Re:Gambler’s Ruin Problem [pdf]
by andirk on Saturday October 01, 2022 @05:30PM
(#33050310)
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?
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Re:Gambler’s Ruin Problem [pdf]
by hackerlight on Saturday October 01, 2022 @11:50PM
(#33052649)
If 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..
So 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.
Re:Gambler’s Ruin Problem [pdf]
by hackerlight on Sunday October 02, 2022 @01:37AM
(#33053173)
The 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.