Gambler’s ruin is a probability concept with several versions. The best-known says that a player with a limited bankroll who keeps betting against an opponent with far deeper pockets, such as a casino, will eventually lose everything if play continues long enough. That holds even in a fair game; with a house edge it happens sooner. The casino does not need to be lucky, it only needs the player to keep playing.
In its original sense, the term describes a staking habit: raising the bet by a fixed fraction of the bankroll after each win, but not cutting it after a loss. Even with good odds on every bet, say 51% or even 80%, stakes keep climbing until a short losing run — perhaps only three losses in a row — wipes out everything won so far. The lesson for players is simple: set a budget and a stopping point, and avoid staking plans that escalate without limit.
The operator’s side
A casino’s bankroll is effectively far larger than any player’s, but short-term swings still matter. Maximum bet and win limits protect a young casino’s cash flow from a few high-stakes sessions. See limits.