Suppose a rare event occurs. For example, suppose someone wins two lotteries in a year. This may have happened because it was rigged or because of chance. The defender of the chance hypothesis could point to how given that thousands of lotteries are played each year, one person winning twice is not that surprising. The defender essentially compares this event to other similar events (in this case lotteries) to rationalize it having occurred by chance. But how similar can the other events be?
Suppose there is a person Joe who tells you to think of a number between 1 and 1,000,000. He then says he'll try to guess correctly. Suppose he fails 1,000,000 straight times. Another person by the name of Jane comes in and says she can do the same thing. On her fifth try, she guesses correctly. Suppose you are now tasked to figure out whether that happened by chance.
If you are an attacker of the chance hypothesis, you might say that the probability of Jane guessing it right within five tries is very low. Therefore, it probably didn't happen by chance. The defender of the chance hypothesis might say "Well, both Joe's and Jane's events were guesses. The probability of atleast one guess being correct out of 1,000,005 guesses isn't that low." In this case, even though the events seem more dissimilar compared to the rigged lotteries case, the defender incorporates those trials.
This begs the question: when can we incorporate other trials? How similar can other trials be? And is similarity an objective property? Can it be said to be objectively true that the event of the New Jersey lottery occurring on Oct 8th and the New Jersey Lottery occurring on November 10th are more similar to each other than the events of Joe and Jane guessing a number? Why or why not?
What about the naturalness of certain categories? For example, suppose Adam thinks of Jane and Jane calls her. You might put this event into the category "thinking of someone and calling you" since it seems natural to do so. Then, you can simply recognize that tons of people have thought of someone and they didn't call. So this particular event may not be surprising.
But what if say you invent some new game where you write down a word of five letters and ask another person in front of you to write it down as well. And they match. The probability of this happening by chance is of course very low. The defender of the chance hypothesis can again try the strategy of putting this into a category of events to increase the probability. But which category does this belong to if this game has not been played before? If it hasn't been played before, does this make this event more impressive than the event of you thinking of someone and having them call you?
