Economics Challenge Series 2025 – Challenge 3: Pick-a-Door

Hi Everyone,

Welcome to the Economics Challenge Series for 2025. For July and August, I am running an economics challenge series. The series consists of six challenges. All the challenges will commence in July and early August. I will publish and announce the results in August.

Five of the seven challenges from last year's Challenge Series return. The Auction Challenge is replacing the Complement vs. Substitute and Tax Game challenges. This year because of time constraints, I have reduced the number of challenges from seven to six. Below is the list of challenges.

Challenge 1: Game Theory Game
Challenge 2: The Buying and Selling Game
Challenge 3: Pick-a-Door
Challenge 4: Ice Cream Game
Challenge 5: Auction
Challenge 6: Even-to-Win

Each challenge could reward winners with as much as 60 Hive Power. The value of the prize will depend on the level of participation. For each new participant, the prize will increase by 4 Hive Power. This increase will continue until 60 Hive Power is reached (15 participants). The first 15 participants will also receive a 50% upvote from this account.

In addition to the prize money, the top few participants will be given points. These points will be used to determine the overall challenge series winner. This winner may receive as much as 80 Hive Power. The value of the prize will equal the sum of the number of participants across all challenges. This will continue until 80 Hive Power is reached.

Welcome to the Pick-a-Door Challenge

How to Play?

In this challenge, participants are required to make decisions based on expected payoff and risk. Participants are presented with 12 doors. Behind each door, there could be a prize (expressed in dollars). Each door has a possible prize worth a different amount. As the value increases, the probability of the prize being behind the door decreases. For example, there might be an 85% chance there is a prize worth $28 behind Door 3, and there might be a 40% chance there is a prize worth $125 behind Door 9. If the prize is not behind the door, the participant will receive a value of zero.

Opening a door incurs a cost. Each participant is given a budget of $60. Therefore, each participant can only open as many doors as their budget permits. Participants are not compelled to use all of the budget. If a participant opens 2 or more doors that have zero value behind them, they are eliminated from the challenge. If not eliminated, the winner is the participant with the highest total value expressed in dollars (i.e., the combined value of prizes minus the cost of opening doors).

All entries must be made in the comments section of this post.

Each account is only permitted one entry.

Objectives of the Game

The objective of the game is to obtain the highest prize value minus costs without opening more than one door that has a value of zero. The participant who can do this will be the winner.

Game Assumptions

The value revealed behind each door is what each participant who selected that door wins. There is no sharing of prizes in this challenge.
All doors cost the same amount to open ($15 for this challenge). Not opening a door has zero cost.
If it is revealed that the door does not have a prize behind it, the value is zero and the fee required to open the door is lost.
Based on the budget allocated and the cost of opening each door, each participant can only open a maximum of 4 doors. However, the participant may choose to open less.
If a participant opens more than one door that does not have a prize, he or she is eliminated from the challenge regardless of the value accumulated from the doors that have prizes behind them.
The order in which the doors are opened does not affect the probability of a prize being behind them.

What Information is Provided?

All possible prize values behind each door are provided.
All probabilities that these prizes will occur are provided.
Cost of opening doors is provided.

How are the Results of the Game Determined?

A Microsoft Excel model is used to determine if the prizes are behind the doors. The model will calculate each participant’s winnings as well as determine the overall winner. The results post will contain a video of the model generating all relevant values. The winner will be announced in both the video and the written post.

Challenge Prizes

The total prize for this challenge could reach as high as 60 Hive Power. The number of participants determines the value of the prize. For every entry, the prize is increased by 4 Hive Power until a value of 60 Hive Power is reached. The winner will receive 2/3 of the prize, and second place will receive 1/3. The first 15 entries will be given upvotes. The winner of this challenge will be given 40 points, second place 15 points, and third place 5 points. These points will be tallied at the end of the challenge series to determine the overall winner.

Let the Challenge Begin!

Participants can choose to open up to 4 of the 12 doors for a chance to win prizes valued in dollars. Figure 1 contains the twelve doors, the value of the prizes that might be behind them, and the probability that this will occur.

Figure 1: Value of Prizes and Probability

The cost of opening each and every door is $15. The fee is deducted from the value won to determine the overall value gained.

Entry Format

For this challenge, I expect to see entries made in the following format:

Doors Opened:
Door: W
Door: X
Door: Y
Door: Z

Example of Entry

Doors Opened:
Door 3
Door 6
Door 9
Door 12

The closing date and time for this challenge is 6PM coordinated universal time (UTC) 27/07/2025. Responses after this time will not be accepted. The results of the challenge will be announced in a separate post.

I hope everyone has fun and enjoys this third challenge. If you have any questions, feel free to ask in the comments section. I look forward to your participation in the next challenge. It will be available in a few days.

The Sapien Loop Series

I am writing a trilogy of books titled Sapien Loop. The first in the series is Sapien Loop: End of an Era and the second is Sapien Loop: Frozen in Time. I published both of these books as ebooks on Amazon, and I have posted completed chapters to my @captainhive account. I anticipate publishing the third book in early 2027. I expect to title this book Sapien Loop: Worlds Collide. In 2025, I plan to write short stories about some of the characters and their adventures. I will post these to my @captainhive over the course of the year.

Brief Summary of Sapien Loop: End of an Era

This story is based on the fictional planet Sapia and its sole country, Sapey. Sapey is portrayed as a form of utopia for all its citizens. No poverty. No war. Almost no crime. Opportunities for all.

This was enough for most citizens, but not all. In one of the small regions, some of the citizens had become discontent. They felt something important was missing in their lives. Their discontent did not go unnoticed. Some of the Sapey elite wanted to weaponise this discontent to gain more power. This created more chaos than they anticipated. This led to further widespread social unrest.

On top of the chaos, ambition and greed provoked another enemy. This enemy was on a mission to settle both new and old scores.

Brief Summary of Sapien Loop: Frozen in Time

This story is based six years after the original story. The Downs Region is still suffering from a serious health crisis caused by the contaminated water. The main characters are desperately trying to find a cure for the illness that has been caused by the water.

One of the main characters has discovered frozen humanoids in hidden chambers. It appears they have been frozen for a long time. These chambers connect to a vast network of tunnels. While exploring the tunnels, one of the frozen humanoids disappears. It appears he has been stolen.

The story takes a step back in time to tell the story of the frozen humanoids. How and why were they frozen? This part of the story also explains the fall of ancient Sapey and the birth of the Sapiens. Can those from the past be able to coexist with those from the present?