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Is it because one can get ruined by hitting 0 but a "win" is subjective because there's no absolute upper bound? If one could go in to negative at 50/50 odds, t
by andirk 4y ago
Is it because one can get ruined by hitting 0 but a "win" is subjective because there's no absolute upper bound? If one could go in to negative at 50/50 odds, then the game will dance around that $1 starting point forever?
- hackerlight 4y agoIf there's no absorbing states and it's the cumulative sum of infinite coin flip (-1, 1), it'll visit every integer an infinite number of times with probability 1 a.s..
- andirk 4y agoSo in real-world, the gambler would owe all the money in the world at some point. But also win all the money in the world at another point! And then cash out and he wins? Sounds beatable.
- hackerlight 4y agoThe gambler will owe all the money (and then some) with probability 1 a.s., but it's not guaranteed to happen because a.s. implies it's not a certainty.