Abraham Wald  developed generalizations of the problem of Gambler's Ruin which play an important role in statistical sequential analysis,and in casino gambling, for players and casino alike. This theory is used worldwide, and it is the main decision in the making of the games. If the casino doesn' t have the better odds then the game will fail. Wald invented the topic of sequential analysis in response to the demand for more efficient methods of testing better uses of machinery during World War II. The idea is simple  yet Wald was the first person to build it into a statistical theory. Wald stated, it is better to analyze data produced sequentially rather than collect all the data and then analyze it. In this approach you do not have to choose a fixed sample size but can end the sampling at any point if the results justify it.    

     Dr Wallis, was working with the Navy as a Statistical Research Group, when he asked Wald to help him with a problem concerning an easier way to find out the best method for firing pins. Wald was determined to find a mathematical way to solve the Navy's problem. Wald assisted Dr Wallis in trying to classify things into categories of acceptable and unacceptable.  After a short time Wald and his team developed a basic theory, it is called SPRT or sequential probability ratio test. This system greatly reduced the effort needed to figure out the Navys dilemma, of which firing method was better. It later was adopted for the purpose of separating war items into three categories, acceptable, marginal, and unacceptable. After the war, Wald and his research group published their work. Soon after scientists in many fields used these techniques to help them figure out if things were feasible, and the affects they could have. Over the years SPRT or now known as confidence interval has produced many other methods and many other uses.

        Wald was the first to solve the general problem of sequential tests of statistical hypotheses. The optimum property of the sequential probability ratio test was theorized by Wald in 1943 and, in a joint paper with Wolfowitz in 1948, where he proved this property. This and other related works were very much aimed for the use of practical applications and his theorems on the distribution of the required number of observations, and on the probabilities associated with errors, found immediate applications. His main conclusion on sequential analysis and the theory of decision functions, another topic which was founded by him, were gathered together in his monograph Sequential Analysis. It was not only in research that Wald had a remarkable influence on statistics, but although he only taught for about ten years, he was also marked as an  influential  teacher. The same qualities of precision and rigour he showed in research were brought to his teaching but this did not mean that his lectures were complicated. His lectures were renowned for their clarity and the notes which his students took during his lectures in Columbia were circulated and because of their outstanding clarity they reached students studying statistics at many different universities in the United States 

In Gamblers Ruin this one of the basic equations used to solve the problem:

Let two players each have a finite number of pennies (say, for player one and for player two). Now, flip one of the pennies (from either player), with each player having 50% probability of winning, and give the penny to the winner. Now repeat the process until one player has all the pennies.

If the process is repeated indefinitely, the probability that one of the two player will eventually lose all his pennies must be 100%. In fact, the chances and that players one and two, respectively, will be rendered penniless are