I think you want to be more precise about &quot;impossible&quot;.<p>It is not mathematically provable that a random walk of finite length will eventually touch 0. Proof by counterexample: the set of every walk of length 1 where you win the jackpot on your first try.<p>However, consider an infinite random walk. You can fix the first n values of the walk to win the jackpot as much as you want, but as the random walk progresses toward infinity, it is highly probable that you will be on a random walk that tends toward negative infinity. (You might have to play a <i>lot</i>; $437 million of $3 tickets would probably be enough tickets to play powerball for a few lifetimes.)