and also that people overestimate the significance of a small chance of 'winning the lottery'

But people also play Martingale systems on roulette. These have a good chance of going well, and a small chance of going really, really, badly. So people don't just overestimate small chances. I think they tend to overestimate the probability of events that benefit them, but this may depend on whether they are in near mode or far mode. If they were in far mode they might begin to fret more and more about the small probabilities.