I was thinking about lottery odds, and how so much of the pitch is, essentially, you miss 100 percent of the shots you don’t take, with the thought that you should at least enter because your odds go up so much with just one ticket. The odds were non existent before, and now they exist even if they’re vanishingly small.
Is the difference between 1 in a million and 0 in a million actually somehow more than the difference between 1 in a million and 2 in a million, or between 492,368 in a million vs 492,369 in a million? Or are all three of these functionally the same?
In: 0
You’re mixing absolute and relative odds. Buying two tickets doubles your odds and buying one “approaches infinitely” improves your odds (it’s division by zero which approaches infinity).
Buuuuut you still just have 2 tickets against a pool of millions of tickets.
If you want a head scratcher: imagine there’s 100 tickets total and you have 98 of them. There’s only 2 outcomes where you don’t win. If you buy 1 more ticket you’ve “doubled” your relative odds because there’s now only 1 outcome left (instead of 2). But absolutely you were already very likely to win because you had 98 tickets before. It works in a similar way when you have 1 ticket vs 2 except the absolute odds are you don’t win.
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