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Secondary Magazine - Issue 20

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 30 September 2008 by ncetm_administrator
Updated on 09 October 2008 by ncetm_administrator

Secondary Magazine  
Welcome to Issue 20 of the NCETM Secondary Magazine. Read on to discover our range of regular fortnightly features. Why not let us know what you want to see in forthcoming issues? If you have thoughts to share you can also add your comments on the portal. This issue features Gambling with education.
Gambling with education?
Gambling, like it or not, is part of our everyday life. Even if you don’t gamble, you’ll know someone who does. The Gambling Prevalence Survey 2007 surveyed 9 003 people between September 2006 and March 2007 and produced some startling figures:
  • 68% of the adult population took part in some form of gambling in the past year;
  • men are more likely to gamble than women – 71% compared to 65%;
  • the most popular form was the National Lottery draw, with 57% of people interviewed having taken part;
  • other forms of gambling included scratch cards (20%), horse racing (17%), slot machines (14%) and private betting (10%).

Since it touches the lives of so many, is there justification for the study of gambling within the curriculum? Surely its rich mathematical content combined with the potential morality debate is too good an opportunity to miss.

Pay £1.
4 coins are tossed into the air.
If they land showing 2 heads and 2 tails, you win £2.

Is this a bet worth taking? First impressions may suggest that it is. Apart from the initial attraction of doubling your money, one might predict an even split of heads and tails over and above any other combination. So what does the maths suggest?

There are 16 possible outcomes of tossing four coins with only 6 of these being 2 heads and 2 tails. Therefore, the probability of winning is a mere 37.5%, signifying that you are more likely to lose than you are to win. Although luck may be initially on your side, in the long term you are destined to lose.

As we know from the lottery, the potential return from the bet is just as important as the odds. The lottery is a prime example: the chances of winning the jackpot is an estimated 1 in 14 000 000, yet the potential return is so great 57% of the UK population are willing to hand over their cash. To weigh up whether the odds are in proportion to the potential winnings, the aforementioned bet can be illustrated in the table below:

Outcome Probability Winnings P × W
2×H 6/16 £2 £0.75
2×T 10/16 -£1 -£0.63
  Total: £0.12

This suggests that although the odds are stacked against you, the long-term return indicates a profit. The bet is worth taking providing it can be repeated again and again.

In order to make a profit, casinos stack the odds in their favour. Roulette offers some of the best odds to the gambler. Bets such as ‘red/black’, ‘odd/even’ and ‘upper eighteen/lower eighteen’ suggest an evens chance of winning. The wheel consists of 36 numbers coloured red and black, however, to tilt the odds in the casino’s favour, an additional 0 is added. Should the ball land on this, the house naturally receives the money. It’s not much but it’s enough to pay the rent and wages. An example is illustrated below.

Were you to put £1 on ‘black’ you are destined to lose in the long term.

Outcome Probability Winnings P × W
black 18/37 £1 £0.49
not black 19/37 -£1 -£0.51
  Total: -£0.02

The attraction of the lottery is the reverse of roulette and presumably attracts a very different kind of gambler. Here the odds are stacked against you yet the potential return is life-changing.

So do the figures add up?

Outcome Probability Winnings P × W
Jackpot 1/13989816 £4 000 000 £0.285922273
Not Jackpot 13989815/13989816 -£1 -£0.999999928
  Total: -£0.71

Although the winnings in the example above are an approximation and do fluctuate from week to week, the long-term reward doesn’t look good. There are however ways to increase your odds. For example:

  • We know any combination is as likely as the next. Many people choose combinations of favourite or lucky numbers including birthdays. Consequently, were you to select numbers greater than 31 you would reduce the chances of having to share your jackpot.
  • Statistically you are more likely to die from a freak accident than win the jackpot, so it would be a shame, having bought your ticket days in advance, never to find out if you are ‘the winner’. Therefore, buy your ticket minutes before the draw itself.

It should be noted that the lottery can be viewed as a tax on people who are bad at maths. Most money invested in lottery tickets would be better placed at the bottom of a large hole in the backyard, which could then be dug up when additional cash was needed in the future. Even at this 0% rate of return, a larger profit would be made than the average return from playing the lottery.
(BBC h2g2 – ‘The Lottery’)

The mathematics suggests that you are best to avoid any bet in which you do not have a high level of expertise; it would be prudent to opt for games of skill rather than chance.

Within the Personal, Social, Health and Economic non-statuary programme of study, students should be given active learning opportunities to:

…recognise and manage risk, take increasing responsibility for themselves, their choices and behaviours.

With an estimated 250 000 ‘problem gamblers’ in the UK, should students be made aware of the facts?

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The Interview, An idea for the classroom, 5 things to do, The Diary, Focus on
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An idea for the classroom
5 things to do
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21 October 2008 10:22
This is an interesting article
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