“The odds of winning the lottery are the same whether you buy a ticket or not.”
This seems nonsensical at first. Obviously, there are lottery winners. Therefore, the odds aren’t the same.
Except we’re not mathematicians doing a math problem (at least most of us). Odds are how we navigate the world. When they’re sufficiently low, the useful approach is to assume that they’re zero. Sort of how we deal with invisible signals: There’s sound in a very quiet room, but we can’t hear it. There’s light in a very dark room, but we can’t see it. These never go to zero, but we treat them as if they do.
The story of playing very long odds might give you hope or solace or energize you. That’s what they make movies about, after all. But in practice, you’re buying that story, not a useful chance of winning something.
Paul McGowan points out that the difference between a $500 stereo and a $5000 stereo is enormous. But the difference between the more expensive stereo’s sound and one costing $50,000 is vanishingly small… Soon it becomes a story, not a sound.
Buy the best story you can afford, with all the benefits it comes with. But don’t be confused by the odds or tiny differences. They’re probably zero.