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He stops gambling only when he has either lost all of his money or reached his goal of B." (p. 182)
Here, there is a stop-loss only applies on individual bets. Across the longer sample, the better demonstrates a willingness to be departed from his seed in its entirety. The human element which inclines the individual to anxiously pursue the single goal of B. has interceded with a rational protection of A. The research by Petersen (2010) confirms this typically application of the Gambler's Ruin Theory where human participants are concerned. The implications of the 'problem' were largely forged on the understanding that the subject is up against the wall, as it were, with respect to an available betting seed. Petersen observes that "gambler's ruin describes the desire to try and win big, by making a large bet when the gambler has almost exhausted her gambling bankroll. The gambler makes a series of small bets, and over time loses money, since the casino has the advantage. When she realizes that she has very little money left, gambler's ruin describes her desire to try and win it all back, rather than accepting the loss and walking away with what money she has left." (p. 1)
This strategy may appeal to one's sense of excitement or one's hope for unlikely good fortune. And there is no hard and fast rule that says this method will fail across a small sample. But across the greater length of time, Gambler's Ruin becomes a powerfully inescapable force. This points to the relationship between certain human irrationalities which precipitate the consistency of the gambler's ruin theory. Truly though, its applications are numerous, varied and not always impacted by human processes or behaviors. Mansfield (1998) considers...
Dubins (1996) applies the theory to an examination of 'random walks' within the confines of a polygonal shape in order to demonstrate the geometric probability of distinct limitations in the destination of such walks.
These instances demonstrate that the Gambler's Ruin Theory has something of a reciprocal relationship with its real world applications. Drawn from the observation of real world occurrences in gambling, refined and reapplied to the discourse on economy, science, spatial reasoning and any number of disciplines, this is a demonstration of the natural inherency of certain probability principles.
Works Cited:
Bak, J. (2001). The Anxious Gambler's Ruin. Mathematics Magazine.
Blass, A. & Braun, G. (2005). Random Orders and Gambler's Ruin. The Electronic Journal of Combinations, 12.
Cargal, J.M. (2008). Chapter 33: The Gambler's Ruin. Discrete Mathematics for Neophytes.
Dubins, L.E. (1996). The Gambler's Ruin Problem for Periodic Walks. Statistics, Probability and Game Theory.
Lengyel, T. (2009). The Conditional Gambler's Ruin Problem with Ties Allowed. Applied Mathematics Letters, 22(3), 351-355.
Mansfield, M.L. (1988). A Continuum Gambler's Ruin Model. Macromolecules, 21(1), 126-130.
Nalebuff, B. (1999). The Gambler's Ruin Problem. Yale School of Management.
Petersen, J.S. (2010). What is Gambler's Ruin. Wisegeek.
Peterson, J. (2008). Gambler's Ruin. Gamblerruin.com.
Shyy, G. (1989). Gambler's Ruin and Optimal Stop…
Works Cited:
Bak, J. (2001). The Anxious Gambler's Ruin. Mathematics Magazine.
Blass, A. & Braun, G. (2005). Random Orders and Gambler's Ruin. The Electronic Journal of Combinations, 12.
Cargal, J.M. (2008). Chapter 33: The Gambler's Ruin. Discrete Mathematics for Neophytes.
Dubins, L.E. (1996). The Gambler's Ruin Problem for Periodic Walks. Statistics, Probability and Game Theory.
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