Re:Here’s $100. Can you win $800M at Powerball?
by cbhl on Friday January 08, 2016 @07:43PM
(#10869437)
I think you want to be more precise about "impossible".
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.
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 lot; $437 million of $3 tickets would probably be enough tickets to play powerball for a few lifetimes.)
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.
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 lot; $437 million of $3 tickets would probably be enough tickets to play powerball for a few lifetimes.)