Bet and Lose: Learning Mathematics or Loosing Money by Juergen Maasz and Hans-Stefan Siller

Bet and Lose:

Learning Mathematics

or

Loosing Money by Juergen Maasz and Hans-Stefan Siller

a. Univ. Prof. Dr. J. Maaß

Hint:

If you have questions or

if you would like to get this

presentation please mail

[email protected]

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MOTION FOR A EUROPEAN PARLIAMENT RESOLUTION

on the integrity of online gambling (2008/2215(INI))http://www.europarl.europa.eu/sides/getDoc.do?pubRef=-//EP//

TEXT+REPORT+A6-2009-0064+0+DOC+XML+V0//EN&language=EN

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Some facts (Germany 2007):

Gambling – 28.000.000.000 Euro

The German Goverment earns 4.250.000.000 Euro (taxes)

Deutsche Hauptstelle für Suchtfragen e.V.

About 220.000 pathologic gamblershttp://www.dhs.de/web/datenfakten/gluecksspiel.php

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In the United States in 1999 the National Gambling Impact Study stated "the high-

speed instant gratification of Internet games and the high level of privacy they

offer may exacerbate problem and pathological gambling"

(Wikipedia)

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Danger? Why?

An online gambler has pleaded guilty to stealing more than £1m

from his employer to feed an "out-of-control" gambling habit

(http://www.vnunet.com/vnunet/news/2160083/online-gambler-guilty-theft)

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ICD Version 2007 Chapter V Mental and behavioural disorders (F00-F99) Habit and impulse disordersThis category includes certain disorders of behaviour that are not classifiable under other categories. They are characterized by repeated acts that have no clear rational motivation, cannot be controlled, and generally harm the patient's own interests and those of other people. The patient reports that the behaviour is associated with impulses to action. The cause of these disorders is not understood and they are grouped together because of broad descriptive similarities, not because they are known to share any other important features.

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Excludes: habitual excessive use of alcohol or psychoactive substances ( F10 - F19 ) and impulse and habit disorders involving sexual behaviour ( F 65.- )

F 63.0 Pathological gamblingThe disorder consists of frequent, repeated episodes of gambling that dominate the patient's life to the detriment of social, occupational, material, and family values and commitments.

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First Summary:a) There is “pathological” gamblingb) The theme is about money, luck

and illnessc) Is this a theme for teaching

mathematics?

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Yes, it is!

General aims of teaching mathematics are• Understanding the world better• Becoming critical citizen• Learning to use mathematics

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How to start?

There are different ways but

students should learn to avoid gambling because of the high risks

Folie # 12


Students should change their behaviour

Therefore it is much better if they find out the important results their self

This means: The best method is self organized learning!

Folie # 13


My proposal:

A simulation of the situation including mathematical analyzing and reflecting

results

Let us organize a sport event, play bookkeeper, bet, document results, analyze them, and reflect our work

Folie # 14


Folie # 15

A sport event?

A simple simulation is O.K.! (kicking on toy goals)

Dices are not a good idea! Why?


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Bets on sport events depend on what is expected. Expectations are subjective and different.

The expectation about the rolling dices are objective (we can calculate them) and equal


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Simulation? Kicking?


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Start: two players

10 kicks

Hits: A 6 times

B 3 times


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And now?

How much would you bet on A or B?

And if you win – how money much do get paid from the bookkeeper?


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First an very simple example: 30 students bet with

10 units game money each

20 bet on A (= 200 units)

10 bet on B (= 100 units)


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Bets on A 200 of 300 unitsBets on B 100 of 300 units

The money you get if you win is calculated by the “QUOTE” This is calculated by division:A = 300/200 = 1,5 (quote for A)B = 300/100 = 3 (quote for B)


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Assume A wins the match. What happens?20 students get 10 * 1,5 = 15 units(together 300 units = all)If B wins, 10 students get 10 * 3 = 3o units(together 300 units = all)...the other get NOTHING...


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Reflection after these first steps:1. Calculating the quote is easy2. high risk – high win3. How is a bookkeeper really

calculating?4. How does he earn money?


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How is a bookkeeper really calculating?

Totalizator: after all bets are done

Bookkeeper: in advance?


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How does a bookkeeper earn money?

a) Lucky winner – bad wayb) Commissiontotalizator: 10%bookkeeper: ? Let us look into internet and calculate!


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First impression: A lot of different bets!

We write down quotes:Rapid Wien versus Sturm Graz 1,47 : 3,95 : 5,95 (1 x 0)Calculating...


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Calculating...1/1,47 = 0,681/3,95 = 0,251/5,95 = 0,160,68 + 0,25 + 0,16 = 1,09A little less than 10% commission


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How does a bookkeeper earn money? Most important: Find a „good“ first quote!Later: Change quotes while bets come in


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Why is it so important to find a „good“ first quote?

Students find it out when they try to do it and to reflect the results


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If students play the role of a bookkeeper they have to decide:Which quotes should they offer for the match A versus B???

Is it a good idea to deduce it from training results?


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A: 6 hitsB: 3 hits => 2 : 1 => Quote A: 1,5 (3:2)and Quote B: 3 (3:1) ???


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Or: A will win always =>Quote A: 1 (1:1)

and

Quote B: ??? (1:0) „about very high“


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Students that play bookkeepers have double expectationsWhat do they expect that betting people will expect?Is there any influence of the offered quote on the betting people?

And how much do they like to earn?


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My hint: let students try it, document it and analyze it.Together they should think about their action and the results. They will find good answers – maybe with a little help of the teacher.


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Possible results:

A bookkeeper tries to have quotes like a totalizator?

Why? A totalizator earns 10 % commission independent from the result!


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Possible results 2:

What happens if a lot of people bet on B ?What happens if ALL people bet on A?


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Experiment:A bookkeeper expects, that 10% bet on BQuote: A: 1,11 B: 10Quote including 10% commissionQuote: A: 1 B: 9


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Quote: A: 1 ???

People who bet on A get their money back if they win and nothing more – will they like this?

=> No commission?


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We learn: High favourites are dangerous for bookkeepers!

In other words: If the soccer match is like ALM versus Manchester United NO clever bookkeeper will offer bets


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Acceptable quotes must be > 1

Is there any rule for the max. quote?

Yes: The bookkeeper must be able to pay the winners! Let the students calculate examples.


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Hint: Spread sheet is very useful!

Let the students type in the formulas and let them use the spread sheet for experiments


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One of many experiments: How fast should a bookkeeper react (=change quotes) if the bets show new tendencies?

Answer: Very fast is very good!


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Thank you very much for your attention!

Juergen


Documents

Bet and Lose: Learning Mathematics or Loosing Money by Juergen Maasz and Hans-Stefan Siller