It’s a Numbers Game

April 08 2009 Samir Khan 519


When I was a toddler and learning about the concept of numbers, I used to play a simple game with my parents.  They’d think of a number, and I’d try to guess it.  They would shout “hotter!” if I were getting closer to the number and “colder!” if I was getting further away.  I’m still fascinated by number games, but now it’s Sudoku, the Countdown numbers game… or balancing my bank account at the end of the month.

I spent many of my callow teenage years playing games of chance involving dice and cards.  But it was only after I stopped playing that I stopped losing money. I guess at that time I never really understood the Gambler’s Fallacy, or probability itself.

(Pop quiz: Toss a coin 40 times - what are the chances of getting six heads or six tails in a row? The answer’s in a post script below, together with some Maple code.)

At university, I became fascinated by a UK quiz show called Countdown (and not just because I had a crush on Carol Voderman – an ex-presenter).  In one of the rounds, the contestants have to find the combination of additions, subtractions, multiplications and divisions to make six seed numbers equal a target. 

I’ve attached a Maple worksheet that automatically solves the Countdown numbers game (a simple click of a button asks Maple to find the solution for you).  Kent – one of the sales people I work with – was so fascinated by the worksheet that he spent an entire weekend playing with it, much to the displeasure of his wife and kids. 

Now, if I want some mental stimulation, I often crack open a book of Sudoku puzzles I’ve got lying around. By the time I’m bored, I usually break out Joe Riel’s fantastic Maple-based Sudoku solver.

P.S The following Maple procedure gives the probability of k heads (or k tails) in a row out of n coin tosses.

Many people underestimate the chances of getting 6 heads in a row out of 40 coin tosses, and find it hard to accept it’s as high as 26%.  Given a large enough sample size, the improbable is likely to happen.  How else do you explain the English football team finally having a run of wins?

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