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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:


Place your bet using the panel below.

Type the amount of your wager below.


Which side of the coin will you bet on?

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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:

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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?'."

Sheila Camp,

Saturday, July 17, 2021

" is a company dedicated to helping those who struggle with addiction and co-occurring mental health conditions. They provide resources for those in need as well as information on how to help loved ones struggling with these issues. Their goal is to make the world a better place by making it easier for everyone to talk about their struggles without fear of judgment or stigma on addiction.

There is an informational guide at "

Helen, Sydney

Friday, September 16, 2022

"This was good until my students discovered "spamming the button" like crazy caused them win thousands of pounds.

[Transum: Thanks for the feedback Helen. By "spamming the button" do you mean clicking the button repeatedly very quickly? I have tried that and the only affect it has is to speed up the process. It doesn't change the probabilities at all]"

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© Transum Mathematics :: This activity can be found online at:

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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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


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