CODEWITHSUNDEEP
phprandomprobability
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Reputation: 1037

Probabilities Function -

This is a bit of a math question, and cause am quite weak at math [ :( ] I can't figure this out

I have an application that must "randomly" decide if you won or not with a maximum daily winners, the problem is that i don't want to do a simple x chance of winning cause this might result in 20 people winning at the start of the day, and then everyone will keep losing, is there a generic formula to do this?

tl;dr

I have x amount of Gifts (x=20) The user must know immediately if he won or not (can't do it at the end of the day) And I want to randomly spread them throughout the day, is there a generic function/script?

After some suggestions in the comments, I could settle with either,

  1. a solution that takes a predictable number of daily contestants (i ll just have a random guess for the first few days and change it accordingly)
  2. a solution considering the time of the day, the gifts won so far, and the remaining gifts

Any ideas?

Upvotes: 0

Views: 79

Answers (1)

John Coleman
John Coleman

Reputation: 52008

There is no math question here, not really, just some decisions that you need to make.

One possibility is to make the probability of winning be X/N where N is the expected number of visitors, until the gifts run out for that day. It is random, so it might be the case that on some days the gifts exhaust early. So what? That is how probability works. Extreme imbalances are unlikely. For example, say you have 20 gifts and 1000 visitors on an average day. The probability that the gifts will be exhausted by the 500th visitor is a binomial probability: the probability of having at least 20 successes in 500 trials where the probability of success is 20/1000 = 0.02. This probability works out to be just 0.003.

On days when there are unclaimed gifts -- increase the gift count for the next day and correspondingly increase the probability of winning. If you spin it the right way, this could increase interest in the game in sort of the same way that people buy more lottery tickets on days when a jackpot goes unclaimed.

Note that essentially the same idea can be implemented on different time resolutions. For example, use 4-hour time slots in place of whole days (with X and N adjusted accordingly). This will guarantee a more even spread of the gifts throughout the day (but to pull it off you might need to take into account that the expected number of visitors in a 4-hour time slot is unlikely to be constant over the course of a day. Different time slots might need different denominators).

Upvotes: 2

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