Abstract
In this study, gambling is defined as gaming. Its banker is called as the gaming enterprise. Winners are defined as the players who earn over the principal. Losers mean the players who cannot earn over the principal. In this study, we use that the repetition trial of coin toss or dice throwing is approximated to normal distribution from each discrete distribution. And its gaming includes the charge by the gaming enterprise based on its trial number. Above mentioned, we set three conditions for examining several characteristics. That is to say, Case 1 is that the probability of head on coin toss is equal to 0.5. Case 2 is that the probability of head on coin toss is less than 0.5. Case 3 is that each probability of dice throwing is same. Moreover, we restrict that all players do not admit leaving from the market so that the player keeps repeating the gaming based on independent and identically distributed. Then, the tendency both the maximum value of the sum total of the expected gain of winners and the expected earnings of gaming enterprise is shown when we use the power regression analysis. Moreover, we can visualize the tendency that both winners' risk averse and loser's risk preference characteristics are considered from the obtained outcome as a reflection effect with charge by the gaming enterprise under an uncertain situation. This is assumed to be two power functions concerning the expected gain. In addition, it is derived that expected earnings of the gaming enterprise and the expected gain of winners is balanced in the stop trial number by proposed model. Finally, we can show that the decision making about stopping rule of gaming trial with including its charge is useful in accordance with the maximization for sum total gains of winners.
