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Suppose you are about to play a football game. Your lucky number is 150. At the end of the game, you throw a game winning pass with 1:50 (1 minutes 50 seconds) left to play. The game ends up finishing at 1:50 PM. At the time of the game, you did not know this would happen. Someone lets you know of this after the game and you wonder if this is some sort of sign. In this case, you found meaning in some events after the fact.

Now imagine if my friend predicted this. He knew that my lucky number was 150 and predicted that I'd throw the game winning pass with that much time remaining and predicted that the game would end at 1:50 PM as well.

The second, intuitively, seems more remarkable and surprising. In hindsight, the probability of something meaningful happening in general in the game is much higher than the probability of my friend predicting those two specific events.

However, the probability of those two specific times coinciding with those specific events in the game is the exact same whether the knowledge of that event was in your mind before or not. So the question is, should this knowledge matter when evaluating the probability of whether or not this happened by chance? If you focus on the probability of those specific events happening, the first and second seem equally remarkable. Which probability is more relevant in determining whether this was by chance or not?

Secondly, even in the first scenario, no one would have found meaning in those times if 150 was not my lucky number before. Doesn't the act of the number 150 being in my mind serve as a sort of potential cause given that it occurred before the relevant events happened? Doesn't this sort of have the same epistemic value as my friend's prediction?

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  • Probability is based on knowledge of the possibilities. If you use the same possibilities, the calculation of the probability is the same. If you update the possibilities based on your latest information (that you know it happened), then the new probability is 1. Commented Jan 22, 2023 at 0:38

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Now imagine if my friend predicted this. He knew that my lucky number was 150 and predicted that I'd throw the game winning pass with that much time remaining and predicted that the game would end at 1:50 PM as well.

What knowledge was required to make these predictions? What calculations or theory was used to predict the ending of the game? What statistics were used to determine that the game winning pass would be thrown?

I see no evidence that this is anything more than coincidence or luck and would not attach any real value to that prediction. Because right or wrong, I learn nothing.

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