Common Core Standards: Math
b. Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.
Here are some fun activities to get students thinking about games and probability. You can mix and match these activities to your liking. The goal is to help students combine and apply their knowledge.
Assign simple concepts like a toss of a fair die. Give payoff values to each number. Have everyone to toss the die and write down the numbers they roll. Calculate the empirical probabilities. Compare to theoretical probabilities and outcomes.
Get a coin that is unfair (or weigh a quarter down with some Play-Doh on one side to make it unfair). Assign numerical values for a heads/tails scenario. Make the students "pay" to play the game. Calculate out which scenario it's actually best to play in the long run, if any, based on payoffs, probabilities, expected values, and the cost to play.
Get a loaded die and a fair die. Give playoff values to each number. Have students roll the dice and record their values. See whether or not, through empirical data, students can determine which die is fair and which is not.