Deal or No Deal Risk Calculator
Reza Naghibi 09/20/2006 (updated 12/11/2018 secure)
- Toggle the X button to add (white) and remove (grey) a value from game play.
- Click on any amount to change its value.
- Fill in how many cases are required to be opened for the next round
Click Calculate to start calculations.
This page is my attempt to put some numbers and analysis behind the popular game show Deal or No Deal. What separates Deal or No Deal from a random game of chance is the fact that you can turn in your set of unopened cases for an offer at the end of each round. The offer is approximately the statistical mean of your unopened cases, whether it's a single case or a set of cases (note that the show will deviate their offer from the statistical mean). By allowing a group of cases to be turned in for an offer, the more cases in your group, the closer your mean will be to the original mean of the group. As the game continues on, your group shrinks and your mean value becomes more volatile and unstable, but it will eventually stabilize on your final case selection (in the show, it's the first case you select). The show counteracts this idea by lowballing your initial offers when your mean is more stable and by increasing the offers as your selection group shrinks and your mean becomes unstable. This idea basically rewards risky game play.
In the above chart, the risk or volatility level is calculated as the coefficient of variation; the standard deviation of every possible elimination combination over the current mean. The volatility percentage means that your offer is likely to change by that percentage after eliminating cases. Since the case values are fewer but comparatively have a heavier weight on the high end, a high volatility level means your next choice(s) has a risk of a large loss. A low volatility means that your next choice(s) are safe and you stand likely to make a modest gain.
Please contact me if you would like to throw in your $0.02. I am very open to hearing your opinions and to furthing my research into strategies of this game.