Simple Questions

Whether or not you should consider each event or draw individually is a statistical question, which can be answered by e.g. repeatedly drawing and estimating the covariance between draws. There are some fancier models and techniques you could use in statistics, but at the basic level, what you're trying to check is that the estimated covariance is near 0, in which case you can somewhat confidently claim independence in each draw.

For the probability side of things, to compute the likelihood of winning sequentially a number of times, you would have to compute the joint probability. There are several ways to obtain the joint probability. One is to repeatedly draw so many times you have enough data to see how many sequential wins you get. This is slow and bad. Another is to accept a model, which means you have to estimate its parameters before you can compute the joint probability. One such parameter is covariance, as mentioned above.

In practice, you can intuit whether or not the lottery permits independent draws based on things like, how do they generate the randomness which selects the winner? Suppose it's a pure random number generator every game which means you can assume that each draw is independent. Then you could consider treating the lottery like a binomial distribution.

/r/math Thread Parent