How to design a profitable lottery algorithm?

Designing a lottery that attracts participants and guarantees profitability requires a clever balance of prize value, winning probability and participation costs. This article discusses how to automatically set the winning probability based on the prize value, striving to maintain a certain degree of fairness while ensuring profits. Assuming the participation fee is RMB 10, the prize pool contains a variety of prizes of varying values.

Problem description

Suppose a lottery event with participation costs of RMB 10, and the prize pool contains N different prizes, such as:

1. Mobile phone (500 yuan)
2. Tablet PC (300 yuan)
3. Watch (100 yuan)
4. Speaker (60 yuan)
5. Headphones (30 yuan)
6. Slippers (18 yuan)
7. Lighter (8 yuan)
8. Nail Claw (9 yuan)
9. Paper towels (6 yuan) ...

Assuming that the inventory of each prize is unlimited, the sum of the winning probability of all prizes is 100%. The goal is to design an algorithm that automatically calculates the winning probability of each prize to ensure the event is profitable.

Algorithm design and challenges

Ideally, the probability of winning each prize is inversely proportional to its value to ensure profitability. However, it is impossible to ensure that there is no loss in total, on the premise of ensuring the "authenticity" of the lottery (that is, every participant has the possibility of winning).

Any probability-based lottery mechanism is risky. Even if the probability is carefully set, there may be continuous draws of medium and high-value prizes, resulting in losses.

Therefore, it is impossible to ensure fairness, truth and absolute profit at the same time. We need to make a trade-off between "fairness" and "profitability".

Feasible strategies: risk control and expected returns

Instead of pursuing absolutely no loss, it is better to focus on how to control risks and maximize expected returns. The following strategies can be considered:

1. Expected income model: Calculate the winning probability of each prize so that the overall expected return of the activity is greater than 0. This requires consideration of the relationship between the number of participants, the value of the prize, and the probability. Mathematical models (e.g., linear programming) can be used to optimize probability allocation to maximize expected profits.

2. Set guaranteed prizes: Set a large number of low-value prizes to reduce the probability of winning medium and high-value prizes, thereby controlling risks. These low-value prizes can ensure that most participants can receive some rewards and improve user experience.

3. Dynamic adjustment probability: Dynamically adjust the winning probability of the prize based on the actual number of participants and the winning situation. For example, if the winning frequency of a high-value prize is too high, it can reduce its probability and vice versa.

4. Limit the number of high-value prizes: Limit the number of high-value prizes to avoid losses caused by continuous draws of medium- and high-value prizes.

In short, the key to designing a profitable lottery algorithm is to balance risks and returns and adopt appropriate strategies to control risks, rather than pursuing an impossible absolute profit goal. A good algorithm should ensure a certain profit while providing a good user experience and improving the enthusiasm of participants.

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