"Deal or No Deal" Probability Game

A very fun game was played in the math class during a sample lesson on probability. We played "Deal or No Deal", based on the game show. We were divided into groups of two. In each pair, one person was the banker and the other was the contestant. We had a chart covered in cards, each of which having a dollar value on the underside of the card. The contestant picked a card at random, and the banker and contestant then haggle over how much the banker will pay for the card. During each round, the values on the remaining cards are gradually revealed, giving the contestant and banker information with which they can try and figure out how much the contestant's card might be worth. The trick is that the banker wants to buy the card for less than it's worth and the contestant wants to sell it for more than its worth. To take an extreme case, suppose all the cards have been revealed and we know that the contestant's card is either worth $1 or $500,000. If the banker offers $250,000, each player has a 1/2 chance of making or losing $250,000. Would that be a good offer from the banker? Perhaps. The interesting part of this game is that while the probability is important, there is also a lot of room for judgement. If I was the contestant, I would take the $250,000. If I was the banker, I would probably offer a lot less than $250,000 since I would rather earn $500,000 or nothing than make or lose $250,000. However, since the contestant only stands to gain, there may be a "bird in the hand" type of reasoning that would make the guarenteed $250,000 more attractive than the $500,000 or nothing. In short, there's a lot of higher-level thinking that can go into strategy for this game, and could have interesting applications in financial math and economics as well. If I ever get to teach data, it's definitely a game I would try to incorporate.