[madnak]

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For instance, if one purchased a quick pick lotto ticket and the numbers came up 1 2 3 4 5 6. There is a good chance that person would be skeptical that the machine randomly produced those numbers. If that same person then purchased another quick pick ticket from the same machine and got the same numbers, 1 2 3 4 5 6, its not unreasonable for that person to think the machine is broke. I speculate that its more likely the machine is broke than it just happened to randomly produce the same set of numbers on two consecutive tickets. Nevertheless the machine can be working perfectly fine, even if it produces the same set of numbers on 10 consecutive quick pick lotto tickets.

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The likelihood of your ratio, given your loose standards, is at least 1/50. The likelihood of the lottery example is at most 1/1,000,000. So the situations are not analogous.

But as you acknowledge, it's perfectly possible for the lotto situation to be a coincidence. In a universe with trillions of ratios to consider, many of those ratios will be 1/1,000,000 longshots purely by chance. It would be a massive coincidence for this not to be the case.

Thus, it's rational to consider real anomalies rather than to parse for ratios that seem pleasing to us. (When the basic likelihood of a "coincidence" is as high as in this case, parsing for patterns is completely useless.)