Gamblers Ruin

AntiPattern Name: GamblersRuin

Problem: In a sequence of trials where the outcomes are governed by an independent RandomVariable?, the pattern user hopes to produce an outcome that locally exceeds the ExpectedValue? of the results of the trials. The name originates from the application of the pattern to approximately even-money games of chance, such as wagering amounts of money at even stakes on the flip of a coin.

Context: One entity (gambler) with limited resources vs. another (house) with less limited resources. For example, a gambler with $1000 vs. a LasVegas casino with $10 million.

Forces: Gambling requires very little physical effort; many gambling games also require very little mental effort. Employing this pattern makes it appear that one can, for example, gain money at a rate comparable to that paid for more arduous tasks (see ProtestantWorkEthic).

Supposed Solution: Devise a wagering pattern that, if extended to arbitrary length, would eventually leave one with a better outcome than the ExpectedValue? of the results. When this event occurs, restart the pattern. A classic version of this applied to coin-flipping is to wager $1 on the first flip and doubling the wager as long as one is unsuccessful. Upon success, return to a $1 wager. A complementary version is to wager $1 on the first flip and doubling the wager until unsuccessful or showing a net gain from the previous high-water mark.

Resulting Context: It can work for a while, but the resource limitations eventually will break the side with fewer resources, even if the game is fair. Applied to the double-after-loss version of the coin-flipping game, for example, the gambler cannot cover the tenth wager in the sequence. At that point, the house is $511 to the good. However, the gambler must be able to execute 24 straight sequences containing fewer than 9 straight losses in order to be able to cover the tenth wager. After this, the gambler must be able to execute an additional 1024 straight sequences containing fewer than 10 straight losses to be able to cover the eleventh wager. On the other hand, the gambler needs to execute 10 million sequences without a catastrophic loss to bankrupt the house.

Design Rationale: The long-term behavior of a process controlled by a true independent RandomVariable? includes arbitrarily large deviations from the ExpectedValue?; larger deviations are less probable, but have a finite chance of occurring. Strategies subject to GamblersRuin normally exchange small deviations between the outcome and the ExpectedValue? when the long-term behavior is near the ExpectedValue? for large deviations when the long-term behavior is far from the ExpectedValue?. Generically, these strategies fail because the chance of ruin (a deviation from ExpectedValue? that causes one side to be unable to continue the pattern) is inversely proportional to resources. The house typically improves its odds by limiting the maximum wager to create another form of ruin, or by running a game with negative ExpectedValue?.

Unfortunately gamblers very seldom follow this logic. See GamblingAddiction.

CategoryAntiPattern