How about the game show "Deal or No Deal". Though not emphasized the banker is checking the probability given the number of remaining suitcases what the probability is that the 1,000,000 dollar prize is in your suitcase. Based on the odds he makes an offer that favors him. Whenever I watch this I am hoping the contestant understands expected gain and expected loss so as to not go for the bankers offer unless it is close to fair and a lot of money. As the game progresses an instructor can explain the odds and show the student how to compute what a fair offer would be.
The famous game show "Let's Make a Deal" had that flavor in it for the deal of the day at the end of the show. A slight modification led to the famous Monty Hall problem that baffled even some famous mathematicians.
Other games have aspects of probability in their decision making. With the spinning of the big wheel, there is the decision to hold with the first spin result or gamble to add to a higher total with the risk of going over $1. Even if you don't have a good prior distribution for the price of an item, bidding strategy can be partially based on an idea of a bet that is going to be reasonable and have a better chance of winning than the competitors. The best example is when you bid in the last position and the highest bid so far has a good chance in your mind to be below the actual price. Then bidding 1 dollar over it (the minimum that you can bid over) is a very good strategy. Many people actually use that strategy and very often are successful.
In addition I think Jeopardy with a statistics board of categories might be a fun way to reinforce concepts through competition. I have seen this work well and be fun for medical topics and once played it on categories for nutrition to teach good eating habits.