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The Mathematics of Gambling

Learn more about probability so that you are better able to make informed choices.

Simulation Description Exam-Style More Probability
Toss Coin Start Again

The coin is biased. It has a 60% chance of landing heads up and a 40% chance of landing tails up. You have the following amount of money to play with:

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Place your bet using the panel below.

Type the amount of your wager below.

£


Which side of the coin will you bet on?

Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

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Arrange the given digits one to nine to make three numbers such that two of them add up to the third. This is a great puzzle for practicing standard pen and paper methods of three digit number addition and subtraction.

Numeracy

"Numeracy is a proficiency which is developed mainly in Mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables."

Secondary National Strategy, Mathematics at key stage 3

Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths main page links to more activities designed for students in upper Secondary/High school.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Transum,

Wednesday, August 14, 2019

"The International Baccalaureate syllabus document suggests topics for discussion such as 'can calculation of gambling probabilities be considered an ethical application of mathematics?' and 'should mathematicians be held responsible for unethical applications of their work?'."

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=810

Description of Activity

This activity represents an experiment conducted to test people's understanding of probability by two investment fund managers.

The Economist reported that Victor Haghani and Rich Dewey invited 61 people, a combination of college-age students in finance and economics and some young professionals at finance firms (including 14 who worked for fund managers), to take a test. They were each given a stake of $25 and then asked to bet on a coin that would land heads 60% of the time. The prizes were real, although capped at $250.

Remarkably, 28% of the participants went bust, and the average payout was just $91. Only 21% of the participants reached the maximum. 18 of the 61 participants bet everything on one toss, while two-thirds gambled on tails at some stage in the experiment. Neither approach is in the least bit optimal.

The best strategy was devised by J. L. Kelly, Jr, a researcher at Bell Labs, in 1956. The idea of this simulation is for players to work towards finding what this best strategy might be. Good luck.

Just for fun, if you accumulate over £1000 you will be awarded with a trophy for being skillful and lucky.

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Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on probability including lesson Starters, visual aids, investigations and self-marking exercises.

Did you know that Blaise Pascal and Pierre de Fermat invented probability theory in 1654 to solve a gambling problem?

WARNING: In the real world commercial gambling operations have a much smaller change of you winning money than this simulation. For more information about the dangers of gambling see RaisingChildren.net.

Example

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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