QUESTION: A gambler playing against the “house” in a game like roulette or slots adopts the rule “Play until you win a certain amount, then stop.”  Will this ensure against player losses? What will be its effect on the house’s profit?

ANSWER: Some look at this rule and figure that it rules out player losses and therefore must have a negative effect on the house.  Others, noting that the rule fails to account for the cases where a losing gambler runs out of money, allow for bankruptcy forcing the player to stop.  If the average bankruptcy level represents more money than the “win” stop threshold, they may reason that the effect on the house would be positive

In fact, the rule has no effect on the house profit, provided it does not reduce the volume of play.  The odds on each play remain the same and are independent from one play to the next. It does not matter to the house when one player gets up and another takes their place.  Visualize the situation as follows: the house is separated from the players by curtains, and cannot see them. The house sees only a steady stream of plays at unchanging odds, and does not care what rule a player is using to determine when to get up and leave.