He does not say “Here, take the Expected value of $131,477.54 and thank you for playing!”. The Banker does not initially offer you money to not even start playing the game! (That would make for very boring TV). “All plans are great until the first shot is fired” If you walk away from the game with more than this amount, you have done well. The expected value of the entire game is $131,477.54 Expected value is the outcome that would be obtained if it were possible to play the game an infinite number of times and the results averaged.Įvery case can be selected with equal probability, so if a case were selected at random and the game played to completion, then this was done over and over and over again, and the results averaged, the expected outcome (gain) would simply be the arithmetic mean of the prize values. Statisticians call this the Expected Value. Mathematically, the potential payout of the game is easy to calculate. Alternatively if the case contained the penny, he might consider making ‘poor’ offers in an attempt to keep the player in the game and eliminating higher prizes as he does). (If the banker was malicious and knew the player had selected the million dollar case, he might want to make ‘good’ offers to the player to encourage him to take a deal and stop. The Banker's attempts to manipulate and tease the player (in the interests of making entertaining TV) have to be done without actual knowledge of what is present in the selected case. Web searches and commentary suggest that the Banker does not know the value of the prize in the player's case, so this removes one angle of the game (the Monty Hall complication). There’s a lot of psychology in this game. Once a player elects to continue the game he must eliminate cases to reach the end of a batch (no matter how ugly things get). After this, cases are opened singly with an offer after each. If the deal is not taken, the player is committed to eliminate the next batch of five cases, then receives another offer. In the US, here is a list of all twenty-six prize values in the standard game (occasionally specials are hosted with different prize structures, most usually replacing the million prize with a higher value): $0.01 $1 $5 $10 $25 $50 $75 $100Īfter selecting his prize case, the player must initially eliminate six cases before receiving his first offer. Is there skill in the game? Is there an optimal strategy? How should the game be played? Case Values A contestant makes choices throughout the game. It’s a gambling game, but it’s not just a lottery. Obviously there is a lot of luck involved. Similarly, the elimination of low-value cases is advantageous to the player.Īs more cases are revealed, more information is learned about what could probably be in the player's selected case. If many high-value cases are eliminated, the banker’s next offers may be lower as it is impossible for these high values to be in the player’s selected case. Since the distribution of prizes is initially unknown, the amount of money offered by the Banker changes as cases are revealed. The prize pool is defined and locked even before the game starts. The second is that the prize structure is clearly defined. The first is that it is impossible to lose! No matter what happens, the contestant will walk away with a prize (small or otherwise). There are some pretty obvious things that come to light immediately when thinking about this game: (The value of this final prize will be known as, through elimination, all other prizes values will have been revealed). In the latter case, the contestant leaves with the prize indicated in his originally selected case. This process continues until either an offer is taken, or all other cases have been revealed. Taking the Bankers offer (deal) ends the game and the player leaves with the offer made by the Banker.Ī call of “No Deal” commits the player to eliminate the next batch of cases. The player has just two options: DEAL or NO DEAL As cases are eliminated, their prize contents are revealed.Īt the conclusion of each batch of eliminations, a host (called ”The Banker”) offers to buy the contestant’s case back from him for a sum certain amount. The value of the prizes ranges from a solitary penny to a million dollars ($0.01 to $1,000,000).Īt the start of game, a show contestant selects one case (either at random, or through some other non-scientific and superstitious way) to be theirs, and then starts to eliminate other cases in prescribed batches. The basic concept of the game is that there are twenty-six identical briefcases secretly containing a spectrum of distinct prizes. All variants of the game are produced by Endermol. This show is based on an original Dutch show called Miljoenenjacht (Hunt for Millions).
There’s a popular game show on TV called Deal or No Deal.