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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 ...
A common example of a first-hitting-time model is a ruin problem, such as Gambler's ruin. In this example, an entity (often described as a gambler or an insurance company) has an amount of money which varies randomly with time, possibly with some drift. The model considers the event that the amount of money reaches 0, representing bankruptcy.
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 ...
Gambler's conceit is the fallacy ... gambler's ruin shows that a player with finite resources ... a casino is more likely over time to take a player's money than a ...
This result has many names: the level-crossing phenomenon, recurrence or the gambler's ruin. The reason for the last name is as follows: a gambler with a finite amount of money will eventually lose when playing a fair game against a bank with an infinite amount of money. The gambler's money will perform a random walk, and it will reach zero at ...
Over the last three months, four accounts on a popular gambling site have placed thousands of bets totalling more than $50 million on Donald Trump winning the US presidential election next week ...
Take some time to debrief, too—if it turns out you both loved the experience, you can come up with even more wicked ways to spoil each other’s orgasms next time. You Might Also Like The Best ...
If p is less than 1/2, the gambler loses money on average, and the gambler's fortune over time is a supermartingale. If p is greater than 1/2, the gambler wins money on average, and the gambler's fortune over time is a submartingale. A convex function of a martingale is a submartingale, by Jensen's inequality.