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In statistics, gambler's ruin is the fact that a gambler playing a game with negative expected value will eventually go bankrupt, regardless of their betting system.. The concept was initially stated: A persistent gambler who raises his bet to a fixed fraction of the gambler's bankroll after a win, but does not reduce it after a loss, will eventually and inevitably go broke, even if each bet ...
Risk of ruin is a concept in gambling, insurance, and finance relating to the likelihood of losing all one's investment capital or extinguishing one's bankroll below the minimum for further play. [1] For instance, if someone bets all their money on a simple coin toss, the risk of ruin is 50%.
Random walks based on integers and the gambler's ruin problem are examples of Markov processes. [33] [34] Some variations of these processes were studied hundreds of years earlier in the context of independent variables.
Then the gambler's fortune over time is a martingale, and the time τ at which he decides to quit (or goes broke and is forced to quit) is a stopping time. So the theorem says that E[X τ] = E[X 0]. In other words, the gambler leaves with the same amount of money on average as when he started. (The same result holds if the gambler, instead of ...
When these constraints apply (as they invariably do in real life), another important gambling concept comes into play: in a game with negative expected value, the gambler (or unscrupulous investor) must face a certain probability of ultimate ruin, which is known as the gambler's ruin scenario. Note that even food, clothing, and shelter can be ...
A Tolerant Markov model (TMM) is a probabilistic-algorithmic Markov chain model. [6] It assigns the probabilities according to a conditioning context that considers the last symbol, from the sequence to occur, as the most probable instead of the true occurring symbol.
Gambler's fallacy; Inverse gambler's fallacy; Parrondo's paradox; Pascal's wager; Gambler's ruin; Poker probability. Poker probability (Omaha) Poker probability (Texas hold 'em) Pot odds; Roulette. Martingale (betting system) The man who broke the bank at Monte Carlo; Lottery. Lottery machine; Pachinko; Coherence (philosophical gambling ...
In actuarial science and applied probability, ruin theory (sometimes risk theory [1] or collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key quantities of interest are the probability of ruin, distribution of surplus immediately prior to ruin and deficit at time of ruin.