More generally though the phrase refers the ever decreasing predictable value of return on a gambler's bank as he continues to gamble with his winnings.
A casino generally has:
Many more pennies than any player consequently ensuring that the player is much
more probable than the casino to experience gambler's ruin;
Odds that favor the casino resulting in negative predictable return for the
player; and
Various risk management techniques that limit their maximum loss.
The mixture of above ensures that the casino will in the vast bulk of cases
come out ahead in the long run.
Casino Games
A typical casino game has a small house advantage. The advantage is the long-run
hope, most often expressed as a percentage of the amount wagered. It remains
steady from one play to the next. If the long-run hope is expressed as a percentage
of the amount that the player starts with, though, then the house advantage
increases the longer the player continues.
For example, the official house benefit for a casino game might be 1%, and thus the expected value of go back for the gambler is 99%. However, this math would merely be true if the gambler never used the results of a charming bet again. Thus after gambling 100 dollars the idealized standard gambler would be left with 99 dollars, but, if he sustained to bet using his 99 dollars in winnings, he would once more lose 1% on average and his predictable value would go down to 98.01 dollars. This descending spiral continues until the gamblers predictable value approaches zero: gambler's ruin.
The long-run hope will not necessarily be the result knowledgeable by any particular gambler. The gambler who plays for a limited period of time may finish with a net win, despite the house advantage, or may go bankrupt much more quickly than the mathematical prediction.