of getting three heads if you flip three coins?

Intuition failed us here but … maths to the rescue! Do 9-year-olds know about exponents? *shrug* Mine did and we got the results quickly and confirmed it with experiments. From there, it was trivial to try four coins and five coins so we moved on to dice.

What are the chances of getting a six if you roll a dice?

Intuition was inadequate again, but again the maths held up (hooray, maths!). Exponents still work if the base is 6 instead of 2 and the experiment confirmed it.

What are the chances of getting two sixes if you roll two dice?

By now it was easy and we zoomed through three dice and four dice. Time for cards.

What are the chances of getting a pair if your draw two cards from a deck?

A deck of cards is trickier because you have to deal with the whole take-one-away thing but, luckily, 51 is divisible by 3 and the maths is not hard, even for a nine-year-old. The experiments are more tedious because you have to deal with a lot of pairs to demonstrate a 1 in 17 chance and nine-year-olds are not famous for their patience. Fortunately my nine-year-old was already a pretty good Logo programmer as he was already a four-year veteran of the business having started to learn Logo in first grade.

I helped him recreate the coin-flip experiment in Logo and then we did it again for the coins. The cards were beyond his programming skills but he followed along OK when I wrote the code and he got a kick out of the results.

Challenger School – where my little clown learned his nine-year-old skills – gets a bad rap for allegedly teaching rote learning. But the rap couldn’t be further from the truth. Having sent one little clown to Challenger and another to public school, I can attest that only one of them was ever subject to rote learning and it wasn’t the Challenger clown.

Challenger is intensely academic and, while I can understand that it is not right for every kid, mine was challenged in ways that he didn’t experience again until high school. In fact, I wonder whether the transition from high-performing fifth grader to coasting sixth grader wasn’t detrimental to his determination as it taught him that coasting was an option; an option unavailable to him at Challenger.

Fast-forward nine years and my little clown is now all grown up and accepted to UC Santa Barbara and, under protest, Ragged Clown Sr and Ragged Clown Jr are on their first road trip together to go check out Jr’s home for the next four years. It’s a long trip so we brought along Jad Abumrad and Robert Krulwich for company.

Jad and Robert – and their magnificent Radiolab podcast – have long been our companions on road trips. On this particular trip, the podcast app summoned up the episode “Are You Sure?”

Radiolab episodes have a certain structure. There is always the main theme – in this episode the theme was doubt –  and they do a powerful job of exploring variations on the theme with an eclectic selection of interviews and zany editing and contributions from psychologists, scientists and moral philosophers – and anyone else who has a good story to tell.

The first segment was interesting albeit not relevant to my story here. A couple of devout Christians were due to get married until one of them started to wonder whether all that stuff in the bible was actually true. That topic would make a great blog post, but it was the second segment that intrigued me more.

Annie Duke is a decision strategist – a poker player – and won the poker world championship in 2004. In her segment, Annie describes the strategy that professional poker players use for winning poker games: know the odds. But knowing the odds doesn’t just mean knowing which hand is likely to win; it means understanding that the hand that is most likely to win will often lose (and vice versa). The secret is in knowing the pot odds.

Annie:

If there is a $300 in the pot and you have to bet $100 to stay in, you could lose the pot three times and still break even if you win the next hand.

Robert:

So you could lose a hundred dollars on Monday, a hundred dollars on Tuesday, you could lose another hundred dollars on Wednesday, but if you win the hundred back on Thursday, you are good.

Jad:

So you just need to win one out of every four times

In other words, it’s not enough to know your chances of winning. The important thing is that your chances of winning are greater than the pot odds.

The climax of the story has Annie playing against her brother in the final of the World Hold’em Championship. They are playing for two million dollars and she’s holding a pair of sixes and her brother goes all in with a pair of sevens before the flop. Her brother is 82% to win the hand. Amazingly, the flop gives Annie a full house and she wins the $2,000,000.

Aside from the lessons on how to play hold’em, Annie’s good luck highlighted some fundamentally different ways of thinking in the Clown household. There’s one strand of thought that says, if there is a chance that a bad thing might happen at a particular event, you should avoid events like that in the future. Bad movie? No more movies! Awkward silence or said the wrong thing at a social gathering? No more social gatherings! On the other hand, the more optimistic clowns are willing to tolerate a lot of crap movies and awkward gatherings in the knowledge that, eventually, you’ll find a movie to enjoy or that a social gathering will sparkle. Even without knowing the pot odds, I’m pretty certain that if you never take a chance, you’ll never win.

A final word from Annie:

It’s not about winning the hand all the time. It’s about winning the hand enough of the time […] That embracing of uncertainty does some really wonderful things for you.

Jad:

You learn how to avoid that very human tendency to feel ashamed or embarrassed when you lose. You just float right above it.

Annie’s brother:

If you are making good decisions, then you are making good decisions.

Annie:

You have to be somewhat outcome blind.

By coincidence, Annie was a psych major and Little Clown is majoring in bio-psych at UCSB. He’s gonna be a scientist!

I hope he’ll learn from Annie and take some chances. I hope he’ll win some too.

We were taught chemistry, physics and biology as separate subjects and, while I enjoyed all the sciences, I enjoyed physics the most because it was more mathematical. Chemistry had less maths and biology, at that level, hardly any at all. In my 11 year old mind, physics was pretty much just applied maths and therefore fun.

In geography, we covered such topics as map reading, how rocks are formed and weather but I never thought of it as science because science was something I enjoyed and I didn’t enjoy geography. Geography had a little bit of counting, measuring and charting but less maths than the sciences. History had no maths at all and I hated it.

At Dylan’s school, they have a single subject called science and they cover such topics as map reading, how rocks are formed and weather. Dylan hates it. In 7th grade he’ll do life science but he already knows he’ll hate it because he hates science. It’s like they want to avoid exposing kids to the hard sciences until it’s too late. Until they have formed an opinion one way or the other.

I have this theory that the people who design school curricula don’t really like science or maths but they know it’s important to the economy and that not enough people are following science careers. The remedy? Make the science in schools appealing to people who don’t like science!

I wonder if they stop to consider the effect it has on people who actually like science? If a kid likes science would making it less science-y make him like it more or less?

I know the answer for me and I know the answer for Dylan. Maths good. Science good. The more the better.

“So, who do you belong to?”
“Dylan”
“Oh! Dylan! He works so hard!”
“No! Dylan Lawrence!”

Apparently, Dylan’s teacher was under the misapprehension that Dylan works hard at maths. I tried to explain to her that maths was Dylan’s favourite subject because it required no work at all. She found the notion very odd. I thought it was obvious.

For me, at Dylan’s age, maths was my favourite subject too. It required no study or work and, every now and then, the teacher would give you some cool puzzles to work on. I would often slyly do maths in other classes when the teacher wasn’t looking. Apparently, it hadn’t occurred to Dylan’s maths teacher that people would enjoy doing maths.

I have encountered this odd attitude before. When Dylan started fourth grade, at back-to-school night, his teacher explained how hard maths was for the children but that she had a bunch of manipulatives to help with the difficult concepts and she would take them through it step by step and, usually, by the end of the year they would understand.

What would it be like, I wonder, to have a maths teacher who enjoyed maths? I had English teachers who enjoyed their subject ..and history …and physics …and chemistry …and biology …and French…but never maths.

What if the default assumption in the maths class was that kids like maths and find it easy? What would that class be like?

Imagine if, at the start of the year, they said

OK. Everyone who loves maths come with me. We are going to teach you separately. Your teacher likes maths too.

What would that class be like?

To their credit, Dylan’s school has advanced placement for maths and they give the new sixth graders a test. If they pass, they go into a class with a bunch of surly seventh graders who don’t like maths.

Anyway, Dylan just passed the test that lets him take high school maths next year. All he needs to do now is get the form signed and handed in on time which, apparently, was the hardest thing he had to do all year in maths class.

Why is it so hard for him to get a form signed? I don’t know where he gets it from.

Rhapsody thought I might like to listen to some Kate Bush which was nice because I haven’t listened to Kate Bush since I was about thirteen with hormones and she was about 19 and hot and she lived in the same town as me – Bexleyheath.

I listened to a few familiar tracks – weird as ever – and then suddenly our Kate seemed to be singing “three point one four one five nine…”. That’s odd I thought and glanced at the title.

Sure enough, the song was called pi.

“I wonder if there is a story behind the song?” I wondered. And googled.

The song is fairly recent and is a tribute to a man who is infatuated with everyone’s favourite transcendental number.

It starts…

“Sweet and gentle and sensitive man
With an obsessive nature and deep fascination for numbers
And a complete infatuation with the calculation of PI

…and then continues with Kate singing the first 150 digits of pi…but she gets it wrong! She skips a few around 137!

Clearly Kate is much too smart to make a mistake like that and there is bound to be a fascinating explanation…and…the interwebs are full of them.

Some of my favourites:

the best Craftsmen always make one deliberate mistake in anything they create so that the Gods don’t punish them for their arrogance.

The supposed mistakes in pi are all deliberate, and she has actually used them (and lots of other tricks) to embed a secret message in the song. It is our job to decode what that message is.

If that’s what Kate says pi is, then thats good enough for me. I’m hacking my calculator and patching my maths libraries.

And my favourite theory of all:

Kate Bush has been looking all her life for a man who is so geeky that he would notice an error in the Pi song. She’ll be reading your blog and fantasising about you now, you lucky bugger,