CASINO (1995) STATISTICAL TEST Harvard Case Solution & Analysis



            In this scene, an informal statistical analysis has been performed where three jackpots have been won in a row among the millions of the players who are playing the game. For this reason, Robert de Niro has been fired in the scene which has been presented. Obviously, it seems senseless and impossible for three players to win three jackpots in a row and win a cash prize of $ 15000. This paper focuses on identifying the informal statistical test and performs an analysis based upon certain assumptions. All the calculations have been performed in the excel spreadsheet.

Statistical Test

            The informal statistical test which has been performed by Robert de Niro is the One Sample t-test and it has been identified through this test that there are very high chances of winning the cash prize of $ 15000 in a single row (John, 2006). This test provides us with the t distribution for the mean when the population variance has not been provided at all and the entire set of the observations are normal. In this case, there are millions of players which come to play this casino game and so the population is large and it would follow normal distribution and t distribution would also be applicable in this case.

            In order to perform the One Sample t-test to show the informal statistical test, a sample of the total players has been chosen from the millions of the players which are near to winning the Casino game. Based upon random probabilities, the winning prize chances or the amount near to $ 15000 has been computed as shown in the table in the next section of this paper.

            The total number of observations chosen is 70 and the level of the significance for determining the p value of this test has been set to be 0.05. The mean of the entire winning cash prizes of these 70 players, its standard deviation and the standard error have all been computed. The degrees of freedom in this case would be 69 since the number of the observations is 70. The statistical analysis of the final results has been performed in the next section.

Statistical Analysis

            The random probabilities and the chances of the winning cash prizes for the 70 players for a random set of observations is shown in the table below. Each winning prize chance for each player in this table is assumed to reflect the number which has been won by each player in rolling the casino. Those values which are near to 15000, show the players who have won.

Players Probability Prizes Prize Winning Chances
1 0.3175 15000 4763.125
2 0.0126 15000 189.246
3 0.4747 15000 7119.994
4 0.5262 15000 7893.284
5 0.4392 15000 6588.505
6 0.2155 15000 3231.866
7 0.2601 15000 3901.244


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