Economics Challenge Series – Challenge 2: Pick-a-Door Results

Hi Everyone,

Welcome to the results post for the Pick-a-Door Challenge. During the month of August, I will post all the results of the 2023 Economics Challenge Series. I will gradually work through all the seven challenges posted in July. This post contains a video generating the results of the challenge using a Microsoft Excel Model.

Winner determined in this video

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▶️ Watch on 3Speak

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What is the Pick-a-Door Challenge?

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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 75% chance of a prize worth $26 and Door 7 had a 50% chance of a prize worth $74. If the prize is not there, the participant will receive a value of zero.

Opening a door cost $15, each participant was given a budget of $60. 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 Power (5 × 8)). The maximum prize for this challenge is 60 Hive Power. 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

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Below are the links to all seven challenges in the series.

• Challenge 1: Buying and Selling Game
• Challenge 2: Pick-a-Door
• Challenge 3: Complements and Substitutes
• Challenge 4: Buying and Selling Game (Business Version)
• Challenge 5: Ice Cream Game
• Challenge 6: Game Theory Game
• Challenge 7: Even-to-Win

Results of Challenge 2

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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 red).

Table 3: Challenge Winner

Out of the 24 participants who entered, 18 were eliminated for opening more than one door with a zero value. Of the remaining 6 participants, @ftouch obtained the highest total value. This amounted to $276. Three of the four doors opened had a positive value. This included doors with high values such as 8 and 12. @ftouch wins 40 Hive and 30 points. In second place is @wealthwess who also selected three doors with positive values and managed to accumulate a total value of $220. @wealthwess wins 20 Hive and 15 points. In third place is @emeka4. @practicaleric obtained the same total value as @emeka4 but lost the tiebreaker based on time of entry. @emeka4 obtained a total value of $146. @emeka4 is awarded 5 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, 8, and 9, and 12. This would have accumulated a total prize worth $430. @wealthwess was just one box away from obtaining this combination. The winning participants did very well. Selecting the optimal combination would have involved considerable luck.

Overall Series Score

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After just two challenges, the overall scores for the Challenge Series are as follows.

Position	Participants	Points
1	Ftouch	30
2	Practicaleric	25
3	Wealthwess	15
4	Semperfortis	10
5	Fatherfaith	5
6	Emeka4	5

This table will be updated in every results post.

Challenge Tips and Analysis

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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 an 83.6% chance of winning, Participant 2 only has a 12% chance of winning and there is a 4.4% they will tie.

Participant 3 could choose to open just Door 2, 3, 4, 5, 6 or 7 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 over a 70% chance of winning, Participant 1 would only have around a 17% of winning (very big drop), and Participant 2 would still have a 12% of winning. There would be less than a 1% chance of a tie. 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.

For this challenge, there were a high number of participants (24). Selecting low percentage high payout options would have been the best strategy. However, the rule of not opening more than one door without a prize, increases the risk from selecting these high payout options. This risk can be mitigated by selecting to open only two or three doors instead of four. For example, just opening Doors 11 and 12. This would have obtained a score of 180. In this challenge, that participant would have placed third.

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More posts

I have several collection of posts. I have organised these collections based on content and purpose.

The first collection contains six collection posts created before PeakD had the collection feature. Four of these posts relate to the core of my content, one of them contains all my Actifit Posts, and one of the them contains my video course ‘Economics is Everyone’.

The second collection consists of the posts that I consider define my channel. These posts are significant in terms of content as well as how they contribute to the growth of the channel. These posts reveal the most about what I believe in.

The third and fourth collection is what I call my ‘Freedom-base Economics living book’. They contain all the posts that support my ideas about the value and power of freedom. Some of these posts explain what we can achieve with freedom and what we need to utilise it. Some of them explain how we are deprived of freedom and how we often give up freedom for security and comfort. The third collection concludes with possible scenarios depending on what we (society) choose to do.

Hive: Future of Social Media

Spectrumecons on the Hive blockchain

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