Deal or No Deal: Lessons in Decision Making
"Deal or No Deal" was a wildly popular American TV show that aired from 2005 to 2019, capturing audiences with its simple yet gripping concept. The show, based on a Dutch format from 2000, inspired versions in over 80 countries and even reruns today. A new spin-off, "Deal or No Deal Island," is set to premiere in 2024, proving the enduring appeal of the game.
The Game's Basics
In "Deal or No Deal," 26 briefcases are presented on stage, each containing a cash value ranging from one penny to one million dollars. The contestant picks one case to hold onto while they eliminate others, hoping their chosen case has the highest value. As they open and discard cases, their chances of winning specific amounts decrease.
The twist? Periodic cash offers tempt contestants to quit the game. These offers are calculated as a percentage of the average remaining amounts. The contestant must decide: take the guaranteed cash or risk it for a potentially higher reward.
The Drama of Decision Making
The real magic of "Deal or No Deal" lies in the drama of these decisions. Contestants face the fear of losing a guaranteed offer versus the greed and hope of winning more. They declare "Deal" to accept the offer or "No Deal" to continue playing.
This game offers a public demonstration of decision-making. Years of gameplay data reveal that most offers made to contestants were mathematically bad deals. Over 80% of the offers were less than the fair expected value of an unopened case. Furthermore, no fair deals were offered when more than six cases remained, likely a tactic to prolong the game.
Calculating Fair Offers
To understand why most offers are mathematically bad, let’s delve into how fair offers are calculated. The expected value of a briefcase is the average of the remaining amounts. For instance, if only two cases are left with $10 and $200,000, the expected value is ($10 + $200,000) / 2 = $100,005. Any offer below this amount is considered a bad deal because it’s less than the statistical average the contestant can expect to win.
The show's producers often offer less than this expected value to increase the game's suspense and encourage contestants to continue playing, creating more dramatic moments. For example, if the expected value is $100,005, the banker might offer $70,000. Mathematically, the contestant should refuse this deal because it’s less than the expected value. However, the fear of ending up with only $10 might push them to accept it, illustrating the psychological impact of asymmetric risk.
Understanding Asymmetric Risk
Asymmetric risk refers to situations where the potential losses and gains from a decision are not balanced. In "Deal or No Deal," the offers made by the "banker" often create an asymmetric risk scenario for the contestant.
Historical Data
Analysis of historical data from the program shows that with more than six cases left, the offers are almost always below the expected value. This is because the producers aim to create tension and encourage risky decisions. By waiting until there are fewer cases, contestants can make more informed choices based on a better understanding of their potential winnings.
Making Smarter Decisions
Given this data, a simple strategy emerges: don't take a deal with more than six cases left. The offers are typically not in the contestant's favor, making it a safer bet to hold out longer.
The Personal Factor
Decisions on "Deal or No Deal" are made under intense pressure—studio lights, a live audience, and loved ones' advice. But ultimately, it's about real-life stakes. The show's drama stems from balancing these high-pressure moments with contestants' real-world needs.
Imagine a contestant with a $75,000 medical bill for a sick child. Even if the offer is slightly less than the mathematical expectation, accepting it ensures her child's health and leaves some money in the bank. Here, the emotional and practical aspects outweigh the pure numbers.
Examples of Asymmetric Risk
Real-Life Scenario
In our example, consider a contestant offered $94,000 when the fair value is $100,005. Mathematically, it's a bad deal. But if she needs $75,000 for a medical bill, taking the offer ensures she can pay for her child's treatment and still have $19,000 left. The risk of refusing the offer and ending up with only $10 is too great, highlighting the asymmetric risk in her situation.
Casino Betting
Another example of asymmetric risk would be to simply bet $100 on red at a roulette table. The best outcome is winning $100, but the worst is losing $100. Although the financial outcomes are symmetrical, the odds are not. An American roulette wheel has 38 slots: 18 red, 18 black, and 2 green (0 and 00). The probability of winning on black is 18/38, or about 47.37%. The odds of losing are higher at 52.63%, making it an asymmetric risk against the player.
Psychological Impact
Understanding asymmetric risk also involves recognizing the psychological impact of potential outcomes. As former Jeopardy host Alex Trebek once said, "I don't gamble because winning a hundred dollars doesn't give me great pleasure, but losing a hundred dollars p***** me off!" This highlights how personal responses to winning and losing can create an asymmetric psychological impact, influencing decision-making.
A Simple Method for Better Decisions
You don't need to be on a game show to apply these lessons. Consider these six questions when faced with a decision:
Best Outcome: What’s the best possible result?
Likelihood: How likely is the best result?
Impact: How would the best result affect you?
Worst Outcome: What’s the worst possible result?
Likelihood: How likely is the worst result?
Impact: How would the worst result affect you?
Pair these questions (1 & 4, 2 & 5, 3 & 6) and assess if the outcomes are symmetrical. Let these insights guide your decisions.
Conclusion
Beyond being a TV game show, "Deal or No Deal" provides a study in decision-making under pressure. By understanding risk symmetry and considering personal contexts, you can make smarter choices in both high-stakes scenarios and everyday life. Recognizing asymmetric risk and its psychological impact can help you navigate complex decisions with more confidence and clarity.