Gambler’s Ruin

Definition of Gambler’s Ruin

The term gambler’s ruin applies to a number of different statistical ideas where a gambler has the chance of losing everything. The idea is based heavily in mathematics, using the amounts bet, the amount that can be won and lost in total, and the amounts that are expected to be won or lost.

Gambler’s Ruin Ideas

There are a number of main ideas that are theorised in association with gambler’s ruin. The first and original meaning is when the player raises their bankroll, which is the amount they have to bet, to a fixed fraction whenever the player wins, but does not reduce it during losses. This will eventually cause the player to lose all of his money, even though the outcome of each round looks seemingly promising.

Another common theory is one where a player with a finite amount of wealth to spend plays a fair game against a player that has an infinite amount of wealth to spend. The player with the finite amount of wealth will, at some point, become broke, and the other player will win the game, and all the money.  This theory can be applied infinitely, where the player with the finite amount of money will always go broke at some point, meaning that there is no way for the player to win, no matter how much time passes at a CAD casino. This is one of the oldest mathematical theories associated with gambler’s ruin, and was first envisioned as a mathematical algorithm by Christiaan Huygens.


In modern time, gambler’s ruin is most commonly used as a way to describe a player playing a game with negative expectations will go ultimately become bankrupt, regardless of how the betting system is handled.

The History of Gambler’s Ruin

The very earliest mentioned idea of gambler’s ruin first came into being in 1656, being in the form of a letter from mathematicians Blaise Pascal to Pierre Fermat. The letter consisted of a story of two gamblers playing a game of dice, and what the eventual outcome of the game would be. The letter was then summarised later on by Pierre de Carcavi before being sent to Christiaan Huygens. Huygens then reformulated the problem into a more cohesive mathematical format before publishing it publicly. The term gambler’s ruin was not used until many years later.

Gambler’s Ruin in The World of Betting

In order to apply the theory of gambler’s ruin to modern betting, players can use sports betting as an example. The average bettor has a fixed, finite amount of money that they are able to bet, whereas the bookie or casino that they are betting against has a much larger amount of money. The bettor, at some point, will be unable to continue betting against the house, as eventually he will run out of money, and the house will not. Even if the bettor is making bets that are in his favour, and he continues making these bets for a long period of time, the bettor will eventually go bankrupt.