True; being deluded about lotteries is unlikely to have positive consequences normally, so unless something weird is going to go on in the future (eg: the lottery machine's random number function is going to predictably malfunction at some expected time, producing a predictable set of numbers; which Omega then imposes on your consciousness as being 'lucky'), that's not a belief with positive long-term consequences. That's not an impossible set of circumstances, but it is an easy-to-specify set, so in terms of discussing 'a false belief which would be long-term beneficial', it leaps readily to mind.