Gamblers Ruin Add Gambler\'s Ruin

Gamblers Ruin Add

Gambler's Ruin (Addendum)

Our discussion has largely focused to this point on Gambler's Ruin as applying to gaming scenarios. Theoretical contexts in which one enters into certain gambling competitions have provided the basis for the observations instigating the Gambler's Ruin model. However, its potential for application has extended well beyond that as speculators and scholars have measured the practical value of this knowledge. For the purposes of our discussion, a real-world application of Gambler's Ruin is appropriate. Therefore, we consider the relevance of this approach to investment strategies on an open stock market.

Here, certain movement principles govern the gains and losses of the market on a second to second basis. As with the example discussed above regarding the flipping coin, it is not necessarily known that the market will move up or that it will move down at any given time and with any degree of continuity. But it is known that over a long enough timeline, both are likely to occur and that decisions are to made accordingly. So denotes the text by Shyy (1989), which points out that "market price movement is a markov process from state I to state I + 1 or state I -- 1 in one unit of time with the stationary transition probability P1, I +1 = p and P1, I -1 = q. In other works, p is the transition probability of the price moving higher and q is the probability of the price moving lower." (Shyy, p. 565)

This is an important application of the Gambler's Ruin problem because it require recognition of the phenomenon such that it may be avoided. It is thus that many stock players employ stop loss strategies as a way of measuring against this phenomenon. Here, the stock speculator will select an 'out' both at the high and low ends such that the elimination of seed money never occurs. In other words, the 'gambler' predetermines a loss threshold, at which point he 'cuts his losses' and retreats with what remains of his seed money. Simultaneously, the 'gambler' will determine a level of profit which, when achieved, marks the point of departure from the market with one's spoils. Shyy expresses this by observing that "each trader sets a stop loss, A, and profit taking price, B. The trader with a long position will sell his long position and get stopped out when the market price is bid at or below A. On the other hand, the trader will take profit when the market price is bid at or above B." (Shyy, p. 565)

To an extent, this is an practical outcome that can also be applied to a gambling scenario. In other words, the use of a stop-loss both to the high and low end does seem to respond adequately to the 'problem' of gambler's ruin. The article by Bak (2001) denotes, though, that the effecter of the gambler's anxiousness applies. In such instances, decisions are equally as inclined by desire for an expedient outcome as they are by the desire for a positive outcome. As Bak reports or the 'anxious' gambler, "in his last-ditch effort, he continues to stake the largest possible amount toward reaching, but not exceeding his goal. Thus, if he currently has A dollars and A (B/2, he risks all of it; if he is more than half-way to his goal, he best the difference, B-A, since winning that amount will bring his purse exactly to B. 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 its application to the formation of crystalline polymers, demonstrating the pertinence of the 'problem' to such disciplines as chemistry and physics. 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.