Gambling in Maths

July 18, 2014

This is the second lesson in a probability project where students use probability to design a casino gambling game. In the first lesson the class created a spinner using fixed probabilities and compared the expected frequency of events with the actual results. This concluded with a discussion about the difference between theoretical and experimental probabilities, bias and relative frequency.

The aim for this lesson is to use the best spinners to set up and play a casino gambling game. The odds for the game were calculated using the relative frequencies of the events on the chosen spinners. The learning objective and success criteria are shown.

Choosing the Spinner

The class are asked to sort themselves into groups of 4 or 5. We discuss the findings from the previous lesson using the results that were obtained from two different spinners.

Teacher: Which was the best built spinner? How do we know this?

Class: Spinner A was the best build since the actual frequencies more closely matched the expected.

Teacher: Which spinner had the greater bias? Where was this bias?

Class: Spinner B had the greater bias since number 10, which is even, occurred more than expected.

Students were then asked to choose the best spinner in their group for the remainder of the lesson. The person who made the spinner was made the banker for their group from this point on.

Deciding the Odds

I explained that the remainder of the lesson would be used to create a gambling game using the spinner. Every student, apart from the banker, would be given an equal amount of pretend money to gamble on the outcome. However, we must first decide the odds for each event. Given that each group was using a unique spinner with its own bias the odds would be different. The banker would decide the odds while the remainder of the group shared the money.

The bankers were challenged to create odds that would encourage players to gamble the most money on the event least likely to occur and the least money on the event most likely. As a teacher I left the decision of these odds completely up to the bankers. The table below shows the odds used for spinner A.

Gambling

With the odds chosen, a banker and spinner appointed and the pretend money equally distributed amongst the players the bankers were given their funds to begin the activity. Quickly enough the students began waging money on their chosen events. After each spin the bankers needed to collect the money from the losing bets and pay the winners. For events with the odds 1 : n this was a simple process. However, with odds such as 2 : 3 students needed to use equivalent ratios to calculate how much to pay back. With the winners eager to collect their money this application of ratio seemed much quicker than when I had taught it a couple of months previous.

The gambling itself lasted 15 to 20 minutes. By this point either all the players were bust or the banker was.

Concluding the project

With the gambling over and the majority of the kids exhausted from the excitement we had a brief discussion in groups as to why some of the bankers went bust and whether this is what happens in real life. Here are the points that arose:

• The odds needed to favour the banker. For instance, rather than choosing 2 : 3 a more suitable ratio could have been 3 : 5. However, this could have been more difficult to calculate when paying back the money.
  
• As the game went on the spinner became damaged which altered the probability of landing on certain events while the odds remained the same.
  
• Using a greater sample size when testing the spinner would have led to more accurate experimental probabilities.
  
• The banker needed to be given a larger fund as eventually, after a large enough sample the probabilities would have levelled out.
  

How would you teach a lesson that reached similar learning objectives?

Do you agree with using gambling in education in this way?