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Apr 3, 2024
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Experiment 1 Results Analysis:
Probability of Winning $80
: The probability being 1.0000 suggests that in every simulated episode of 1000 bets, the player always reached the target of $80. This high success rate is likely due to the nature of the betting strategy (Martingale system) and the absence of a betting limit. The strategy involves doubling the bet after each loss, which theoretically ensures eventual recovery of all losses plus the initial bet amount. However, this result might not be realistic in practical scenarios due to table limits and the gambler's finite bankroll.
Expected Value
: The expected value being exactly $80 indicates that, on average, the player ends up with their target amount in each episode. This aligns with the probability result and reaffirms the effectiveness of the strategy under these idealized conditions.
Experiment 2 Results Analysis:
Probability of Winning $80
: The probability of 0.7820 (or 78.20%) in
Experiment 2 is significantly lower than in Experiment 1. This reduction
is due to the introduction of a $256 bankroll limit, which adds a realistic constraint to the betting strategy. It shows that while the player still has a high chance of reaching the $80 target, there are instances where they deplete their bankroll before achieving this goal.
Expected Value
: The expected value of $6.75 is the average amount the player ends up with after 1000 bets. This lower expected value, as compared to Experiment 1, reflects the impact of the bankroll limit. While the player often reaches the $80 target, the instances of losing the entire $256 bankroll significantly bring down the average winnings.
Implications and Real-World Relevance:
These results highlight the influence of betting limits and finite resources on gambling strategies. While the Martingale system can be effective in an idealized scenario (unlimited bets, no table limit), its practical application is risky and can lead to substantial losses, as seen
in Experiment 2.
The high probability of success in Experiment 1 is an artifact of the simulation's assumptions and should be interpreted with caution, especially in real-world gambling scenarios where such conditions are rarely, if ever, met.
The findings from Experiment 2 are more aligned with realistic gambling situations, showing a mix of successful and unsuccessful outcomes based on the imposed bankroll limit.
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Related Questions
A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were
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B = individual purchased the product
S = individual recalls seeing the advertisement
BnS = individual purchased the product and recalls seeing the advertisement
The probabilities assigned were P(B) = 0.20, P(S) = 0.40, and P(BS) = 0.12.
a. What is the probability of an individual's purchasing the product given that the individual recalls seeing the advertisement (to 1 decimal)?
Does seeing the advertisement increase the probability that the individual will purchase the product?
- Select your answer -
As a decision maker, would you recommend continuing the advertisement (assuming that the cost is reasonable)?
- Select your answer -
+
b. Assume that individuals who do not purchase the company's soap product buy from its competitors. What would be your estimate of the company's market
share (to the…
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70% chance that the patent will be awarded and
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