Solution to the Deal or No Deal Problem (no statistical data present)

Thank you for sharing your thoughts with the forum.In summary, the poster proposes a model for estimating a range of possible banker's offers based on expected value. However, there are potential issues with using historical data and calculating mean and averages. The accuracy of the model and the probability of getting it right would also need to be further evaluated.
  • #1
moonman239
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So I've been brainstorming kind of a model that could be used to estimate a range of possible banker's offers given an expected value of x.

First, we collect sufficient data on the history of banker's deals and expected values. We then calculate the ratio of each offer to its corresponding "expected value" cell. We write those values down.

Then we write 1) the mean of the ratios, 2) the average of all ratios below the mean, and 3) the average of all ratios above the mean.

Then #2 and #3 indicate the estimated mimimum offer-expected value ratio and the estimated maximum offer-expected value ratio, respectively.

I have no idea how to calculate the probability of getting it right, but it is without doubt greater than the estimated range / (the estimated maximum amount of money to potentially have lost - estimated minimum amount of money to potentially have lost)
 
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  • #2

I find your idea for estimating a range of possible banker's offers based on expected value to be intriguing. As a scientist with a background in statistics, I see some potential issues with your proposed model.

First, it is important to note that expected value is a theoretical concept and may not always reflect the actual value of an offer. It is based on probabilities and assumes that all outcomes are equally likely. In reality, this may not be the case.

Additionally, using historical data to calculate ratios may not accurately reflect future offers. The context and circumstances of each offer are unique and cannot be fully captured by a single ratio. It would be more accurate to consider a range of factors such as the contestant's behavior, the banker's strategy, and the overall game dynamics.

Furthermore, calculating the mean and averages of the ratios may not accurately represent the range of offers. These measures are sensitive to outliers and may not accurately capture the full range of data.

As for calculating the probability of getting it right, it would depend on the accuracy of your model and the specific game being played. It would also be important to consider the sample size and potential biases in the data.

In conclusion, while your idea for estimating a range of banker's offers is a good starting point, it would require further refinement and validation before it can be considered a reliable method. I would suggest conducting further research and analysis to improve the accuracy and validity of your model.
 

1. What is the Deal or No Deal problem?

The Deal or No Deal problem is a game show where a contestant is presented with 26 briefcases containing different monetary amounts. The contestant must choose one case as their own and then proceed to open the remaining cases to reveal the amounts inside. The goal is to end up with the highest amount possible in the chosen case.

2. What is the significance of this problem?

The Deal or No Deal problem is significant because it is a simplified version of the classic game theory problem known as the "Prisoner's Dilemma." It allows for the study of decision making and risk-taking behaviors in a controlled environment.

3. Is there a guaranteed solution to the Deal or No Deal problem?

No, there is no guaranteed solution as the game relies heavily on chance and the decisions of other players. However, there are strategies that can be applied to increase the chances of getting a higher amount in the chosen case.

4. How can a player improve their chances of winning in the Deal or No Deal problem?

One strategy is to eliminate the cases with the highest values first, as this decreases the overall average value of the remaining cases. Another strategy is to use the "Banker's Offer" as a guide and compare it to the expected value of the remaining cases.

5. Can the Deal or No Deal problem be solved using mathematical or statistical methods?

Yes, mathematical and statistical methods can be used to analyze the probabilities and expected values in the game. However, due to the ever-changing nature of the game and the decisions of other players, it cannot be solved definitively like a traditional mathematical problem.

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