In statistics, gambler's ruin is the fact that a gambler playing a game with non-positive expected value will eventually go bankrupt, regardless of their betting system. The concept was initially stated: A persistent gambler who raises his bet to a fixed fraction of the gambler's bankroll after a win, but does not reduce it after a loss, will eventually and inevitably go broke, even if each bet has a positive expected value.
In statistics, gambler's ruin is the fact that a gambler playing a game with non-positive expected value will eventually go bankrupt, regardless of their betting system. The concept was initially stated: A persistent gambler who raises his bet to a fixed fraction of the gambler's bankroll after a win, but does not reduce it after a loss, will eventually and inevitably go broke, even if each bet has a positive expected value.
Source: Wikipedia "Gambler's ruin" · CC BY-SA 4.0
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