Economics 7 Week Challenge Series – Challenge 7: Pick-a-door and Challenge Series Results

What is the Pick-a-door challenge?

For the benefit of those who did not enter this challenge, here is a brief explanation of how the game works.

In this challenge, participants were required to make decisions based on expected payoff and risk. Participants were presented with 12 doors. Behind each door there could be a prize (expressed in dollars). Each door had a possible prize worth a different amount. As the value increased the probability of the prize being behind the door decreased. For example, Door 3 had a 72% chance of a prize worth $40 and Door 7 had a 40% chance of a prize worth $88. If the prize is not there, the participant will receive a value of zero.

Opening a door cost $10, each participant was given a budget of $40. Therefore, each participant could open as many as 4 of the 12 doors. Participants were not compelled to use all of the budget. If a participant opened 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. combined value of prizes minus cost of opening doors).

Responses to the challenge were made in the comments section of the challenge post. If several participants make the same profit, the person who entered (commented) first wins. The total prize for this challenge is equivalent to 5 times the number of participants (e.g. if challenge has 8 participants the prize will be 40 Hive (5 × 8)). The maximum prize for this challenge is 60 Hive. The winner receives 2/3 of the prize and second place receives 1/3 of the prize. In addition to the winning prize, the first 12 entries are given upvotes.

The format of the required entry is explained in detail in the challenge itself.

For a more detailed explanation, you can access the challenge post using the following link.

Other challenges

There are six other challenges in the series. The links to all the challenges can be found below.

• Challenge 1: Auction
• Challenge 2: Buying and Selling Game (Business Version)
• Challenge 3: Tax Game (New)
• Challenge 4: Game Theory
• Challenge 5: Make Me Happy
• Challenge 6: Buying and Selling Game (Original Version)
• Challenge 7: Pick-a-door (New)

Results of Challenge 7

Table 1 contains the participants and the doors they selected.

Table 1: Doors selected by participants

Table 2 contains the potential prizes behind each door, the probability that the prize will be there, and the actual prize based on the Excel Model.

Table 2: Prizes behind each door

Table 3 contains the prizes each participant won, total value of prizes, the criterion of no more than one door with a value of zero (eliminated participants totals are in red font), and the Challenge winner (highlighted in green).

Table 3: Challenge Winner

Out of the 23 participants who entered, 11 were eliminated for opening more than one door with a zero value. Of the remaining 12 participants, @joshstick28 obtained the highest total value of $258. Every door opened had a positive value. This included doors with high values such as 7 and 9. @joshsticks28 wins 40 Hive and 40 points. In second place is @khingstan who selected three doors with positive values and managed to accumulate a total value of $198. @khingstan wins 20 Hive and 20 points. In third place is @ksam who also selected three doors with positive values. The total of these values were less than @khingstan's total and amounted to $189. @ksam is awarded 10 points.

None of the participants managed to open the combination of doors that would have achieved the highest possible total. This combination would have been Doors 5, 7, 8, and 9. This would have accumulated a total prize worth $312. The participants still did very well. Selecting the optimal combination would have involved considerable luck.

Challenge Tips and Analysis

This challenge relies very heavily on luck. Any of the doors could have prizes behind them. As more participants enter the results depend even more greatly on luck. Even so, a good strategy could increase your chances of winning. It helps if participants have a good idea of the number of participants entering and the choices they have made. Therefore, entering late offers an advantage in that aspect. For example, if only two participants have entered. Participant 1 has decided to open only Door 1 and Participant 2 to only open Door 12. At this point, Participant 1 has a 64% chance of winning, Participant 2 only has a 20% chance of winning and there is a 16% they will tie. Participant 3 could choose to open just Door 2, 3, 4, or 5 to have a better chance of winning than either Participant 1 or 2. If Participant 3 knows no other participant will enter, opening Door 2 is the best option. Participant 3 would have a 60% chance of winning, Participant 1 will only have a 16% of winning (very big drop), and Participant 2 would still have a 20% of winning. As more participants enter, the chances of winning from selecting high percentage low payout options decreases significantly. Low percentage high payout options may fall but by a lower percentage.

Race to become the Challenge Series Champion

We have the results from all 7 Challenges. Therefore, we can declare an overall challenge series winner. The table has been updated with the results from Challenge 7; see below.

Overall Series Score

The overall winner of the 2022 Economics Challenge Series is @pana1. Congratulations on your consistently strong performance across several challenges. @pana1 came first in both versions of the Buying and Selling Game (Challenges 2 and 6 respectively) second place in Challenges 1 (Auction) and 5 (Make Me Happy).

Your prize is determined by the total number of participants across all seven challenges. Each participant adds 1 Hive to the prize until the prize is capped at 80 Hive. Across all seven challenges there were 100 participants. Therefore, @pana1 has won the maximum prize of 80 Hive.

Over the seven challenges 530 Hive has been given away (120 Hive was given away in Challenge 4 to 2 winners). It was this high because of the level of participation. It would not have been possible if so many people had not entered. A big thank you to all those who participated.

More posts

If you want to read any of my other posts, you can click on the links below. These links will lead you to posts containing my collection of works. These 'Collection of Works' posts have been updated to contain links to the Hive versions of my posts.

My CBA Udemy Course

The course contains over 10 hours of video, over 60 downloadable resources, over 40 multiple-choice questions, 2 sample case studies, 1 practice CBA, life time access and a certificate on completion. The course is priced at the Tier 1 price of £20. I believe it is frequently available at half-price.

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