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Looked at some lottery wins and something was fishy. This a lottery where you pick 5 numbers out of the set (1,2, ..., 50). When no one wins, the money goes to the next iteration of the game so the prize gets bigger and bigger. It seemed that a win was too regular around every 2 or 3 weeks and never occurred in consecutive draws. As if people were waiting for the money to accumulate, which is probably true but there is another possibility also, and that is fraud by the organizers: too few people play, no wins occur at all for ages, and because this demotivates players and could reduce sales to a possible collapse, the organizers cheat and win the prize themselves periodically. How would you investigate this mathematically based on the observed distribution of time between wins? What is the expected mean and standard deviation of the time between (full-match) wins? Given the number of 5-number sets played in each iteration: K = 100,000 and iterations per week = 2.

The observed time between wins seems to have a sharp distribution with a mean around 2.5 weeks and this is fishy. Based on an observation like this, what is the probability that the organizers cheat?

What should K be to match the observed mean time between wins?

The observed time between wins seems to have a sharp distribution with a mean around 2.5 weeks and this is fishy. Based on an observation like this, what is the probability that the organizers cheat?

What should K be to match the observed mean time between wins?

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