Thanks for taking the time to compare these strategies in a quantitative manner. I wanted to ask though, Ii you took the opportunity to say double the trial length, Did results ever change in favor of the pop-pop strategy?
Hey there! Thanks for writing, and for the great questions! You can show (using probability) that neither strategy has a *statistical advantage over the other (although Pop Pop's method certainly is easier to fill out the ticket!). The reason I use this problem is so that my students can see how a margin of error can be used to either support or refute statistical significance. Of course, with Powerball, you know exactly how many possible tickets there are (almost 200 million!) so you can enumerate exactly how many winners there are. In research statistics, you have no such luxury, in general - you usually can't enumerate the population. So, you draw a random sample and add a MOE. Your question also made me think of the comparison of practical versus statistical significance: sure, we could run the randomizer as many times as we liked (assuming you had a better CPU than mine!), and, perhaps, one result might show a slight advantage (due to decreasing MOEs with increasing sample sizes). But, again, that's a slightly convoluted strategy - almost like repeating an experiment until you get a result you desire, and then stopping. But! Therein lies the catch-22: in this case, we can show (probabalistically) that there is no difference in the two methods. But that's only because we can exactly enumerate the possibilities. In research stats, you generally *can't...and therein lies the need for controlled, unbiased, replicated experiments: tO tease out what might (or might not) be there, and to analyze the chances that we're wrong. Be well!
