The Mathematics of GamblingLearn more about probability so that you are better able to make informed choices. 
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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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 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK: "I am an NQT and have only just discovered this website. I nearly wet my pants with joy. 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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© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=810
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 collegeage 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 twothirds 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.
Close
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you donâ€™t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
Exam Style Questions  A collection of problems in the style of GCSE or IB/Alevel exam paper questions (worked solutions are available for Transum subscribers).
More on probability including lesson Starters, visual aids, investigations and selfmarking 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.
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?'."
Sheila Camp,
Saturday, July 17, 2021
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There is an informational guide at https://www.addictionresource.net/behavioraladdictions/gambling/ "